Download analytical chemistry - Львівський національний медичний

Міністерство охорони здоров’я України
Львівський національний медичний університет
імені Данила Галицького
Кафедра токсикологічної та аналітичної хімії
ANALYTICAL CHEMISTRY
Manual for Pharmacy Students
Lviv – 2009
Посібник складено і підготовлено до друку на кафедрі токсикологічної та аналітичної хімії
Львівського національного медичного університету імені Данила Галицького старшим
викладачем Бідниченком Ю.І.
Рецензенти:
Завідувач кафедри аналітичної хімії Національного фармацевтичного університету
доктор хімічних наук, професор Болотов В.В.
Завідувач кафедри фармацевтичної хімії Тернопільського державного медичного
університету ім. І.Я.Горбачевського, кандидат хімічних наук, доцент Вронська Л.В.
Доцент кафедри медичної хімії Одеського медичного університету кандидат хімічних
наук Сідельникова Т.А.
Методичні вказівки затверджені та рекомендовані до друку цикловою методичною
комісією з фізико-хімічних дисциплін фарамцевтичного факультету Львівського
національного медичного університету імені Данила Галицького як навчально-методичний
посібник для студентів вищих фармацевтичних навчальних закладів і фармацевтичних
факультетів вищих медичних навчальних закладів IV рівня акредитації спеціальностей
„Фармація” та „Клінічна фармація” (протокол № 1 від 30 січня 2009 р.)
Відповідальний за випуск: проректор з навчальної роботи Львівського національного
медичного університету ім. Данила Галицького проф. М.Р.Гжегоцький
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ANALYTICAL CHEMISTRY AND CHEMICAL ANALYSIS
Analytical chemistry is one of the chemical disciplines. Analytical chemistry is
united with other chemical sciences with common chemical laws and based on studying of
chemical properties of substances.
Analytical chemistry is the chemical science about
– theoretical base of chemical analysis of substances;
– method of detection and identification of chemical elements;
– methods of qualitative determination of substances;
– methods of selection (separation) of chemical elements and its compounds;
– methods of establishing the structure of chemical compounds.
Subjects of analytical chemistry are: chemical elements and its compounds and
processing of transformation of substances in run chemical reactions.
The main tool of analytical analysis is chemical reaction as a source of information about
chemical composition of substances using for qualitative and quantitative analysis.
Aims of analytical chemistry are:
1. Establishing the chemical composition of analysed object (isotopic, elementary, ionic,
molecular, phase) – qualitative analysis.
Qualitative analysis consist from
– identification – establishing of identity of researched chemical compounds with wellknown substance du to compare its physical and chemical properties
– and detection – checking the presence in analysed objects some components,
impurities, functional groups etc.
2. Determination of content (amount and concentration) some components in analysed
objects – quantitative analysis.
3. Determination (establishing) of structure of chemical compound – nature and number of
structural elements, its bonds one to another, disposition in space.
4. Detection of heterogeneity on surface or in volume of solids, distribution of elements in
layers.
5. Research process in time: establishing character, mechanism and rate of molecular
regrouping.
6. Developing of present analytical methods theory, working out the new methods of
analysis.
Analytical chemistry achieves the aims by various methods of analysis:
I. Physical – determination of components of investigated substances without chemical
reactions (destroying of sample):
1. Spectral analysis – investigation of emission and absorption spectra.
2. Fluorescence analysis – investigation of luminescence, caused action of UV-radiation.
3. Roentgen-structural analysis – using X-ray.
4. Mass-spectra analysis.
5. Densimetry – measurement of density.
II. Instrumental (physical-chemical) – based on measurement of physical parameters
(properties) of substances in run of chemical reaction. This method divides on
1. Electrochemical – measurement of electrical parameters of electrochemical reactions.
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2. Optical – investigation the influence of various electromagnetic radiation on
substance.
3. Thermal (heating) – investigation the changes the properties of substance by heat
(undergo) action.
III. Chemical – measurement of chemical bonds energy.
Chemical analysis has some steps:
1. Sampling.
2. Dissolving the sample (in water, acid or alkali).
3. Executing (running) the chemical reaction X + R → P.
4. Measurement of definite parameter.
In accordance to analytical reaction (X + R → P) applies three groups of chemical
analysis methods:
I. Measurement of amount (quantity) of reaction product P: mass, physical properties.
II. Measurement of amount of reagent R that interacted with determined substance: volume
of solution reagent R with known concentration.
III. Registration changes of substance X acting with reagent: measurement of gas volumes.
IUPAC Classification of analytical methods in accordance with mass and volume of
analytic sample
Method name
Gramm-method
Cantigramm-method
Milligramm-method
Microgramm-method
Nanogramm-method
Picogramm-method
Mass of sample, g
1–10
0,05–0,5
10-6–0,001
10-9–10-6
10-12–10-9
10-12
Volume of sample, ml
10–100
1–10
10-4–0,1
10-6–10-4
10-10–10-7
10-10
Analytical Reactions and Requirements to Analytical Reactions
For identification (detection) and determination of substances the chemical reactions
runs in solution or by “dry” way. These reactions always accompany the various external
effects (analytical signals):
– precipitation or dissolving of precipitate;
– formation of coloured compound;
– evolution of gas with specific properties (colour, odour).
“Dry” way testing (without dissolving of sample) can be make by:
1) pyrochemical methods:
– flame test (colouring of gas torch flame),
– making a glass (alloys with Na2CO3, K2CO3, Na2B4O7, Na(NH4)2PO4),
– tempering;
2) crush (rub) sample to powder with analytical reagent;
3) microcrystalloscopic analysis – produce (receive) the specific crystals with analytical
reagent and watching its with microscope (forms of crystals);
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4) analysis in drops on filter paper – reaction between analysed substance and analytical
reagent run on filter paper with some drops (1-2) of solutions – arise a coloured spots.
Requirements (demands) to analytical reactions:
1) reaction must run quickly, in practice – immediately;
2) reaction must accompanied with accordance (special) analytical effect;
3) reaction must be irreversible – run in one way (in one side);
4) reaction must have high specificity and have high sensitivity.
Description (characteristic) of analytical reactions.
At field of application in qualitative analysis the analytical reactions divide into group and
individual (characteristic) reactions.
Group reactions use for selection from complex (complicated) mixes some substances.
Substances with definite properties are united in special analytical groups.
This reactions use for:
a) detection the present analytical group;
b) selection this analytical group from another during systematic path (way) of analysis;
c) concentration of small amounts of substances;
d) separation groups, which prevent to analysis path.
Characteristic reactions named analytical reactions that have the individual substance
nature. These reactions distinguish to selectivity.
Selective reactions give identical or alike analytical effects with small (little) number
of ions (2-5).
Extreme form of selectivity is specificity. Specific reaction gives an analytical effect
only with one individual substance.
For examples: – iodine with starch – complex compound blue (navy) colour;
– or Fe+3 with K4[Fe(CN)6] – complex compound blue (navy) colour.
Analytical reactions allow us to determine same quantity (amount) of substance.
Sensitivity of analytical reaction is the least amount (quantity) of substance, which
can be detected with the reagent in one drop of solution (1 mm3).
The sensitivity express to next correlated values:
Limit of detection = Detected limit (m) – the least amount of substance, which
present in analysed solution and which detect with the reagent. Calculate in µg. 1 µg =
0,000001 g.
Limit of concentration = Minimal concentration (Cmin) – the least concentration of
solution with still can be detected an analysed substance in definite (one drop) volume.
Limit of dilution (W = 1/Cmin) – quantity (ml) of water solution, containing 1 g of the
analysed substance, which detect with definite reaction (reagent).
Thus, the sensitivity of analytical reaction is as more as limit of detection and limit of
concentration are less.
These parameters are connected such:
m = Cmin·Vmin·106 = Vmin·106 / W
Sensitivity is the most importance description of quantitative analytical reaction.
Methods (modes, ways) to raise the sensitivity
1. To rise the concentration of detected substance:
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– to steam (soften by steam) of solution to small volume;
– to extract with organic solvents to small volumes;
– to distillate (rectify).
2. To precipitate of detected substance and dissolving the sediment in another solvent.
3. To use collector – substance, which adsorb the detected substance.
4. To mask the preventing ions (substances).
For example, using the complex compounds for detecting Fe+3 and Co+2 ions by
reaction of with thiocyanate-anion:
Co+2 + 6NH4SCN → [Co(SCN)6] –4 + 6NH4+,
blue soution
Fe+3 + 6NH4SCN → [Fe(SCN)6]–3 + 6NH4+
bloody-red solution
Mixture of these cations cannot be analysed directly because Fe3+-complex has very
colour that prevents watching the Co+2-complex. For masking of preventing Fe+3 cation to
analysed solution ads ammonia fluoride, which forms strong colourless complex with
iron(III) cations:
Fe+3 + 6NH4F → [FeF6] + 6NH4+
Formed fluoride complex not reacts with ammonia thiocyanate and not prevents aim
reaction run. Masking (repression) is neutralisation influence of preventing agents.
The analysis of complex (complicated) mixes makes to next modes (ways):
I.
Divide the mix on components (submixes) du to separation the detected substances
and the preventing substances on various parts of mix (in various submixes) –
systematic path (way) of analysis.
The systematic analysis - is full analysis of researched objects, which made du to separation
of mix on groups (analytical groups) in definite (strong) sequence in accordance to various
analytical properties of components. These separation makes until in one submix (phase)
stay components, which simple detect (identify) with selective reagent.
II.
Separate and detect one component in the researched mix (without divide) with the
help of (by means of) specific reactions (reagents) – fractional path (way) of analysis.
The fractional analysis - the all mix divide on identical (the same) parts. And in each part
detect only one individual component.
At this path of analysis often use a masking.
Cations Classification
For selection of cations on analytical groups used group reagents. Accordance to
applied group reagents all cations are divided on various systems. Cations divide to
analytical groups in according with solubility of salts, formed by its.
Use of general and group reagents gave rise to creation the series of analytical
cations classifications. Most widely used from them are sulphide, acid-basic and ammoniaphosphate. Analytical classifications of cations are based on chemical properties of their
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compounds and are associated with disposition of elements in periodic table, their structure
and physico-chemical properties.
In all classifications there is a cations group, which does not have group peagent
(cations of lithium, potassium, sodium, and ion of ammonium, which has the ion radius
similar to the potassium ion). These are cations of the s1 elements with electronic structure
of inert gas, low electronegativity, with small radius, and small polarisation properties.
Majorities of their salts are well water-soluble by reason of high tie polarity. In periodic
system they dispose in ІА-sub-group. In sulphide classification to this group is concluded a
magnesium cation, which has similar lithium cation properties.
In all of classifications identical is the group of cations, which sediment by sulphate
acid, ammonium carbonate, and sodium hydrogenphosphate in ammonia presence. There
are the cations of the s2 elements: calcium, barium, and strontium, which are found in ІІАsub-group of periodic system. Precipitates of their carbonates, sulphates and phosphates
formed with complicated anions of oxygen-containing acids, which lightly polarize. In
phosphate classification here are included cations of the s-elements – magnesium, and delements – iron (ІІ and ІІІ), chrome (ІІІ), manganese (ІІ), which form precipitates with
three-charged phosphate-ion, and cations of the р-elements – aluminum (ІІІ) and bismuth
(ІІІ), which have similarly low electronegativity).
All classifications also include a group of cations, which form precipitates with НСІ:
silver (I), mercury (I), and lead (ІІ). First two are the d-elements and lead is the р-element.
From cations of other groups can be picked out the ampholytic cations of the р- and
d-elements, which have amphoterric properties and disposed bias of periodic table – zinc
(ІІ), aluminium (ІІІ), teen (ІІ, IV), arsenic (ІІІ, V), chrome (ІІІ). They are found identical
groups of analytic classifications. The ampholytes inherent small electronrgativity, high
polarising properties and their compounds is capable to dependence on conditions to display
oneself both base and acids.
Sameness disposition attitude in analytic groups has cations giving the complexes
with ammonia. There are cations of the d-elements – nickel (ІІ), cobalt (ІІ), cadmium (ІІ),
mercury (ІІ), copper (ІІ). High ability to complex compounds formation intrinsic explains
by acceptor properties of unfilled in d-orbitals.
Anions Classification
p-Elements and some d-elements (chrome, manganese) form anions. High ability to
anions formation have the p-elements, disposed in right top quadrant of the periodic table.
On the strength of that the р-elements have a variable oxidation degree, they are capable to
form various acids and acids force increases with increasing of element oxidation degree.
For oxidising-reducing properties the anions divide on anions-oxidisers with high
oxidation degree (nitrate-anion), anions-reducers with lower oxidation degree (chlorides,
bromides, iodides) and neutral anions, which not display nor reducing no oxidising
properties (carbonate-, sulphate-, phosphate-anions). Oxidising-reducing properties of some
anions can change (sulphite-, nitrite-anions) dependency on reaction conditions.
The analytical classification of anions is based on formation of insoluble in water
precipitate with barium and silver salts. In accordance to this classification all anions divide
on three groups:
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– the first group of anions forms precipitate with barium salt: sulphate-, sulphite,
carbonate-, phosphate-, thiosulphate-, oxalate-, tetraborate-, iodate-, arsenate-,
arsenite-, fluoride-, tartrate-, citrate-ions;
– the second group of anions form insoluble in water and nitrate acid precipitates
with silver salt: chlorides, bromides, iodides, thiocyanates, cyanides, benzoates;
– the third group of anions not form insoluble compounds with barium and silver
salts: nitrate-, nitrite-, acetate- bromate-, perchlorate-, salicylate-ions.
Majority of anions detect by fractional method, that's why the group reagents use
only for separation of anions groups, that exclude necessity to search in solution the anions
of given group in case of negative reaction with group reagents.
Types of Analytical Classifications of Cations
Group
Group reagent
Cations
ACID-BASIC
I
ІІ
There are not
HCl
ІІІ
H2SO4
IV
NaOH
V
NaOH
VI
NH3
I
There are not
ІІ
(NH4)2CO3 + NH3 + NH4Cl
ІІІ
IV
V
I
ІІ
ІІІ
V
VI
K+, Na+, Li+, NH4+
Ag+, Pb+2, Hg2+2
Chlorides, insoluble in water and acids
Ca+2, Sr+2, Ba+2
Sulphates, insoluble in water, acids and bases
Al+3, Zn+2, Cr+3, Sn+2, Sn+4, As+3, As+5
Hydroxides with amphoteric properties
Mn+2, Mg+2, Fe+2, Fe+3, Sb+3, Sb+5, Bi+3
Hydroxides insoluble in ammonia and bases
Cu+2, Co+2, Cd+2, Ni+2, Hg+2
Hydroxides soluble in ammonia with ammonia complexes
formation
SULPHIDE
K+, Na+, Li+, NH4+
Ca+2, Sr+2, Ba+2, Mg+2
Carbonates insoluble in water
(NH4)2S + NH3 + NH4Cl
Mn+2, Fe+2, Fe+3, Co+2, Ni+2, Zn+2, Cr+3, Al+3
Sulphides insoluble in water, ammonia but soluble in НСІ
H2S + HCl
Cu+2, Cd+2, Hg+2, Sn+2, Sn+4, As+3, As+5, Sb+3, Sb+5, Bi+3
Sulphides insoluble in НСІ
HCl
Ag+, Pb+2, Hg2+2
Chlorides, insoluble in water and acids
AMMONIA-PHOSPHATE
There are not
K+, Na+, NH4+
+2
+2
+2
+2
(NH4)2НРO4 + NH3
Ca , Sr , Ba , Mg Li+, Mn+2, Fe+2, Fe+3, Cr+3, Al+3 Bi+3
Phosphates insoluble in water and ammonia
Nа2НРO4
Cu+2, Co+2, Cd+2, Ni+2, Hg+2, Zn+2
Phosphates soluble in ammonia with ammonia complexes
formation
НNO3
Sn+2, Sn+4, As+3, As+5, Sb+3, Sb+5
Oxidize to compounds with the highest oxidation numbers
HCl
Ag+, Pb+2, Hg2+2
Chlorides insoluble in water and acids
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Scheme of Fractional Analysis of Complex Mixtures
Mixture of components I, J, K, L, M
groups
Aliquots identical mixtures
Components
I÷M
Components
I÷M
Components
I÷M
Components
I÷M
Components
I÷M
Reagent F
Reagent W
Components J ÷ M
Component I
Component L
Reagent Q
Component J
Components I, J, K, M
Components I, K, L, M
Scheme of Systematic Path of Complex Mixtures Analysis
Mixture of substances of I, J, K, M
groups
Reagent A
Group I
Components I1, I2, I3
Mixture of substances
of groups J … M
Reagent B
Mixture of substances
of groups K, M
Group J
Components J1, J2, J3
Scheme of Analysis of Group J
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Components J1, J2, J3, J4, J5
Reagent N
Components J1, J2
Components J3, J4, J5
Reagent Y
Reagent Z
Component J1
Component J3
Component J2
Components J4, J5
Reagent T
Component J4
Component J5
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LAW OF MASS ACTION AND ITS APPLICATION TO VARIOUS TYPES
OF IONS EQUILIBRIUM IN ANALYTICAL CHEMISTRY
THEORY OF ELECTROLYTES, STRONG AND WEAK ELECTROLYTES.
ANALYTICAL CONCENTRATION AND IONS ACTIVITY,
DEPENDENCE BETWEEN ITS, COEFFICIENT OF ACTIVITY
The laws of mass action have universal importance in chemistry. The law of mass
action is a reaction that states that the values of the equilibrium – constant expression Kc are
constant for a particular reaction at a given temperature, whatever equilibrium
concentrations are substitute.
aA + bB ↔ cC + dD
Kc =
[C] c ⋅ [ D ]d
[ A]a ⋅ [ B] b
Getting the maximum amount of product from a reaction depends on the proper
selection of reaction conditions. By changing these conditions, we can increase or decrease
the yield of product. We might change the yield by:
1. Changing concentrations by removing products or adding reactants to the reaction vessel.
2. Changing the partial pressure of gaseous reactants and products.
3. Changing the temperature.
The equilibrium-constant expression is defined in terms of the balanced chemical
equation. All analytical reactions, as a rule, run in solutions. For solutions we can not
change the pressure. Sometimes we might heat or freeze the reaction vessel. But, in general,
all reactions (processes) occur at isothermal condition. Therefore, we may use the
equilibrium-constant expression in term of concentrations for both types of equilibrium:
I. A homogeneous equilibrium is an equilibrium that involves reactants and products in a
single phase (in solution, particle):
– solutions of electrolytes;
– protolytic equilibrium (hydrolysis, buffer systems);
– complex compounds;
– red-ox systems.
II. A heterogeneous equilibrium is an equilibrium involving reactants and products in more
than one phase:
a) liquid–solid systems:
– saturated solution–precipitate (sediment);
– colloids;
b) liquid–liquid system:
– extraction.
In analytical chemistry law of mass action use for calculation of:
1) equilibrium ions concentration of dissociated weak electrolyte;
2) equilibrium concentration of reactants and products of chemical-analytical process;
3) equilibrium concentration of hydrogen and hydroxide ions and ionisation degree of
electrolytes solutions;
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4) equilibrium concentration of hydrogen and hydroxide ions in buffers and solutions of
hydrolysed salts;
5) equilibrium concentration of cations and anions and solubility of electrolytes;
6) equilibrium concentration of ions of oxidant and reduce agent in red-ox reactions;
7) equilibrium concentration of ions in complex compounds solutions;
8) equilibrium-constants of various chemical processes.
Contemporary Theories of Electrolytes
A substance, that dissolves in water to give an electrically conducting solution is
called an electrolyte. A substance, that dissolves in water to give nonconducting or very
poorly conducting solutions is called a nonelectrolyte.
When electrolytes dissolve in water they produce ions, but they do so to varying
extents. A strong electrolyte is an electrolyte that exists in solution almost entirely ions. A
weak electrolyte is an electrolyte that dissolves in water to give equilibrium between a
molecular substance and a small concentration of ions.
According to Svante Arrhenius concept:
Acid is any substance that, when dissolved in water, increase the concentration of hydrogen
ion H+.
Base is any substance that, when dissolved in water, increase the concentration of hydroxide
ion OH–.
NaOH → Na+ + OH–
HCl → H+ + Cl–
The most short comings of Arrhenius concept:
1. Arrhenius concept (theory) does not explain the cause of dissociation of electrolytes on
ions.
2. Arrhenius concept (theory) does not explain an acid or base property of organic
substances, which not produced ions in water solution.
3. Arrhenius concept (theory) does not take account of interaction between solvent and
dissolved substance.
According to Johannes N. Brønsted and Thomas M. Lowry concept:
Acid is the species (molecule or ion) that donates a proton to another species in a protontransfer reaction.
Base is the species (molecule or ion) that accepts a proton in a proton-transfer reaction.
HCl + NH3 → NH4Cl
acid
base
NH3 + H2O → NH4+ + OH–
base
acid
acid
base
A conjugate acid-base pair consists of two species in an acid-base equilibrium, one acid and
one base, which differ by the gain or loss of a proton. The acid in such a pair is called the
conjugate acid of the base, whereas the base is the conjugate base is the conjugate base of
the acid.
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The Brønsted-Lowry concept of acids and bases has greater scope than the Arrhenius
concept:
1. A base is a species that accept protons; the OH– ions is only one example of a base.
2. Acids and bases can be ions as well as molecular substances.
3. Acid-base reactions are not restricted to aqueous solutions.
4. Some species can act as either acids or bases, depending on what the other reactant is.
Such species, which can act either as an acid or a base (it can lose or gain a proton),
called an amphiprotic species:
HCO3– + HF → H2CO3 + F–
base
acid
acid
base
HCO3– + OH– → CO32– + H2O
acid
base
base
acid
According to G.N.Lewis concept:
Lewis acid is a species that can form a covalent bond by accepting an electron pair from
another species.
Lewis base is a species that can form a covalent bond by donating an electron pair to
another species.
H+ + :NH3 –→ NH4+
electron-pair
acceptor
Lewis acid
electron-pair
donor
Lewis base
The Lewis and the Brønsted-Lowry concepts are simply different ways of looking at certain
chemical reactions. The Lewis concept could be generalised to include many other
reactions, as well as proton-transfer reactions.
Acids and bases are classified as strong or weak.
Strong acids are acids that ionise completely in water (that is, they react completely to give
ions).
Weak acids are acids that are only partly ionised as the result of equilibrium reaction with
water.
Strong bases are bases that are present in aqueous solution entirely as ions, one of which is
OH–.
Weak bases are bases that are only partly ionised as the result of equilibrium reactions with
water.
The strongest acids have the weakest conjugate bases, and the strongest bases have
the weakest conjugate acids. The terms strong and weak are used only in a comparative
sense. The strengths of acids and bases are relative. In acid base interaction the water (or
another solvent) exhibits a levelling effect on the strength of the strong acids.
Acid and base with water produce hydrogen ion or hydroxide ion (relatively) and its
conjugated ions. The process is called electrolyte ionisation or electrolyte dissociation.
For the strong electrolyte (acid or base), which completely ionise in solution, the
concentration of ions are determined by the stoichiometry of the reaction from the initial
concentration of electrolyte:
[H+] ≈ [HA]
[OH–] ≈ [BOH]
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The weak electrolyte (acid and base) ionises or dissociates to a small extent in water (about
1 % or less, depending on concentration of electrolyte). For the weak electrolyte (acid or
base) the concentration of ions in solution are determined from the acid ionisation (or
dissociation) constant (Ka) or the base ionisation (or dissociation) constant (Kb), which is the
equilibrium constant from the ionisation of a weak electrolyte.
Ka =
[ H + ] ⋅ [A − ]
[ HA ]
Kb =
[ HB + ] ⋅ [OH − ]
[ B]
Value of ionisation constants depends on:
1) nature of solvent,
2) nature of electrolyte,
3) temperature.
And not depends from electrolyte concentration.
[H+] =
[OH–] =
Ka ⋅ Ca
(pH = ½pKa – ½lgCa)
Kb ⋅ Cb
(pOH = ½pKb – ½lgCb)
The degree of ionisation (α) of a weak electrolyte is the fraction of molecules that react with
water to give ions. This also may be expressed as a percentage, giving the percent
ionisation:
αa =
αb =
[A − ]
[ HA ]
[OH − ]
[ B]
[H+] = [A–] = α⋅[HA] = α⋅Ca
[OH–] = [B+] = α⋅[BOH] = α⋅Cb
For very small concentration of electrolyte α have very small value, and percent of
ionisation can be shown approximately on Ostwald’s dilution rule:
Cα 2
Kc =
1− α
α=
Kc
C
The aqueous solutions of strong electrolytes and concentrated solutions of weak
electrolytes not submit to classic law of mass action in full. Peter Debye and Erich Hückel
were able to show that the properties of electrolyte solutions could be explained by
assuming. The electrolyte is completely ionised in solution but that the activities, or
effective concentrations, of the ions are less than their actual concentrations as a result of
the electrical interaction of the ions in solution. The Debye-Hückel theory allows us to
calculate these activities. When this is done, excellent agreement is obtained for dilute
solutions:
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a = C⋅γ
lgγ = – A z 2 I
a – active concentration of ions;
C – relative concentration of ions;
γ – activity index;
A – value, calculate theoretically, depends from temperature, ion-dipole force
etc.;
for water solutions at t = 25 °C A = 0,509;
I – ionic strength;
z - charge of ion.
In solutions ion is a charged particle, surrounded ionic atmosphere with solvent ions. Ionic
atmosphere parameters are definite by ionic strength:
I = ½ ∑ Ci ⋅ z i2
Ci – ions concentration (M)
Thus, we have seen that equilibrium-constant of electrolyte solutions change value
accordance to activities of ions and depend from ionic strength of solution.
15
PROTOLYTIC BALANCE IN ELECTROLYTES SOLUTIONS
Equilibrium in Solutions with Ions of the Same Kind
The effect of adding another solute to a solution of a weak acid or base called the
common-ion effect. It is significant effect acid or base ionisation - that is, strong acids or
bases and salts that contain an ion in common with the weak acid or base.
The common-ion effect is the shift in an ionic equilibrium caused by the addition of a solute
that provides an ion that takes part in the equilibrium.
Thus strong acid provide an ion H+ common to an acid ionisation equilibrium. For
example, ionisation of acetic acid:
CH3COOH ↔ CH3COO– + H+
In this solution is added a solution of HCl:
HCl ↔ H+ + Cl–
Because HCl is a strong acid, it provide H+ ion, which is present on the right side of
equation for acetic acid ionisation. According to LeChateilier’s principle, the equilibrium
composition should shift to the left. Thus the degree of ionisation of acetic acid is decreased
by the addition of a strong acid. The repression of ionisation of acetic acid by HCl is an
example of the common-ion effect.
Equilibrium in Solutions with Ions of Various Kinds
Addition a strong electrolyte to solution of weak acid or base increased the common
concentration of ions in solution. Because the strong electrolyte ionises in solution
completely, amount of all ions increases and, as a cause, change the activity of ions. This
increasing of ionic strength of solution called salting effect.
According to LeChateilier’s principle, when shift in general concentration of
reactants, should shift the equilibrium to the right. Thus the concentration of all ions and,
respectively, the ionic strength of solution is increased. Increasing the concentration of all
ions caused the increasing the H+ ion concentration. Thus, the value pH is changes, becomes
more.
Hydrolysis
One of the successes of Brønsted-Lowry concept is its explanation of the acid-basic
properties of salt solutions. The reaction of ions with water called hydrolysis. The
hydrolysis reaction produces either hydrogen-ion or hydroxide-ion. It is a typical acid-base
reaction, which change protolytic (protons) equilibrium. Such ions may produce H+ or OH–
ions, so they may give acidic or basic solutions.
16
Hydrolysis of various types salts
I. Salts, formed by strong acid and strong bases not hydrolyse. They completely ionise
(dissociate):
KCl → K+ + Cl–
II. Salts, formed by strong acid and weak base (NH4Cl):
Cat+ + H2O ↔ CatOH + H+
Solutions of these salts are acid – pH < 7
III. Salts, formed by weak acid and strong base (CH3COONa):
An– + H2O ↔ HAn + OH–
Solutions of these salts are base – pH > 7
IV. Salts, formed by weak acid and weak base (NH4CN):
Cat+ + An– + H2O ↔ CatOH + HAn
[H+] ≈ [OH–]
In general, a solution of this salt is acidic, base or neutral by comparing the
hydrolysis constants of the two ions from the salt. The hydrolysis constant of the cation will
be its Ka, and that for the anion it’s Kb.
The solution will be acidic if Ka (cation) > Kb (anion).
The solution will be neutral if Ka (cation) = Kb (anion).
The solution will be basic if Ka (cation) < Kb (anion).
The concentration of ions in solution is determined from the constant of hydrolysis of
salt. From this constant we may determine concentration of hydrogen and hydroxide ions
and, accordingly, the pH of solution. And we may calculate the degree of hydrolysis.
The degree of hydrolysis (αh) of a salt is the fraction of molecules that react with
water to give ions.
Using hydrolysis in analysis
1. Detecting some ions. The salts of this ions during hydrolysis forms insoluble compounds.
This phenomenon is thypical for salts of metalloids or salts of very weak bases or acids:
SbCl3 + H2O → SbOCl↓ + HCl
Bi(NO3)3 + H2O → BiOH(NO3)2↓ + HNO3
Some salts, formed by weak bases and weak acids, hydrolyse completely with producing
another chemical compounds:
2CrCl3 + 3(NH4)2S → Cr2S3 + 6NH4Cl
17
Cr2S3 + 6H2O → 2Cr(OH)3↓ + 3H2S↑
2. Separation of ions. For example, Al+3 and Cr+3:
CrCl3 + 4KOH → KCrO2 + 3KCl + 2H2O
AlCl3 + 4KOH → KAlO2 + 3KCl + 2H2O
t°
KCrO2 + 2H2O → Cr(OH)3↓ + KOH
KAlO2 not hydrolyses
3. Changing the concentration of hydrogen or hydroxide ions:
2BaCl2 + K2Cr2O7 + H2O ↔ 2BaCrO4↓ + 2KCl + 2HCl
1)
Formed strong acid HCl may dissolves precipitate BaCrO4. In presence of CH3COONa:
2CH3COONa + 2HCl → 2CH3COOH + 2NaCl
Formed weak acid CH3COOH, concentration of H+ ions decreases, and precipitate not
dissolves.
K3AlO3 + 3H2O ↔ Al(OH)3↓ + 3KOH
2)
Formed strong base KOH may dissolves precipitate Al(OH)3. In presence of NH4Cl:
3NH4Cl + 3KOH → 3NH4OH + 3KCl
Formed weak base NH4OH, concentration of OH– ions decreases, and precipitate not
dissolves.
Equations for Hydrolysis Parameters Calculation
Type
Constant of
of salt hydrolysis Kh
II
Kh = Kw
Kb
III
Kh = Kw
Ka
IV
Kh =
Kw
Ka ⋅ Kb
Degree of hydrolysis (αh)
Kh
=
[salt]
Kh ⋅[salt]
=
[salt]
Kh =
Kw
Kb ⋅[salt ]
Kw
Ka ⋅[salt ]
Kw
Ka ⋅ Kb
[H+]
[OH–]
Kh ⋅[salt ] =
Kw ⋅[salt ]
Kb
Kw ⋅ Kb
[salt ]
Kh ⋅[salt ] =
Kw ⋅ Ka
[salt ]
Ka ⋅ Kh =
Kw ⋅ Ka
Kb
Kw ⋅[salt ]
Ka
Kb ⋅ Kh =
Kw ⋅ Kb
Ka
18
Repressing and intensification of hydrolysis
Sometime hydrolysis prevents to run an analytical reaction. In this case we may to
repress or to intensify the hydrolysis. As any chemical equilibrium process, the hydrolysis
submits to LeChateilier’s principle. Accordance to our purposes we may do next:
1. Add to solution the salt of another hydrolysed electrolyte (salt, acid or base).
2. Change the salt concentration.
3. Heat or freeze the solution.
Buffers
A buffer is a solution characterised by the ability to resist changes in pH when
limited amounts of acid or base are added to it. Buffer contains either a weak acid and its
conjugate base or a weak base and its conjugate acid.
Suppose a buffer contains approximately equal molar amount of weak acid HA and
its conjugate base A–. When a strong acid is added to the buffer, it supplies hydrogen ions
that react with the base A–:
H+ + A– → HA
On the other hand, when a strong base is added to the buffer, it supplies hydroxide
ions. Then ions react with the acid HA:
OH– + HA → H2O + A–
Thus a buffer solution resists changes in pH through its ability to combine with both
H+ and OH– ions.
There are three types of buffers which distinguish its components:
I. Buffer contains weak acid and its salt (pH of buffer < 7):
HCOOH + HCOONa;
CH3COOH + CH3COONa.
II. Buffer contains weak base and its salt (pH of buffer > 7):
H3BO3 + Na2B4O7;
NH4OH + NH4Cl
III. Buffer contains salts of polyprotic acids (pH of buffer ≈ 7):
Na2HPO4 + NaH2PO4
Na2CO3 + NaHCO3
Two important characteristics of a buffer are the pH and the buffer capacity.
The buffer capacity - is the amount of acid or base the buffer can react with before
giving a significant pH change.
Buffer capacity depends on the amount of acid and conjugated base in the solution.
The ratio of amounts of acid and conjugated base is also important. Unless this ratio is
approximately 1 (between 1:10 and 10:1), the buffer capacity will be too low to be useful.
19
BC = ∆С
∆pH
∆C – amount of added base or acid (in equivalents);
∆pH – region of pH change.
The other important characteristic of a buffer is its pH. Buffer always must be
prepared from a conjugated acid-base pair in which the acid ionisation constant is
approximately equal to the desired H+ ion concentration.
The Henderson-Hasselbalch equation relates the pH of a buffer for different
concentrations of conjugate acid and base:
pH = pKa + lg [base]/[acid]
By substituting the value of pKa for the conjugate acid and the ratio [base]/[acid], we obtain
the pH of the buffer.
Equations for Calculation [H+] and pH of Buffers
Acid buffer
Base buffer
[H+] = Ka⋅[acid]/[salt]
[H+] = Kw⋅[salt]/Kb⋅[base]
pH = pKa – lg[acid] + lg[salt]
pH = 14 – lg[salt] – pKb + lg[base]
It must be remembered, however, that pH is not entirely established by ratio of
conjugate base to conjugate acid bat can be affected by concentration. For typical buffers
(i.e. concentration less than 0.1 M or with K values of 10-3 or less) the HendersonHasselbalch equation can be used.
20
SOLUTIONS OF AMPHOTERIC COMPOUNDS.
SOLUTIONS OF COMPLEX COMPOUNDS.
ORGANIC REAGENTS AND THEIR APPLICATION IN ANALYSIS.
Ampholytes
The term amphoteric refers to a substance that has both acidic and basic properties. For
example, aluminium oxide dissolves in acids to produce the cation Al+3, as expected for a
metal oxide:
Al2O3 + 6HCl → 2AlCl3 + 3H2O
But the oxide also dissolves in strong base:
Al2O3 + 3H2O + 2KOH → 2K[Al(OH)4]
In this case the aluminate anion, Al(OH)4–, is formed.
In more common sense, accordance to Brønsted-Lawry concept of electrolytes, amphoteric
substances are concluded to class (type) of species called ampholytes.
Ampholytes are species that may to accept and to donate the protons. They are both neutral
and charged particles (substances).
There are three types of ampholytes:
I. Ampholyte that contain hydrogen ion (HCO3–, H2PO4–, HSO3–):
Dissociation equations:
Matter balance:
HX– ↔ H+ + X–2
HX– + H+ ↔ H2X
H2O ↔ H+ + OH–
[H+] = [X2] + [OH–] – [H2X]
II. Ampholyte that contain hydroxide ion [Al(OH)6+3, Ni(OH)+]:
Dissociation equations:
Matter balance:
MOH+ ↔ M+2 + OH–
MOH+ + OH– ↔ M(OH)2
H2O ↔ H+ + OH–
[OH–] = [M+2] + [H+] – [M(OH)2]
III. Ampholyte – salt, containing both protons donor and acceptor (CH3COONH4, NH4CN):
Dissociation equations:
Matter balance:
MH+ ↔ H+ + M
X– + H+ ↔ HX
H2O ↔ H+ + OH–
+
[H ] = [M] + [OH–] – [HX]
21
Equations for Calculation Ampholytes Solutions Parameters
[H+]
Type of ampholytes
I.
II.
pH
pKa1 + pKa 2
2
pKb1 + pKb 2
14 −
2
1
[ (7 + pKa) − pKb]
2
Ka1 ⋅ Ka 2
14 − Kb1 ⋅ Kb 2
III.
Kw ⋅ Ka
Kb
Using ampholytes in analysis
1. Dissolving insoluble hydroxides:
Al(OH)3 + 3KOH → K3AlO3 + 3H2O
2. Changing degree ionisation of cation-ampholyte:
2Cr(OH)3 + 3H2O2 + 4KOH → 2K2CrO4 + 8H2O
KHCrO2 = 9⋅10–17
KH2CrO4 = 1,8⋅10–1
3. Separation of cation (in insoluble hydroxides):
To mixture of sediments Fe(OH)3, Al(OH)3, Mn(OH)2 add mix NH4OH + NH4Cl – to
solution pass MnCl2. To sediment Fe(OH)3, Al(OH)3 add KOH – to solution pass K3AlO3.
Complex Compounds
A complex (or coordination compound) is a compound, which consist either of
complex ions with other ions of opposite charge or a neutral complex species.
Complex ions are ions formed from a metal atom or ion with Lewis bases attached to
it by coordinate covalent bonds.
Ligands are the Lewis bases attached to the metal atom in a complex. They are
electron-pair donors, so ligands may be neutral molecules (such as H2O or NH3) or anions
(such as CN– or Cl–) that have at least one atom with alone pair of electrons.
Cations only rarely function as ligands. We might expect this, because an electron pair on a
cation is held securely by the positive charge, so it would not be involved in coordinate
bonding. A cation in which the positive charge is far removed from an electron pair that
could be donated can function as a ligand. An example is the pyrazinium ion.
A polydentate ligand ("having many teeth") is a ligand that can bond with two or
more atoms to a metal atom. A complex formed by polydentate ligands is frequently quite
stable and is called a chelate. Because of the stability of chelates, polydentate ligands (also
called chelating agents) are often used to remove metal ions from a chemical system.
The formation constant, or stability constant, Kf, of a complex ion is the equilibrium
constant for the formation of the complex ion from the aqueous metal ion and the ligands:
22
Ag+ + 2NH3 ↔ Ag(NH3)2+
Kf =
[Ag(NH 3)2 ]+
[ Ag]+ ⋅ [ NH 3]2
The dissociation constant, Kd, for a complex ion is the reciprocal, or inverse, value of Kf:
+
+
Ag(NH3)2 ↔ Ag + 2NH3
1 [Ag ]+ ⋅ [ NH 3]2
=
Kd =
Kf
[Ag(NH 3)2 ]+
Influence various factors on complex compound stability
1. Stability of complex compounds is more in complexes with high coordination number.
2. Concentration of complex compounds in solution direct depends to ligand concentration
and is inversely proportional to metal ion concentration.
3. Equilibrium in solution of complex compounds depend to pH (concentration of
hydrogen ions) and dissociation constant. Increasing the pH value is a cause of complex
compounds destroying (hydrolysis).
4. The most complicated is temperature influence on complex compound stability.
Reaction of complex formation may be endothermic or exothermic. Heating can induces
such chemical processes:
–
changing acidic-basic equilibrium,
–
destroying some ligands,
–
oxidation some ligands or metal ions,
–
hydrolysis complex ions.
The most important complex compounds with inorganic ligands, used in analysis
1. Ammonia:
–
selection (colourless complex): [Ag(NH3)2]+, [Zn(NH3)4]+2, [Cd(NH3)4]+2;
–
detection (coloured complex): [Cu (NH3)4]+2, [Co(NH3)6]+3, [Ni(NH3)4]+2.
2. Halogen and rhodanide:
–
selection with extraction in inorganic solvents;
–
detection (coloured complex): [Fe(SCN)3]–3, [BiJ4]–, [CoCl4]–2.
3. Fluor – separation and masking (colourless complex): [FeF6]–3.
4. Cyanide – determination (coloured complex): [Fe(CN)6]–3, [Fe(CN)6]–2.
Using complex ions in analysis
1. On application and investigation of complex compounds in analysis may arise next
problems:
1)
determination of nature and quantity of complex particles in solution;
2)
determination of structure of complex compounds in solution;
3)
calculation of dissociation constant;
4)
determination of molar particles of metal ions and ligands in complex
compounds.
1. Determination of cations with coloured complex compounds.
2. Masking of preventing cations in stabile colourless complex compounds.
23
3. Selection of cations with hydroxo- or ammonia- complex compounds on systematic
analysis.
4. Dissolving of insoluble sediments: AgCl + NH4OH, HgO + KCN.
5. Changing of acidic-basic properties of weak electrolytes: boric acid + glycerine.
Organic Reagents in Analysis
Organic reagents are more selective than inorganic precipitants or complex ions. Solubility
of compounds with organic ligands is less of compounds with inorganic ions. Completeness
of precipitation achieves already with small surplus of precipitant. Sediments (precipitates)
inorganic ions with organic compounds not contain impurities and have very intensive
colour.
Possibility of interaction ions with reagent depends to specific atoms group in structure of
organic compound. These specific atoms groups called functional or analytic-active groups.
Organic reagent bond cation through the active analytical group. Another structural
components (parties) of organic reagent molecule give the additional properties to
compound: increase or decrease solubility of formed substance, intensify colour compound
etc.
All organic reagents are weak electrolytes and reactions with its participation are classic
ion-changing processes. These reactions run in water solutions and are the acid-basic
equilibrium reactions. Organic reagents take part in reaction formation of:
1) insoluble compounds;
2) traditional complex compounds, which are soluble in water or organic solvents;
3) chelates.
Chelates not have external sphere. They are very stabile because formed structure
with some cycles, which consolidate steric (space) disposition of complex
compound.
Examples of organic reagents application
Formation of organic dyes – detection of NO2– ion with aromatic amines.
Formation of coloured complex compound – identification of Ni+2 with dimetylglioxime.
Formation of coloured precipitate – detection of Ba+2 with sodium rhodizonate.
Formation of compound which change colour depending to red-ox potential –
diphenilamine.
5. As specific reagents for definite cations (anions).
1.
2.
3.
4.
24
USING LAW OF MASS ACTION DU TO REDOX PROCESSES
Oxidation-reduction reaction (or redox reaction) is a reaction in which electrons
are transferred between species or in which atoms charge oxidation number. Such reactions
consist of two parts – one called oxidation, the other called reduction.
Oxidation is the part of a redox reaction in which there is a loss of electrons by a
species or an increase in the oxidation number of atom.
Reduction is the part of a redox reaction in which there is a gain of electrons by a
species or a decrease in the oxidation number of atom.
A species that is oxidised losses electrons or contains an atom that increases in
oxidation number. Similarly, a species that is reduced gains electrons or contains an atom
that decreases in oxidation number. An oxidising agent is a species that oxidises another
species; thus, the oxidiser agent it is itself reduced. A reducing agent is a species that
reduces another species; it is itself oxidised.
Oxidation number (or oxidation state) is the charge an atom in a substance would
have it the pairs of electrons in each bond belonged to the more electronegative atom.
Types of Redox Reactions
1. The reaction in which electrons are transferred between a free element and a monatomic
ion are often called displacement reactions:
Cu + 2AgNO3 → 2Ag↓ + Cu(NO3)2
2. Disproportionation is a reaction in which a species is both oxidised and reduced:
Hg2(NO3)2 + 2NH4OH → Hg↓ + NH2HgNO3 + NH4NO3 + 2H2O
3. Redox reaction involving oxoanions. Source of oxoanions are chemical combination
with oxygen:
4.
10KBr + 2KMnO4 + 16HCl → 5Br2 + 2MnCl2 + 12 KCl + 8H2O
5. Autocatalytic – in run of redox reaction forms species that is catalyst (catalyses) this
reaction:
2H2C2O4 + 2KMnO4 + 3H2SO4 → 10CO2↑ + 2MnSO4 + 2K2SO4 + 8H2O
Formed in reaction Mn+2 ion accelerates oxidation of oxalic acid.
6. Conjugated redox reactions called such two reactions, one of that runs spontaneously,
and second – only in case the first reaction running in same solution. The first reaction
called primary (or initial) reaction, and another reaction – secondary.
A species, which take parts in both reactions, called actor, a species that takes part only
in primary reaction is inductor, and a species that takes part only in secondary reaction is
acceptor:
25
KMnO4 + 5FeCl2 + 8HCl → 5FeCl3 + MnCl2 + KCl + 4H2O – primary (initial) reaction
actor
inductor
2KMnO4 + 16HCl → 2MnCl2 + 5Cl2 + 2KCl + 8H2O – secondary (inducted) reaction
actor
acceptor
Calculation of Redox Equilibrium
The maximum potential difference between the electrodes of a voltaic cell is referred
as the electromotive force (emf).
The standard electrode potential, E°, is the electrode potential at 25 °C when the
molarities of ions and the pressures of gases (in atmosphere) equal 1. Standard electrode
potential is also known as a standard reduction potential. Oxidation potential – that is, the
electrode potential with its sign reversed.
The table of standard electrode (reduction) potentials helps us determine whether an
oxidation-reduction reaction is spontaneous. It also enables us to judge the strength of a
particular oxidising or reducing agent under standard conditions. Thus, because electrode
potentials are written as reduction potentials by convention, those reductions half-reactions
with large (more positive) electrode potentials have a greater tendency to go as written (left
to right). On the other hand, those half-reactions with lower (more negative) electrode
potentials have a greater tendency to go right to left. This can be expressed in a more
general manner:
If E° > 0, the reaction is spontaneous.
If E° < 0, the reaction is nonspontaneous.
The emf of a cell depends on the concentrations of ions and on gas pressure. The Nernst
equation is relating the cell E to its standard emf E° and the reaction quotient Q, which has
the form of the equilibrium constant, except that the concentrations are those that exist in
the voltaic cell:
2,303RT
⋅lnQ
E = E° –
nF
R – the gas constant, equal to 8,31 J/(mol⋅K);
F – Faraday's constant, equal to 9,65⋅104 c;
n – equivalent.
If we substitute in the Nernst equation all values and concentration of ions express in
molarities, we get:
E = E° –
0,0592
⋅ lg Q .
n
We can chow from the Nernst equation that the emf decreases as the reaction proceeds. The
concentrations of products increase and the concentrations of reactants decrease. Thus the
emf becomes smaller. Eventually the emf goes to zero, and the reaction comes to
equilibrium. In certain moment the analytical concentration of both components of redox
26
pair become equal (identical). In this moment – moment of equilibrium – in redox system is
settled the real (or formal) potential:
EOx = E°Ox –
0,0592
⋅ lg[Ox] ;
n
ERed = E°Red –
EOx/Red = E°Ox/Red –
when [Ox] = [Red]
0,0592
⋅ lg[ Red ] ;
n
0,0592
[Ox]
⋅ lg
.
n
[Red]
If the real potential of redox pair E°Ox – E°Red > 0, than reaction run. In redox reaction form
more weak oxidisers and reducing agents.
The full quantitative characteristic of direction and completeness of redox reaction is
its equilibrium constsnt:
( E1o − E o2 ) ⋅ n
lgKp =
0,0592
The redox reaction run in direct side if Kp > 1. The completeness of oxidation-reducing
process indicates the value (size) of Kp.
The real potential of redox reaction depends on:
1) concentration of oxidation and reducing agents;
2) temperature;
3) the pH value;
4) formation of insoluble compounds;
5) formation of complex compounds.
Though concentration of OH– or H+ ion does not include in Nernst equation, but acidify of
solution influences on formal potential. The high concentration of H+ ion shifts on
hydrolytic process in solution and changes the ions forms:
MnO4– + 8H+ → Mn+2 + 4H2O
MnO4– + 2 H2O → MnO2↓ + 4OH–
MnO4– → MnO4–2
E° = + 1,51 V
E° = + 0,60 V
E° = + 0,558 V
Formation of insoluble compounds decrease the real potential (emf) of the system:
1) if oxidised form is insoluble compound:
OxA↓ + ne ↔ Red + A
E = E° +
0,0592
⋅ lg KST Ox ;
n
E = E° –
0,0592
⋅ lg KST Red
n
2) if reduced form is insoluble compound:
Ox + A + ne ↔ RedA↓
KST – solubility constant
Formation of complex compounds also decreases the emf of system:
27
1) if oxidised form is complex compound:
OxL + ne ↔ Red + L
E = E° +
0,0592
1
⋅ lg ;
n
β
2) if reduced form is complex compound:
Ox + L ne ↔ Red + L
E = E° +
β – complex formation constant
0,0592
⋅ lg β
n
Redox Properties of Water
Potential of standard hydrogen electrode is in convention equal zero (E°H+/H = 0). The
Nernst equation for hydrogen electrode:
2H+ + 2e = H2
E=
RT [ H + ]
ln
.
F
pH2
p – partial pressure of gases
In pure water [H+] = 1,00⋅10-7 and pH2 = 1: EH+/H = 0,0592 ln 1,00⋅10-7 = – 0,413 V.
Consequently, reducing agent, which have E° < – 0,413 V, can decompose water
with hydrogen evolving. The reducing properties of water (pO2 = 1):
2H2O = 4H+ + O2 + 4e
EO2/H2O = 1,23 + 0,0592 lg[H+]⋅pO2 = + 0,82 V.
Hence, oxidising agent, which have E° > 0,82 V can oxidising water with oxygen evolving.
Therefore, in water (or aqueous solutions) are resistant redox system with potential
from – 0,41 V to + 0,82 V.
Using Redox Reactions in Analysis
1. Calculation equilibrium concentrations of all substances, which take part in redox
process.
2. Development kinetics method of analysis.
3. Detecting of cations and anions:
2Mn(NO3)2 + 5PbO2 + 6HNO3 → 2HMnO4 + 5 Pb(NO3)2 + 6H2O;
HgCl2 + H2[SnCl4] → Hg↓ + H2[SnCl6]
4. Dissolving of insoluble sediments:
As2S3 + 28HNO3 → 2H3AsO4 + 3H2SO4 + 28NO2↑ + 8H2O
5. Separation in systematic analysis of cation mixes:
2CrCl3 + 10KOH + 3H2O2 → 2K2CrO4 + 6KCl + 8H2O
AlCl3 + 3KOH + H2O2 → K3AlO3 + 3HCl + H2O2
28
USING LAW OF MASS ACTION TO EQUILIBRIUM IN HETEROGENEOUS
SYSTEM PRECIPITATE–SATURATED SOLUTION
Heterogeneous equilibrium is equilibrium involving reactants and products in more
than one phase. Example of the heterogeneous equilibrium is system consisting from
saturated solution of ionic compound and its sediment (precipitate).
A precipitate is a solid formed by a reaction in solution. Precipitation reactions
depend on one product's not dissolving readily in water.
A saturated solution is a solution that is in equilibrium with respect to a given dissolved
substance.
Solubility equilibrium. The solid crystalline phase is in dynamic equilibrium with ions in a
saturated solution. The rate at which ions leave the crystals equals the rate at which ions
return to the crystal.
Solubility of a substance in a solvent is the maximum amount that can be dissolved at
equilibrium at a given temperature. The solubility of one substance in another is determined
by two factors. One of these is the natural inclination toward disorder, reflected in the
tendency of substances to mix. The other factor is the strength of the forces of attraction
between species (molecules and ions). These forces, for example, may favour the unmixed
solute and solvent, whereas the natural tendency to mix favours the solution. In such a case,
the balance between these two factors determines the solubility of the solute.
Definition the solubility of common ionic substances:
− soluble – a compound dissolves to the extent at 1 gram or more per 100 ml;
− slightly soluble – a compound is less than 1 gram, but more than 0,1 gram per 100 ml;
− insoluble – a compound is less than 0,1 gram per 100 ml.
There are three types of solutions:
1. Real solutions:
–
molecular solutions (depends on London forces);
–
ionic solutions (depends on ion-dipole forces).
2. Colloid systems.
Molecular Solutions
If the process of dissolving one molecular substance in another were nothing more than the
simple mixing of molecules, we would not expect a limit of solubility. Substance may be
miscible even when the intermolecular forces are not negligible. The different
intermolecular attractions are about the same strength, so there are no favoured attractions.
Therefore the tendency of molecules to mix results in miscibility of the substances.
Ionic Solutions
Ionic substances differ markedly in their solubility in water. In most cases, their
differences in solubility can be explained in terms of the different energies of attraction
between ions in the crystal and between ions and water.
29
The energy of attraction between an ion and a water molecule is due to an ion-dipole
force. The attraction of ions for water molecules is called hydrolysis. Hydration of ions
favours the dissolving of an ionic solid in water. If the hydration of ions were the only factor
in the solution process, we would expect all ionic solids to be soluble in water.
The ions in a crystal, however, are very strongly attracted to one another. Therefore,
the solubility of an ionic solid depends not only on the energy of hydration of ions but also
on lattice energy, the energy holding ions together in the crystal lattice. Lattice energy
works against the solution process, so an ionic solid with relatively large lattice energy is
usually insoluble.
Colloids
Colloids are a dispersion of particles of one substance (the dispersed phase) throughout
another substance of solution (the continuous phase).
The Solubility Product Constant
When an ionic compound is dissolved in water, it usually goes into solution as the ions.
When an express of the ionic compound is mixed with water, equilibrium occurs between
the solid compound and the ions in the saturated solution:
KtxAny ↔ xKt+ + yAn–.
The equilibrium constant for this solubility process can be written:
[ Kt + ]x ⋅ [An − ]y
.
Kc =
[ KtxAny ]
However, because the concentration of the solid remain constant (in heterogeneous
systems), we normally combine its concentration with Kc to give the equilibrium constant
Ks, which is called the solubility product constant:
Ks = Kc⋅[KtxAny] = [Kt+]x⋅[An–]y
In general, the solubility product constant, Ks, is the equilibrium constant for the solubility
equilibrium of slightly soluble (or nearly insoluble) ionic compounds. It equals the product
of the equilibrium concentrations of the ions in the compound, each concentration raised to
a power equal to the number of such ions in the formula of the compound.
At equilibrium in saturated solution of slightly soluble compound at given temperature and
pressure the value of Ks is constant and not depend on ions concentration. The solubility
product constant is thermodynamic constant and depends on temperature and ions activity
(ionic strength).
30
The reaction quotient, Q, is an expression that has the same form as the equilibrium constant
expression Ks, but whole concentration values are not necessarily those at equilibrium.
Though the concentrations of the products are starting values:
Q = [Kt+]⋅[An–]
Here Q for a solubility reaction is often called the ion product, because it is product of ion
concentrations in a solution, each concentration raised to a power equal to the number of
ions in the formula of the ionic compound.
– Precipitation is expressed to occur if the ion product Q for a solubility reaction is
greater than Ks: Q > Ks.
– If the ion product Q is less than Ks, precipitation will not occur (the solution is
unsaturated with respect to the ionic compound): Q < Ks.
– If the ion product Q equal Ks, the reaction is at equilibrium (the solution is
saturated with the ionic compound): Q = Ks.
Calculation of Solubility
Solubility, S, is the molar concentration of compound in saturated solution.
I. Saturated solution of slightly soluble ionic compound:
S=
x+ y
Ks
.
x ⋅ yy
x
II. Saturated solution of good soluble ionic compound.
This type of solutions not used in analytical practice. Such solutions are very concentrated
and have large ionic strength. Components of these solutions (ion, molecules) can associate
and form various polymers and colloids.
III. Saturated solution of slightly soluble compound with very small solubility:
– the substance have limited solubility but create ion pairs and various molecular forms.
The ionic strength of this solution is high and solubility depends on common
concentration of all molecular and ionic forms;
– slightly soluble compound takes part in protolytic reaction with water with the pH
change. The solubility is affected by pH. If the anion is the conjugate base of a weak
acid, it reacts with H+ ion. Therefore, the solubility slightly soluble compound to be more
in acid solution (low pH) than it is in pure water.
In sour environment solubility of slightly soluble compounds is more than more is its Ks and
more is the hydrogen ion concentration:
 [H + ] 
Ks
SKtAn = [Kt ] =
= Ks ⋅ 
+ 1 ;
[An − ]
 Ka

+
If [H+] = Ka, than SKtAn = 2Ks .
31
Factors Influencing on Solubility
1. Temperature.
Solubility for most of substances is endothermic process. Increase temperature occurs
decrease solubility. But crystal compounds at various temperature form hydrates another
structure (composition). Hydrates formation may be exothermic reaction.
2. Ionic strength of solution.
Increasing of ionic strength causes decreasing of ions activity and, accordingly, Ks
will increase. Because, solubility will increase. An example of it is salting effect.
Salting effect is increase the solubility of slightly soluble compounds in presence of strong
electrolytes, which not have common ions with precipitate and not react with precipitate
ions.
3. Common-ion electrolytes. Completeness of precipitation.
The importance of the solubility product constant becomes apparent when we
consider the solubility of one salt in the solution of another having the same cation or anion.
The effect of the common ion is to make slightly soluble salt less soluble than it would be in
pure water. This decrease in solubility can be explained in terms of LeChatelier’s principle.
It is example of the common-ion effect.
Decrease of solubility of slightly soluble compounds in presence of electrolyte with
common ions called common-ion effect.
But solubility of slightly soluble compounds decrease to moment when ionic strength of
solution will begin to influence to solubility.
The ion is completely precipitated when its residual concentration (Cmin) is less than 1⋅10-6
M (Cmin < 1⋅10-6 M). Amount of precipitant must be more at 20-50 % it is necessary to
stoichiometry equation.
If in solution are ions, which form slightly soluble compounds with precipitant, the
sequence of its precipitation determines (depends on) Ks value.
Fractional precipitation is the technique of separating two or more ions from a solution by
adding a reactant that precipitates first one ion, than another, and so forth.
4. The pH value (see above).
5. Complex compound formation.
Solubility increases with increasing concentration of ligand, complex compound
stability and Ks value.
6. Redox process.
Redox reaction shift on equilibrium in heterogeneous system and change solubility of
slightly soluble compounds.
Using Precipitation and Solubility Processes in Analysis
1. Reaction of ions detection.
32
2.
3.
4.
5.
Fractional precipitation.
Dividing ions on analytical groups in systematic analysis with group reagents.
Precipitation with controlled pH value.
Selective dissolving:
SrC2O4↓ + CH3COOH → Sr(CH3COO)2 + H2C2O4
CaC2O4↓ + CH3COOH → not dissolves
6. Conversion (transformation) one slightly soluble compounds to another:
CaSO4↓ + Na2CO3 ↔ CaCO3↓ + Na2SO4
33
COLLOID SYSTEMS, THEIR IMPORTANCE FOR CHEMICAL ANALYSIS
Signs of Colloids Formation on Chemical Reaction
For analytical purposes often carry out reactions of sulphides and hydroxides
precipitation. In these reactions may form colloids and may be observed next phenomenon:
1) precipitates pass through the filters;
2) slightly soluble compounds are soluble in water more than determined by Ks;
3) substance not forms precipitate even with great surplus of precipitant.
Colloids are a dispersion of particles of one substance (the dispersed phase)
throughout another substance of solution (the continuous phase). Colloids differ from true
solutions in that the dispersed particles are larger than normal molecules, thought they are
too small to be seen with a microscope. The particles are from about 1⋅10-9 m to about 2⋅10-7
m in size.
Colloids are characterised accordingly to the state (solid, liquid, or gas) of the
dispersed phase and the state continuous phase: aerosol, foam, emulsion, sol, gel:
– fog and smoke are aerosols, which are liquid droplets or solid particles dispersed
throughout a gas;
– an emulsion consist of liquid droplets dispersed throughout another liquid;
– a sol consist of solid particles dispersed in liquid.
Colloids with water continuous phase are divided on two major classes:
I.
II.
Hydrophilic colloid is a colloid in which there is a strong attraction between the
dispersed phase and the continuous phase (water) – for example, H2SiO3, Fe(OH)3.
Many such colloids consist of macromolecules (very large molecules) dispersed in
water. Except for the large size of the dispersed molecules, these are like normal
solution.
Hydrophobic colloid is a colloid in which there is a lack of attraction between the
dispersed phase and the continuous phase (water) – for example, AgI, As2S3.
Hydrophobic colloids are basically unstable. After different time, the dispersed phase
comes out of solution by aggregation into larger particles. In this behaviour, they are
quite unlike true solutions and hydrophilic colloids.
Hydrophobic sol (solid phase dispersed in water) are often formed when a solid
crystallises rapidly from a chemical reaction or a supersaturated solution. When
crystallisation occurs rapidly, many centres of crystallisation (called nuclei) are formed at
once. Ions are attracted to these nuclei and very small crystals are formed. These small
crystals are prevented from setting out by random thermal motion of the solvent molecules,
which continue to buffer them.
These very small crystals aggregate into large crystals because the aggregation would
bring ions of opposite charge into contact. However, sol formation appears to happen when,
for some reason, each of the small crystals gets a preponderance of the kind of charge on its
surface.
For example: iron (III) hydroxide forms a colloid because an excess of iron (III) ion
+3
(Fe ) is present on the surface, giving each crystal an excess of positive charge. These
positive charged crystals repel one another, so aggregation to larger particles is prevent. A
34
positively charged colloidal particle of iron (III) hydroxide gathers a layer of anions around
it. The thickness of this layer is determined by the charge of the anions – the greater
magnitude of the negative charge; the more compact the layer of charge:
FeCl3 + 3NaOH → {Fe(OH)3⋅Fe+3⋅Cl–}↓ + 3NaCl.
When molecules that have both a hydrophobic and a hydrophilic end are dispersed in water,
they associate or aggregate to form colloidal-size particles, or micelles.
A micelle is a colloidal-size particle formed in water by the association of molecules
that each has a hydrophobic end and hydrophilic end. The hydrophobic ends point inward
toward one another, while the hydrophilic ends are on the outside of the micelle facing the
water. A colloid in which the dispersed phase consists of micelle is called an association
colloid.
Scheme of Micelle Structure
aggregate
ions definite
potential
anti-ions
layer
diffusion
layer
AgNO3 + KI → {m[AgI]⋅nI–⋅ (n-x) K+}x-⋅xK+ + KNO3 (surplus of KI)
nucleus
granule
KI + AgNO3 → {m[AgI]⋅nAg+⋅ (n-x)NO3–}x-⋅xNO3– + KNO3 (surplus of AgNO3)
Structure of Al(OH)3 micelle in:
– acidic solution
{m[Al(OH)3] ⋅nH2O⋅ (n-x)Al+3}x-⋅3xCl–
– basic solution
{m[Al(OH)3] ⋅nH2O⋅ (n-x)AlO2–}x-⋅xNa+
Coagulation is the process by which a colloid is made to come out solution by aggregation.
Coagulation causes when
– heat the colloid or
– add to colloid solution strong electrolyte with great charge of ions (Schulze-Ghardi rule).
Example of hydrophilic colloid coagulation:
1. Heating accelerates the random thermal moving of the colloid particles. The micelles get
in touch one to another frequently and can stick together. These cause the colloid
coagulation.
2. An iron (III) hydroxide sol can be made to aggregate by the addition of an ionic solution,
particularly if the solution contains anions with multiple charge (such as phosphate PO43–
). Phosphate ion gathers more closely to the positively charged colloidal particles than
chloride ions. If the ion layer is gathered close to the colloidal particle, the overall charge
is effectively neutralised. In that case, two colloidal particles can approach close enough
to aggregate.
35
Washing the precipitate by water removes the electrolyte-coagulant and restores precipitate
in colloid. Transition the precipitate into colloid solution called peptisation. Washing of
precipitates occurs removing of ions layer around colloid particles. For peptisation
prevention precipitates must be washed by suitable electrolyte solution.
Using Colloids in Analysis
1. All colloids (sols) are inclined to adsorption of another substance from solutions. On this
phenomenon based techniques of:
– detection reactions. Some colloids (hydroxides, in particular) are colourless and not
visible. To reaction mixture add the coloured substance, which would be adsorbed on
colloids particles:
2NaOH + I2 → NaOI + NaI + H2O
(iodine solution becomes colourless)
MgCl2 + 2NaOH → Mg(OH)2 + 2NaCl (colourless colloid)
Mg(OH)2 + NaOI + NaI + H2O → Mg(OH)2⋅I2 + 2NaOH
brown
(adsorption of iodine on
colloid particles)
– and common precipitation with concentration of small amounts of detected
substances:
ZnCl2 + H2S → ZnS↓ + 2HCl
MnCl2 + H2S → MnS↓ + 2HCl
ZnS is collector (adsorbent)
concentration of Mn+2 ions on collector surface
2. Identification of ions:
H3PO4 + 12(NH4)3MoO4 + 21HNO3 →
→ (NH4)3PO4⋅12MoO3⋅2H2O↓ + 21NH4NO3 + 10 H2O
colloid with navy colour
2Na3AsO4 + 5Na2S + 16H2O → As2S5↓ + 16NaCl + 8H2O
colloid with yellow colour
Prevention of Colloids Formation
For prevention of colloids formation on analytical reactions is necessary:
1) to add a small surplus of precipitant. It promotes the little solubility of precipitant and
prevents to colloid formation;
2) to carry out precipitation process at heating;
3) for precipitation and washing of precipitates add electrolytes;
4) do not dilute the water solutions over precipitate (sediment).
36
METHODS OF SEPARATION AND CONCENTRATING OF SUBSTANCES
EXTRACTION IN ANALYTICAL CHEMISTRY
Extraction is the process of evolution (transition) of substance, dissolved in one solvent (as
a rule - water), to another solvent (extragent), which not mixes one another.
The reverse process of substance evolution from organic phase to water called rextraction.
Extraction may be single (when extragent add one time with all amount) and multiple when extragent add several times by little portions. Multiple extractions also called
fractional extraction.
Mechanisms of Extraction Process
1. Physical distribution.
In any solution molecules have shall with molecules of solvent. In water it is hydrate shall
with water molecules dipoles, in nonaqueous solution is solvate shell with organic solvent
molecules. Shacking of extracting mixture decompose of solvate /hydrate shells around
molecules, and native molecules pass throughout the phase boundary. Amount of extracted
substance depends on it solubility in given organic solvent.
Substance can pass through phase boundary when it is in associated (molecular) state.
Molecule have not electrical charge (is neutral). Ion can not pass through interface.
2. Chemical reaction.
For extraction of ions and particles with electrical charge use organic solvents with
dissolved on it special reagent. This reagent reacts with ions or other charged particles and
forms chemical compound, which have high solubility in organic solvent. On phase
boundary substance react with solvent-reagent and go out water solution.
Types of Chemical Compounds that Can Be Extracted from Water Solution
These compounds pass in extragent in definite forms. These compounds may state in water
solution in given form. Another compound may transform during extraction process after
interaction with solvent:
1. Simple substances with covalent bond (I2, SbCl3).
2. Substances with acidic properties: weak acids, complex acids (acidocomplexes) – form
in reaction cations (Fe+3, Sb+5) with halogen acids, and heteropolyacids
(H3[As(Mo3O10)4], H3[P(Mo3O10)4) extract with active (polar) and oxygen-content
solvents.
3. Chelates dissolve in organic solvents more than in water. This reagents form complexes
with metallic ions in organic phase. Solvent for extraction prefers nonpolar.
4. Ionic associates – salts, formed by large anions and large cations. Frequently they
consist from complex cation and complex anion. Between ions there are not solvent
37
molecules. In solution ionic associates not hydrate, but have strong attraction of ions for
solvent molecules. Such complex ions, which form ionic associates, are antipyrine,
crystalviolet, phenantroline.
Substance distribution constant (Po) is equilibrium thermodynamic constant, which shows
the ratio of substance concentration in both phases. The substance must be in one molecular
state in both phases. This constant is the sense of W.Nernst law of distribution:
Po =
[A ]o
,
[A ]w
[A]o – concentration of substance in organic solvent;
[A]w – concentration of substance in water.
Value of distribution constant (as any equilibrium constant) depends on
– substance nature,
– solvent nature,
– and temperature.
In extraction systems substances rarely are in same molecular state. In various solvents
occur dissociation, association, solvation, hydration, or complex compound formation of
dissolved substances. Such solutions are not in equilibrium and for its calculate (definite)
the distribution factor.
Distribution factor (D) is the ratio of common concentration of substance in both phases:
D=
Co
,
Cw
Co – common concentration of substance in organic solvent;
Cw – common concentration of substance in water.
Degree of extraction (R), or completeness of extraction, is a fraction of extracted substance
amount to common (general) concentration of substance. This also may be expressed as a
percentage, giving the percent of extraction:
R=
mex
m
mex – amount of extracted substance,
m – common amount of substance.
Factors influencing on distribution factor and degree of extraction
1. Substance nature.
2. Solvent nature.
38
3. Temperature. Heating shift in solubility of substances in various solvents differently. But
heating increase solubility in organic solvents and more amount of extracted substance
pass through the boundary phase.
4. The pH. The low pH (great concentration of H+ ion) represses weak acids dissociation.
Ions associate in neutral molecule and can be extracted. Also the high pH (little
concentration of H+ ion) repress weak bases dissociation and neutral molecule pass in
organic solvent. But strong acids and strong bases can not be extracted, because we can
not to repress its ionisation completely.
5. High ionic strength of aqueous solution increases the substance solubility and destroy
hydrate layer of ions. Molecule loses its charge and pass through the boundary phase.
Equations for Extract Parameter Calculation
R=
Vw
Vo
Po =
1− R
R⋅
Po
,
Vw
Po +
Vo
Vw – volume of water solution;
Vo – volume of organic solvent.
Number of fractional (multiple) extraction cycles:
Ci
Cr
n=
Po ⋅ Vo 

lg1 +

Vw 

lg
Ci – initial concentration of substance in water;
Cr – residual concentration of substance in water (after multiple extraction).
Using extraction in analysis
1. Many substances are more soluble in organic solvents than in water. Aqueous solutions
of slightly soluble substances are much diluted. Extraction allows making solution in
organic solvent more concentrated.
2. On extraction process the substance not precipitates and not changes.
3. Using the solvent-reagent allow to extract and to detect substance in one step in one
sample.
Requires to organic solvents for extraction
1. Extracted substances must good dissolve in given solvent.
2. Solvent must be selective to one or two-three substances.
3. Solvent must have little solubility in water, and water must not dissolve in solvent.
4. Solvent must has high boiling temperature.
39
5. Density of solvent must distinguish to water density in grate value.
6. Extragent not must be inflammable and poisoning.
SEPARATION AND CONCENTRATING TECHNIQUES ON ANALYSIS
Separation (selection) is an analytical process (or technique) after which form the
fractions with individual components on its.
Concentrating is an analytical process (or technique) for increasing of maintenance
of analysed substance in sample.
Quantitatively separation and concentrating definite on degree of separation
(concentrating):
F=
Ccon
,
Cin
Ccon – concentration of substance in separated (concentrated) sample;
Cin – initial concentration of substance in sample.
Classification of separation and concentrating techniques
1. Techniques based on new phase formation:
1) freezing out an analysed substance or preventing chemical compounds;
2) selective dissolving of analysed components in various solvents accordance to
different solubility of each substance;
3) precipitation (sedimentation) of analysed substance;
4) distillation – evaporation and condensation of analysed substance in another
sample.
2. Techniques based on various distribution of substance between different phases:
1) adsorption of analysed compound on chemically inert sorbent with next thermal
desorption or elution with solvent;
2) extraction with organic solvent;
3) co-sedimentation with collectors;
4) chromatography of various techniques.
40
CHROMATOGRAPHIC METHODS OF ANALYSIS
Chromatography is the name given to a group of similar separation techniques that
depend on how fast a substance moves in a stream of gas or liquid, pass a stationary
material to which the substance may be slightly attracted.
Although the phenomenon of chromatography was used in the 19th century by dye
chemists to analysis dye solutions, the Russian botanist Mikhail Tswett was the first to
understand the basis of chromatography and to apply it systematically as a method of
separation. In 1906 Tswett separated pigments in plant leaves by column chromatography.
He first dissolved the pigments from the leaves with petroleum ether, a liquid similar to
gasoline. After packing a glass tube or column with powdered chalk, he poured the solution
of pigments into the top of the column. When he washed the column by pouring in more
petroleum ether after the solution, it began to show distinct yellow and green bands. These
bands, each containing a pure pigment, became well separated as they moved down the
column, so that the pure pigments could be obtained.
The name chromatography originates from this early separation of coloured
substances (the stem chromato- means “colour”), though the technique is not limited to
coloured substances.
Chromatography is based on different substance distribution between two
immiscible phases – moving and stationary. On contact with surface of stationary phase
components of mixture distribute between moving and stationary phase's accordance to
substance properties (adsorption, solubility etc.) – settles a dynamic equilibrium. Molecules
of separated mixture some time are in stationary phase and some time – in moving phase.
Molecules move (run) along chromatographic system in moving phase only. Various
substances have different attraction to stationary and moving phases. Substances, which
stronger interact with stationary phase, will slowly run through chromatographic system,
those substances, which interact poorer.
For separation of various molecules stationary phase must require even if one condition:
1) physically sorbs substance from moving phase;
2) chemically sorbs substance from moving phase;
3) dissolves separated substance;
4) has porous structure and thus to keep some substances and not delay others
accordance to its sizes and forms.
Chromatographic separation is possible because of irregular distribution of components of
mixture between stationary and moving phases. It is cause different attraction of individual
components to these phases and different diffusion on these phases.
The chromatographic separations carry out by the three modes (operations):
1. Frontal analysis.
The sample inject in column continuously during all process. We can isolate in pure
only the least sorbed substance. Use only in special cases and not use for preparative
purposes.
2. Displacement chromatography.
41
At the first in column inject some amount of separated mixture, than continuously
feed the solution of substance with the largest attraction to stationary phase. This compound
– displacement agent – supplants (push out) all early retained in stationary phase
components and push out it’s from column. Components with the least attraction to
stationary phase are eluted from column first. Use for preparative purposes, but not is
suitable for analytical purpose.
3. Development (efluent) chromatography.
In the column inject little amount of sample solution. Effluent attraction to stationary
phase is more than any component of solution. On column the components separate on
zones (bands). Each component is eluted independently one after another. Speed of
components moving depends on triple interaction (equilibrium) in system: component–
solvent–stationary phase.
Classification of Chromatographic Methods
in Accordance with Distribution Principles
Name of method
Adsorption
Partition
Ion exchange
Gel filtration
Affinity
Nature of basic distribution
principle
Adsorption
Extraction
Electrostatic action and diffusion
Diffusion
Biospecific interaction with
affinity ligand
Phenomenon, which define
substance attraction to phase
Adsorption coefficient
Distribution constant
Ions charge, effective ions radii,
dissociation constant
Effective molecule diameter
Constant not conventions (may
be inhibition constant or
dissociation constant)
1. Adsorption chromatography
Concentration of individual components of mix, dissolved in one phase, change on
boundary phase. On this boundary phase frequently dissolved components concentrate. This
phenomenon called adsorption. Degree of concentrating of some components is
proportional to its adsorption coefficients. If one phase moves relatively (along) another
takes place (happens) the chromatographic distribution.
Adsorption analysis is used as solid also liquid phase.
2. Partition chromatography
The mixture, dissolved in system of two immiscible liquid phases, distribute between
these phases accordance to solubility of individual components, or, exactly, to components
attraction to this phases. Distribution of components is definite of its constant of
distribution. Distribution efficiency depends on component distribution constant differences.
For chromatographic separation in the system of two liquid phases one phase must
moves along another phase. One of these liquid phases is immobilised (strongly fixed) and
called stationary phase. Another phase, that flow along boundary stationary phase, called
moving phase. The moving phase may be gas or liquid (organic solvent). The both phases
must be reciprocal saturated – that is being in equilibrium.
42
3. Ion exchange chromatography
The components of selected mixes can dissociate in solution on ions. These ions
electro-statically interact with ionogenic functional groups of ion exchange resin. Ions with
greater charge have more attraction to resin, than ions with small charge. Interaction with
functional groups of ion exchange resin depends on dissociation constant of ionogenic
groups, the pH value, and ionic strength of solution. These factors definite the distribution
degree of separated components between phase of ion exchange gel (resin) and phase of
solution. Mixture select when one of this phase moves along another.
4. Gel chromatography
Frequently components of analysed mixture are much distinguished by molecule
size. If solution of such mixes contact with solid porous phase, those molecules of some
components try to diffuse from the solution to solid phase. In this two-phases system settles
the equilibrium: small molecules penetrate into pores and distribute in both phases; the
largest molecules retain only in liquid phase; and the middle-size molecules particularly
penetrate in pores but in general retain in liquid phase.
As a porous phase use the various gels.
5. Affinity chromatography
This method based on specific interaction, which are characteristic of some
biological and biochemical processes. This interaction occurs between pairs of substances
with high selectivity reactions: antibody and antigen, enzyme and substrate, t-RNA and
aminoacid, hormone and receptor. Desolubilised specific preparation can be immobilised in
column on solid phase. When the solution of analysed mixture flows through the column,
the necessary component binds and retains in the column. The column is washed down with
an appropriate desorption solvent, and component can be selectively eluted.
6. Sedimentary chromatography
Some special techniques, which are based on no chromatographic principles, also
called chromatography. For example, sedimentary chromatography that based on chemical
reaction, which run during precipitation process. Following separation occurs on different
solubility of reaction products.
There are two ways of chromatography termination:
1. Flowing.
An analysed substance passes out the chromatographic system with effluent flow. The
components detect outside the stationary phase directly in stream of solution in effluent. For
detection use special detectors that measure some physical parameter of solution.
2. Zone.
An analysed component not elute from chromatographic system. It remains adsorbed on
stationary phase forms zones of it presence. The analysed substance detects directly in zones
with specific chemical reaction or some physical parameter measurement.
43
Classification of chromatographic methods according to applied equipment:
– column – stationary phase is packed in tube (glass, metal or polymer);
– plate – thin layer of stationary phase is fixed on surface of inert planar support;
– capillary – liquid stationary phase covers the external surface of thin metal or glass tube
(capillary);
– paper – sheet of special paper is the stationary phase.
Using Chromatography in Analysis
Majority of substances can be analysed by chromatographic method. In analysis of organic
substances, amounts of which is more than inorganic in hundreds thousands times, the
chromatography is a main method. Choice of chromatographic technique is presented
below:
Substances properties
Volatile (molar mass < 400)
– gases
– liquids and solids
Non volatile with molar mass 102-104:
– non polar
– low polar
– high polar:
– – ionised
– – non ionised
Non volatile with molar mass 103-106
Preferred chromatographic technique
Gas:
– adsorption
– gas-liquid (partition)
Liquid:
– adsorption on direct phase
– on reverse phase
Ion exchange
Liquid on reverse phase
Gel filtration (penetration)
44
THEORY OF CHROMATOGRAPHIC SEPARATION
Sorption is taking up of analysed substance (sorbate) on solid or liquid. There are
two types of sorption:
– adsorption is concentrating of substance on surface of boundary phase (adsorbent), and
– absorption is taking up of substance or gaseous mix in the bulk of the solid or liquid.
The reverse processes is called desorption.
Adsorption is concentrating of substance (adsorbate) on surface of boundary phase
caused by physical and chemical interaction with adsorbent and adsorbate. If adsorption is
accompanied by chemical compounds formation that process called chemosorption.
In any chromatographic system take place the reversible moving of substance
molecules from moving phase to stationary phase (As ↔ Am).
This process is definite by equilibrium constant:
K=
[As]
Vm
=k
[Am]
Vs
[As] and [Am] – component concentration in stationary and moving phase
accordingly;
Vm and Vs – volumes of moving and stationary phases;
k – coefficient of capacity.
Coefficient of capacity and retention time are related as:
k=
tR − t 0
t0
tR – retention time of analysed component;
t0 – retention time of substance, that not interact with stationary phase.
Fundamental retention equation: tR = L⋅(1+k)/u
tR – retention time;
L – column length or, more general, length of sorbent bed;
k – coefficient of capacity;
u – speed (rate) of moving substance zone
Retention time depends on flow rate (speed) of effluent, because in column
chromatography use such parameter as retention volume. Retention at any chromatographic
process described by equation:
VR = Vm + k⋅Vs = tR⋅F
F – flow rate of effluent.
45
The chromatographic process may be described by two theories:
1. The rate theory.
Sorbent bed is macroscopic homogeneous medium with participation of small
amount of molecules. In bed of stationary phase species distribute and sets in equilibrium.
An individual molecule moves along column with rate depended on speed of penetration
through the boundary phase.
Really the substance sorption process consists on two stages:
1) moving the substance from gaseous phase to sorbent surface (external diffusion
stage);
2) transfer the substance from surface into sorbent (internal diffusion stage).
At one time part of molecules diffuses from gas bulk to sorbent surface and into sorbent,
and another part of molecules moves along sorbent layer (bed). This causes erosion of
chromatographic zone.
2. The plate theory.
In the plate theory, we treat our chromatographic column as though it was a "static"
system in equilibrium. The sorbent bed consists from great amount of sequential elementary
steps (plates). Separated substances pass through every plate by discontinuous portions,
carried by gas-carrier. On every this plates each species exhibits equilibrium between the
mobile and stationary phase.
As a result, separated substance is placed a few several plates. On middle plates the
substance concentration is more than next. Thus, the substance is "spread" on a few plates.
The large amount of plates are occupied by substance, the more is erosion.
The plate theory bases on hypothesis that chromatographic process is stepwise
(discrete). On fact, this process is continuous. Plate theory not accounts selective properties
of sorbent.
Therefore, number of plates, occupied by the substance, is a measure of sorbent
(column) efficiency.
L
H=
n
H – height equivalent to a theoretical plate;
L – length of sorbent bed, on which occur separation process;
n – number of theoretical plates needed for mixture separation.
n = 16⋅(VR/x)2 = 16⋅(l/x)2 = 16⋅(tR/x)2
x – width of the component peak on chromatogram;
l – distance from injection moment to the component chromatographic peak.
Relaxation factor describes relative mobility of separated species accordance to carrier rate.
Relaxation factor is kinetic coefficient, which characterises sorption time. This factor
calculates in all chromatographic techniques.
In zone methods it definite as Rf.
In elution methods it calculate as R = 1/(1 + k).
46
Separation efficiency is definite as
β = m/(x1 + x2)
m – distance between two chromatographic peaks, or spots, or bands;
x1 and x2 – width of these peaks, or bands, or spots diameter.
VARIOUS CHROMATOGRAPHIC TECHNIQUES
PLATE CHROMATOGRAPHIC TECHNIQUES
In plate chromatographic techniques the sorbent is layered on hard plate support or it
support itself (sheet of paper). The plate chromatography is zone method.
The analysed sample dissolve in organic solvent and drops on sorbent surface. After
separation all components stay on sorbent surface (as bands or spots).
The plate chromatography is partition mode. Sample components are carried by a
mobile phase through a bed of stationary phase. Individual species are retarded by the
stationary phase based on various interactions such as:
– Surface adsorption
– Relative solubility
An example of paper chromatography. We put on a line of ink near one edge of a paper and
than place the paper upright with this edge in a solution of methanol and water. As the
solution creeps up the paper by capillary action, the ink moves upward, separating into a
series of different-coloured bands that correspond to the different dyes in the ink. The
reason the ink is separated into bands containing the different dyes is that each dye is
attracted to the wet paper fibres, but with different strengths of attraction. As the solution
moves upward, the dyes that are less strongly attracted to the paper fibres move more
rapidly.
Sorbents for plate chromatography:
1) paper. It is paper made with poor cellulose and, for special purposes, impregnated
with specific reagents. Chromatographic paper is washed by acid and organic
solvents. New scientific achievement is glass fibre paper.
2) powdered silica gel,
3) aluminium oxide,
4) magnesium silicate,
5) granulated cellulose or acethylcellulose,
6) glass balls.
Thin layer of sorbent may be fixed (by starch, gypsum) or not fixed on support. Supports for
stationary phase are glass plate, metal foil, and polymeric films.
The main rule of effluent choice is "similia similibus solventur". All solvents are
regulated in eluotropic row. Solvents on this row places accordance to its polarity:
aliphatic hydrocarbons → aromatic hydrocarbons → halogen-deviates of hydrocarbons →
ethers → cetones → alcohols → water.
47
The mobile phase (effluent) for plate technique, as a rule, consists of two or more
components.
One component move separated components. The analysed substance good dissolves
in this solvent.
Another component of eluting mixture not dissolves the separated substance. This
solvent decelerates (becomes slower) the separated substance moving. This solvent
increases the separated substance attraction to stationary phase.
For separation of liophylic substances uses reverse phase chromatographic systems.
On such systems liophylic solvent is a liquid stationary phase (fixed or impregnated in
sorbent) and polar solvents are the mobile phase. In case of paper chromatography the
chromatographic paper impregnates by non-volatile organic solvents, which not mixes with
lipophylic liquid: ethylenglicole, bromnaphtalene.
There are various ways of effluent giving (regime) on sorbent (plate) surface:
1. Descending chromatography. Plate lies with little slope (incline). Effluent (mobile
phase) stream down on stationary phase surface.
2. Ascending chromatography. Edge of plate dips into effluent at 1,0 - 1,5 cm depth.
Effluent moves upwards under the capillary action.
3. Circular chromatography. Effluent gives into sample spot centre. Effluent moves to
radial (all) directions. Separated substances move with effluent and form circular zones.
4. Two dimension chromatography. The sample at first separates in one direction. Then
sorbent dries up, plate rotates and separation make ones more in perpendicular direction.
At both separations may be used mobile phase with different composition of solvents.
5. Multiple elution. Separation repeats (reiterates) few times with the same mobile phase.
After each elution the plate dries up and repeats chromatographic process from
beginning.
Chromatographic separations carry out in special chambers. Before beginning of process the
bulk of chamber saturates with streams of used solvents mixture. Saturation of solvents
stream prevents non-equilibrium separation on stationary phase surface.
Line, on which is placed sample and from which begin to move separated components,
called start line.
Detection of analysed components is carrying out:
1) work out specific chemical reactions with separated components on plate surface;
2) sorbent may consist the non-visible dye (visible only under UV-light). UV-radiation
develops the substances as dark spots (bands) on blue background of plate;
3) measurement of physical parameters of separated substances: UV- or IR-absorption, γradiation;
4) substance extraction with appropriate organic solvent from spot (band). Paper cuts out
the paper sheet or sorbent scrapes off the thin layer.
Identification of developed substances
I. The substance moves with rate (speed) which depends on its attraction to sorbent and
solubility in mobile phase. Substance places between start line and solvent finish line.
Ratio of solvent distance (H) to component distance (h) is characteristic of substance
mobility and called rate fraction (Rf):
48
Rf =
H
.
h
This value uses for analysed substance identification (at constant analysis conditions).
Rf is equivalent to coefficient (factor) of capacity (used in column technique). Rf shows
(demonstrate) the retention degree.
II. For identification of unknown substances may be used also markers. Marker is standard
well-known substance for chromatographic parameter comparison. Spot of standard put on
start line beside the sample and put on trial with the sample on the same plate in the same
analyse conditions (chamber, effluent, temperature). If way (distance) of unknown
substance is equal to markers way, we can suppose its identity.
Quantity determination of analysed substances carries out:
1) calculation of spots area and plots calibration curve on the √S – m coordinates.
S – area of spot, m – substance amount;
2) photometry (densitometry) of reflected or absorbed colour light. Intensity of light
absorption or reflection is proportional to substance amount in spot (band).
GAS CHROMATOGRAPHY
Gas chromatography is chromatographic process with gaseous or steam moving
phase. Apply in column only. Gas chromatography is the first chromatographic method
developed commercially. Reason – it is relatively easy to produce a stable flow and pressure
for the mobile phase.
Flow control. All that is really needed is a tank of compressed gas, pressure regulator
and a valve.
There are two variants of gas chromatography:
– If the stationary phase is liquid, layered on inert support (hard carrier), and dissolves an
analysed substance. This substance distributes between stationary phase and moving phase.
Such chromatographic systems are partition and called gas-liquid.
– If the stationary phase is solid and adsorbs an analysed substance, such chromatography
called gas-adsorption.
Preferences of gas chromatography:
1) quality and quantity determination of individual components in complicated mixtures;
2) investigation of various properties and physical-chemical interactions in gases, liquids or
on solid surface;
3) high legibility of separation and high speed of process, caused small viscosity of moving
phase;
4) automatically registration of results;
5) analysis of many substances – from light gases to high-molecular organic compounds
and some metals;
6) extraction of pure substances on preparative and manufactory equipment;
49
7) using complex (hybrid) techniques of gas chromatography:
– reacting chromatography – combination chemical transformation of analysed
substances with its chromatographic separation,
– chromato-mass-spectrometry – combination chromatographic separation with
mass-spectrometric identification of components,
– pyrolytic chromatography – thermal destruction (pyrolysis) of analysed substances
with next chromatographic separation and identification of products.
Moving phase and eluent in gas chromatography is gas. In gas chromatography this gas
called gas-carrier.
1. Requirements to gas-carrier:
– must be inert to analysed substances and used sorbents,
– to have great thermal conductivity,
– viscosity of gas-carrier must be the least.
2. The gas-carrier flow rate influence on HETP value and the best is rate with the lowest
HETP value.
3. The chromatographic column efficiency increases with gas-carrier pressure increasing.
The pressure increasing practically not influence on HETP value.
As a gas-carrier use:
1. Pure nitrogen. This gas can be used with various detectors. Absolutely careless and
cheap. Have small viscosity and low thermal conductivity.
2. Air. Have the same properties as nitrogen. But oxygen (component of air) can reacts with
some analysed substances.
3. Hydrogen. Have the largest thermal conductivity, but is explosive.
4. Helium. Can be used instead hydrogen. But is dear.
5. Argon. Have large viscosity and concludes many impurities.
6. Carbon dioxide. Use for work with pressure and in supercritical fluid chromatography.
7. Water steam and organic solvents steam. Use for special cases of analysis.
Stationary phase in partition gas chromatography called stationary liquid phase. There are
non-volatile (at process temperature) liquids, layered on solid support. In capillary column
the solid support is internal walls (surface) of capillary. These liquids dissolve the separated
components.
1. Requirements to stationary liquid phase:
– high selectivity and optimal sorption capacity;
– not interact chemically with separated substances, solid support, column material and
gas-carrier;
– chemical stability and law vapour pressure.
2. Quantity of stationary liquid phase
– appoint HETP value;
– influence on column selectivity;
– definite efficiency and retention of adsorption.
2. Liquid phase must not evaporate from column at working temperature, because its
vapour can perverse the detector signal.
50
Solid stationary phase is the support for liquid phase.
1. Requirements to solid stationary phase (support):
2
– to have great specific surface (more than 1 m /g);
– slightly adsorbs separated substances;
– not have catalytic activity and be chemically inert;
– to be mechanically strong;
– to be stabile at high temperature;
– good moistened by liquid phase.
1. As a support use:
– natural sorbents (diatomic clay and ceolites). The natural origin support have
adsorption properties and, as a rule, are modified by washing with acid, or work out
with small amount of polar liquid, or chemically deactivated,
– glass spheres (balls),
– porous Teflon or another polymer balls.
2. Particles size influence on separation efficiency. Crushing of particle size causes
increasing of column efficiency and increases value HETP.
In gas-adsorption chromatography the solid stationary phase is adsorbent.
1. Requirements to solid stationary phase (adsorbent):
– have high selectivity to separated substances;
– not have catalytic activity and be chemically inert to analysed substances and gascarrier;
– to be mechanically strong.
2. There are three types of adsorbents:
I.
Non-specific – not have any functional groups or ions on its surface: charcoal,
soot.
II.
Have on surface positive charge: silica gel, aluminium oxide, ceolites, and
inorganic salts.
III.
Have on surface bonds or atoms groups with concentrated electron density:
porous polymers or styrene resin.
These adsorbents may be modified by
– water washing for dissolving of acids, alkalis and inorganic salts;
– bonding of hydroxyl groups with silanes;
– covering of organic non-volatile liquids;
– producing of colloid systems;
– covering (layering) the inert support of adsorption dust.
Temperature programming.
The column sits in an oven. For optimal adsorption–desorption process (equilibrium)
load required temperature.
If the temperature is held constant during the entire analysis it is isothermal.
If you vary the temperature during the analysis, you typically use a temperature program.
51
Injection methods.
There are two basic approaches:
– injection ports,
– sampling loops/valves.
Chromatography is flow method. We need a way to measure our effluent as they
evolve from the column. We continuously definite the properties of gas-carrier flow as
function of time or volume of passed substance. For definition of analysed mixture
components are used special detectors. There are common types of detectors (such
measured parameters, such definite properties):
1) measurement of difference of heat (warmth) conductivity of eluate and pure eluent;
2) measurement of density of eluate and pure eluent;
3) measurement of ionisation current of eluate;
4) measurement of flame temperature, in which burn eluate;
5) measurement of ionisation current of flame, in which burn eluate.
The gas-carrier with desorbed component flows through the sensitive element of
detector. Detectors signal is registered. Curve of dependence of detector signal on volume
of gas-carrier or on time called chromatogram or elution curve. Chromatogram shows
(draw) sequence elution of components.
The chromatogram has such characteristic elements (lines):
1) zero line – registration of detector signal of pure gas-carrier,
2) peak of nonsorbed component (may be solvent steam or air),
3) peak of separated component – registration of detector signal of one of the analysed
substance.
Qualitative determination (identification) of analysed substances in gas
chromatography may be carried out
1) on retention parameters – retention time and retention volume. Experimental data
compares with the same values of standard
2) or with markers using. To analysed sample add the expected substance (as internal
standard). This addition modifies (changes) component peak drew on chromatogram. If
analysed substance is the same as standard, the chromatographic peak rises (becomes
higher). If these substances are different, the chromatographic peak becomes wider or
divides on two peaks.
Quantity determination of separated component is based on common rule of flow
chromatography: the chromatographic peak area is directly proportional to substance
amount. Wide (base) of chromatographic peak is defined by nature of substance and sorbent
and, as a rule, non changes at constant conditions of analysis. But high of chromatographic
peak changes very mach accordance to substance amount.
The chromatographic peak area (S) calculates as triangle area:
S = 1/2⋅h⋅x
h – high of chromatographic peak,
x – wide (base) of chromatographic peak.
52
There three modes of quantity determination of analysed substances:
1. Absolute calibration technique.
Calibration curve draw in the coordinates S – m, where are S – area of
chromatographic peak, m – amount of substance in sample. This technique is simple but not
precise. Sample dosage has many complications.
2. Internal standard technique.
To all analysed samples adds the internal standard, and its amount is constant in all
samples. For quantitative determination compares the standard and unknown substance
peaks area. The main order of this technique – the internal standard must separate
completely.
3. Additions technique.
At first make chromatographic separation of analysed sample. Than to new sample
adds some amount of the same substance (addition) and calculate the chromatographic peak
enlargement degree.
LIQUID CHROMATOGRAPHY
First chromatographic method described (as a non-instrumental method). Since
samples do not need to be initially vaporised, potentially any compound can be analysed by
this method. Instrumental development lagged behind that of gas chromatography because
of difficulties a stable solvent flow.
Basic HPLC equipment is presented on figure:
For achievement the stable solvent flow using special pumping systems, which can
make pressure to 40 MPa. This method with high-pressure effluent flow called high
performance liquid chromatography (HPLC).
Basic types of pumping systems:
1. With the constant pressure:
– pressurised vessel;
53
– pressure intensifier.
2. With the constant flow:
– motor driven syringe;
– piston: reciprocating and multiple reciprocating.
There are several types of interaction than have been used to separate effluents in HPLC:
surface adsorption,
solvent partitioning,
ion exchange,
relative solute size.
Chromatographic columns for HPLC are packed by spherical sorbents' particles with 3,510 µm size. Such columns have the largest separation efficiency (can take 40.000-150.000
theoretical plates per 1 m).
As stationary phase use:
– silica gel with specific surface 100–700 m2/g;
– aluminium oxide;
– modified silica gel with
–(CH2)4–CN, –(CH2)4–NH2,
–(CH2)4–OH, and –(CH2)4–C6H5 groups.
HPLC mobile phase (effluents) are various organic solvents. HPLC is limited our
coverage to normal and reverse phase work. Solvent selection is much more critical for
these methods.
Detector systems must measure in solution every chemical and physical property.
Detectors fall roughly into two dashes:
– bulk property – measure an overall change in the mobile phase,
– solute property – measures a solute specific property.
As detectors may be used:
– UV-spectrophotometers,
– refractometers,
– fluorescent photometers,
– electrochemical cells.
Gradient elution
Unlike gas chromatography, variations in temperature have minimal effect on a
liquid chromatography separation. With HPLC, temperature programming is not typically
an option in dealing with homologous series.
However, variations in solvent polarity can greatly affect retention.
This can be accomplished by altering the solvent mix during an analysis.
Instead, we rely on altering the nature or polarity of the solvent – gradient elution.
ION EXCHANGE CHROMATOGRAPHY
Ion exchange chromatography is a reverse process of stoichiometry exchange of ions
from analysed solution to moving anti-ions of sorbents, called ion exchangers.
As ion exchangers use natural or synthetic resins are solid, non-dissolved in water
high molecular acids and its salts, concluding active groups. Ion exchangers divide on
cation exchangers that capable of hydrogen ion exchange on cations and anion exchangers
that capable of hydroxide ion exchange on anions.
54
Ion Exchange Groups
Anion exchangers:
Cation exchangers:
Diethylaminoethyl
–O–CH2CH2N+(C2H5)2–H⋅Cl–
Carboxymethyl
–O–CH2COO–⋅Na+
Quaternary aminoethyl
–O–CH2CH2N+(C2H5)2–CH2CH(OH)CH3⋅Cl–
Sulphopropyl
–O–CH2CH2CH2SO3–⋅Na+
Quaternary amine
–CH2–N+(CH3)3⋅SO42–
Sulphonate
–CH2–SO3–⋅Na+
Scheme of cation exchange:
R–SO3–H+ + M+ ↔ RSO3–M+ + H+
Scheme of anion exchange:
R–NH3+OH– + A– ↔ RNH3+A– + OH–
Ion exchange process (sorption) depends on:
1. Nature of analysed substances.
Attraction to ion is proportional to ion charge and inversely proportional to hydrated
ion radius. The ion exchangers' selectivity to dissociated ions can be described by selectivity
rows:
1) Ba2+ > Pb2+ > Sr2+ > Ca2+ > Ni2+ > Cu2+ > Co2+ > Zn2+ > Mg2+;
2) Ag+ > Rb+ > K+ > NH4+ > Na+ > Li+;
3) I– > NO3– > Br– > SCN– > Cl– > F–.
2. Nature and structure of ion exchangers.
Strong ion exchangers are ionised over a wide pH range, and have almost constant
ionic capacity within this range. Fluctuations in pH will not titrate the ion exchange groups
so the matrix does not display a buffering effect. Strong exchangers may also exhibit
slightly better selectivity than weak ones.
Weak ion exchangers are only ionised over a limited pH range, and may start to lose
their charge at pH values below 6 (cation exchangers) or above 9 (anion exchangers). Use of
a weak exchanger close to these pH values (i.e. close to its pKa) can lead to complex
separation mechanisms, as the ion exchange groups will be titrated and display a buffering
effect. At neutral pH, either strong or weak ion exchangers can be used.
Loading capacity
As loading capacity is a function of available capacity, no general rule for sample
loading can be given. This value can be exceeded if the resolution is adequate.
Available capacity is a measure of the accessibility of the binding sites inside the
pores of the matrix to any particular charged biomolecule; it can be found by a simple
column or test tube experiment.
Total capacity is a measure of the ability of the matrix to bind exchangeable counter ions
–
(Cl for anion exchangers or Na+ for cation exchangers). It is measured by titration of the
charged groups with a strong acid or base.
55
3. An experiment conditions (temperature, pH etc.).
pH stability means that the gel will withstand regular use within this range. Working
pH range is the range in which the ion exchanger is charged and has effective capacity.
Using ion exchange chromatography in analysis:
1) separation of complicated cations mixture;
2) concentrating of several metals, for example, gold from sea water.
SEDIMENTARY CHROMATOGRAPHY
Sedimentary chromatography bases on different solubility of precipitates, formed at
interaction analysed components in mobile phase dissolved with reagent-precipitant.
Precipitant in mixture with effluent combines the stationary phase.
As effluent stationary phase use dispersed substance (Al2O3, silica gel, cellulose,
starch, charcoal, ion exchange resins) or filter paper. Accordance to used support for
stationary phase the sedimentary chromatography can be column or plate.
As mobile phase use pure solvent or solution, in which solubility of precipitates,
formed by various compounds, are different (for example, solution of acids or alkalis).
The mixture separation occurs because of multiple repetition precipitates formation
and dissolving act. Rate of precipitates (sediments) moving be proportional to its solubility
in given solvent and defined by activity product of formed slightly soluble compounds.
Sedimentary chromatography is zone technique. The sedimentary chromatogram is
draw (picture) of chromatographic zones (bands or spots) separation on stationary phase
layer or bed.
In diffusion sedimentary chromatography as stationary phase applies gel of gelatine
or agar-agar in which preliminary is added precipitant. Separation of components occurs
under diffusion action.
Detection of components on chromatogram carries out with colouring reagent or UVlight radiation. Identification makes on the Rf value.
Quantity determination of components may be provided:
1) high or volume of zone – in column technique,
2) area of spot or colour intensity – in plate technique.
Application in analysis
1. Identification and quality determination of inorganic compounds.
2. Identification and quality determination of organic compounds, which form
precipitates with different solubility.
3. Establish of solubility constants in various solvents.
GEL CHROMATOGRAPHY
Stationary phase is gel – chemically inert, sewing together, not dissolved polymer
matrix, saturated by liquid, usually by water. The same liquid is the mobile phase. In
polymer matrix there are pores, size of which depends on used gel.
56
Analysed substances may be divided on tree groups accordingly to its molecular size:
– compounds with high molecular weight,
– compounds with smaller molecular weight,
– and low molecular weight compounds, for example, salts.
Solution of these compounds mixture puts to column, packed with gel, and elutes by
pure solvent. Great molecules can not penetrate to gels pores. They pass through the column
with solvent flow that detour gel particles.
Small molecules can diffuse to gels pores. They uniformly (evenly) distribute in
mobile phase inside and outside gel. Molecules, placed inside stationary phase, elute the
most slowly.
Middle size molecules partially diffuse inside gel. They concentration in gel is less
than concentration of molecules with little weight. Because compounds with middle size
molecules are eluted later than compounds with high molecular weight but earlier than
small molecules components.
Thus, compounds come out the column in order its molecular weight decreasing.
As stationary phase (gel) use:
1) dextrane – polysaccharide produced by micro-organisms Leuconostos mesenteroides;
2) agarose;
3) various polymers;
4) porous silica gel or porous glass.
Gel chromatography uses in biochemical analysis for:
1. Separation of substances with molecular weight from 103 to 107.
2. Group selection of peptides, nucleic acids, enzymes etc.
3. Molecular weight determination.
AFFINITY CHROMATOGRAPHY
Affinity Chromatography is a versatile and highly specific technique for the
separation and purification of all classes of biomolecules utilising differences in biological
activities or chemical structures. The affinity chromatography is based on the dextrane and
agarose accepted gel matrix:
1) Coupling gels. Activated adsorbents allow immobilisation of ligands. The developed a
wide range of high capacity gels with a variety of coupling chemistries for immobilising
ligands a chosen functional groups: –NH2, –SH, –COOH, –CHO.
2) Group specific gels. Group specific adsorbents have affinity for a wide range of related
substances rather than for a single substance: immunoglobulins, proteins, nucleic acids,
polysaccharides, glucoproteins, lipoproteins, and enzymes.
3) Gels for covalent chromatography. Covalent chromatography provides a mild and
straightforward group separation method for molecules, which contain reactive thiol
groups (–SH).
4) Gels for metal chelate affinity chromatography. The amino acids histidine, cysteine and
tryptophan, present in almost every protein, form complexes with many transition metal
ions. A matrix charged that a suitable metal ion therefore selectively retains proteins
when these residues are exposed. Metal chelate affinity chromatography is also known
as immobilised metal ion adsorption.
57
Using in analysis
1. The high selectivity of this technique results in good purification and high recovery of
activity. The same general ligand can be used to purify several substances (e.g. a class of
enzymes).
2. It is also a useful concentrating technique, eluting the active fraction in a small,
concentrated volume.
3. Separation of various biochemically active molecules.
4. Isolation and determination of individual substances.
58
GRAVIMETRIC METHOD OF ANALYSIS
Gravimetry based on measurement of weight of an analysed species or a compound
containing the analysed species. There are three groups of gravimetric methods:
Isolation methods. Analysed component quantitatively isolates from sample in pure
substance and weights. For example, determination of gold, silvers, and cooper in ore or
alloys.
Volatilisation methods. There are direct and indirect volatilisation methods. In direct
method a volatile compound reacts with specific absorbent, which weighed. At indirect
method analysed species is volatilised, weighed and the loss is determined. For example,
determination of crystallisation water in hydrates:
BaCl2⋅2H2O → BaCl2 + 2H2O↑
Precipitation methods. Based on isolation of an insoluble precipitate of known
composition. A sample dissolves and analysed component precipitates. The precipitate is
filtered, washed, dried (or tempered) and weighed. Thus, substance that is precipitated and
substance that is weighed, can not be the same compound. There are two different
compounds:
– precipitating form – the compound formed by precipitant in analysed solution
– and weighting (gravimetric) form – the weighed compound.
For example:
I. The same substance are precipitating form and after drying – weighting form:
BaCl2 + H2SO4 → BaSO4↓ + 2HCl
AlCl3 + 3C9H6NOH + 3CH3COONH4 → Al(C9H6NO)3↓ + CCH3COOH + 3NH4Cl
8-oxyquinoline
II. Precipitating form and weighting form are different substances:
CaCl2 + Na2C2O4 → CaC2O4↓ + NaCl – precipitating form
CaC2O4 → CaO + CO2↑ + CO↑ – weighting form
MgCl2 + Na2HPO4 + NH4OH + 5H2O → MgNH4PO4⋅6H2O↓ + 2NaCl – precipitating form
2MgNH4PO4⋅6H2O → Mg2P2O7 + 2NH3↑ + 7H2O↑ – weighting form
Precipitation is the most important stage of gravimetry. Accuracy of gravimetric
methods depends on:
– precipitant choice,
– precipitant amount,
– precipitation conditions.
On precipitation process influence:
1) precipitant amount. Precipitation is complete, when residue amount of analysed
species is less than balance sensitivity (0,0002 g). Precipitant surplus causes
common-ion effect or salting effect. As a rule, precipitant surplus can not be more
than 50 % of stoichiometric amount;
59
2) temperature. Temperature increasing, frequently, causes precipitate solubility
increasing;
3) pH value. Change the pH value represses dissociation of analysed weak electrolytes
or dissolves its;
4) complex formation process. Process of complex compounds formation competes
with process of precipitate formation. Effect depends on solubility-product value and
formation-constant value.
Properties of Precipitates
To obtain good results, we must be able to produce a “pure” precipitate that can be
recovered with high efficiency.
We want the precipitate to:
1) have low solubility. Precipitates solubility-product (SP) must be less than 1⋅10-8,
2) be easy to recover by filtration and washing. From this point of view crystalline
precipitates should preferred be used than amorphous,
3) easy and completely transforms to weighed form,
4) be unreactive to air, water…
5) be something where our analysed species is only a small portion of the precipitate.
Precipitation from homogeneous solution
When a precipitation reagent is added as a solution to our analysed species there will
be locally high concentrations. This is responsible for many of our problems regardless of
how slowly we add the reagent or how fast we stir. Precipitation from homogeneous
solutions is an approach that can avoid this problem.
Precipitates can be crystalline or amorphous.
Crystalline precipitates – this type of precipitate is much easier to work with.
They are easier to filter and purified.
We have greater control over the precipitation process.
Sizes and speed of crystallisation is definite by experimental equation of relative
solution supersaturating (RSs):
Q−S
RSs =
S
Q – concentartion of precipitated component;
S – solubility of precipitated component.
As more is RSs value that more is amount of centres of crystallisation and that small
is crystallisation speed. In accordance to equal, for decreasing of amount of centres of
crystallisation we must diminish (decrease) the Q value and enlarge (increase) the S value.
Because of, the analysed solution would be diluted (for diminish the Q value) and heated
(for enlarging the S value). And also for increasing the S value we may add electrolyte or
acidify analysed solution.
In general, the best approach is to slowly form your precipitate using rules of crystalline
precipitates formation:
1. Analysed solution must be diluted.
60
2.
3.
4.
5.
6.
Precipitant added slowly (even on drops).
Continuously stir.
Used warm analysed solution and warm precipitant solution.
Solution with precipitate filtrates after cooling.
Added substances, which increase precipitate solubility.
Colloidal precipitates are coagulated colloids. As an example, the following
precipitate formation through out:
AgNO3 + NaCl ↔ AgCl↓ + NaNO3
NaCl will be our precipitating reagent.
AgCl tends to form colloidal (amorphous) precipitates.
Rules for amorphous precipitates coagulation:
1. Use warm solutions of analysed species and precipitant.
2. Use concentrated solution of precipitant.
3. Precipitant adds quickly.
4. Add strong electrolytes.
Coprecipitation
When an otherwise soluble compounds is precipitated along with your analysed
species. This does not include materials that would normally be insoluble.
Sources of coprecipitation
+
– surface absorption. For example, on surface BaSO4 precipitate adsorbs Pb ions;
– occlusion. Coprecipitated impurities placed not on precipitant surface but into precipitate
particles. For example, CaC2O4⋅Na2C2O4;
– mixed crystal formation. Different substances form the same crystal lattices. Ions of
impurities built in the units cells of analysed species crystal lattices. For example,
KAl(SO4)2⋅12H2O, KCr(SO4)2⋅12H2O;
– mechanical entrapment.
For prevention of coprecipitation the precipitant must be volatile substance. It was
not adsorbed on precipitate and was volatised at drying or tempering. For example, NH4NO3
or urea [CO(NH2)2].
Precipitate Drying
After filtration, the precipitate must be dried to constant weight by means:
– removes excess solvent,
– drives off any volatile species,
– in some cases, the precipitate is heated to a point where it decomposes to a stable form
for weighing. Heating to large temperature for transformation of precipitate in weighed
form called tempering. For example:
CaC2O4⋅2H2O → CaC2O4 + 2H2O↑
CaC2O4 → CaCO3 + CO↑
CaCO3 → CaO + CO2↑
(200 °C)
(475-525 °C)
(900-1000 °C)
61
Thermobalances can be used to determine optimum drying time and temperatures.
Demands to weighed (gravimetric) form:
1. Composition stoichiometry corresponds to chemical formula.
2. Chemical stability. Not reacts with air components (CO2, O2, another gases) and not
absorbs water steam.
3. Conclusion of analysed element must be the less. In this case measurement error not
influence on calculation results.
Gravimetric Calculations
Gravimetric calculations are simply an extension of stoichiometric calculations. Our
stoichiometric factor is most often based on the amount (in moles) of our analysed species
in the material actually weighed.
GF =
moles analysed species in weighed form ⋅ FW analysed species
formula weight of weighed form
GF – gravimetric factor.
FW – formula weight.
Summary of Method
– A relative slow method of analysis – however, most time is spent waiting for little effort
for user.
– Minimal requirements – major equipment is a good balance and an oven.
– No calibration is required – results are based on formula weight.
Example Applications
1.
2.
3.
4.
5.
Inorganic precipitating agents.
Many cations and anions can be precipitated as groups.
With a proper design, you can use this to precipitate a single species.
Determination of humidity (moisture) of materials.
Determination of crystallisation water in hydrates.
62
TITRIMETRIC METHODS OF ANALYSIS
Based on the measurement of the amount of reagent that combined with an analyte.
Titrimetic methods are widely used for routine analysis because they are rapid, convenient,
accurate, and readily automated. There are such variants of titrimetry:
1. Volumetric. Volume of reagent solution required for a complete reaction.
2. Gravimetric. Weight of reagent required for a complete reaction.
3. Coulometric. Time/current required for complete oxidation or reducing of an analyte.
Requirements to chemical reaction used in titrimetric methods of analysis:
1. Reaction between reagent and analyte must be specific. Titrant can not react with
impurities or additions of analyte solution.
2. Reaction must be stoichiometric.
3. Titrant must react rapidly with the analyte so that the time required between additions of
reagent is minimised.
4. Titrant must react more or less completely with the analyte so that satisfactory end points
are realised.
5. Undergo a selective reaction with the analyte that can be described by simple balanced
equation. Equilibrium constant must have high value.
Classification of Titrimetric Analysis Methods
Method
Neutralisation
(acid-basic titration)
Redoximety
(reducing-oxidising)
Precipitation titration
Complexometry
(complex compounds formation)
Nonaqueous titration
Technique
Titrant
Alkalimetry
MeOH
Acidimetry
HAn
Halometry
HAn, MeOH
Permanganatometry
KMnO4
Iodometry
I2, Na2S2O3
Bromatometry
KBrO3
Cerimetry
Ce(SO4)2
Vanadatometry
NH4VO3
Titanometry
Ti2(SO4)3
Nitritimetry
NaNO2
Argentometry
AgNO3
Mercurometry
Hg2(NO3)2
Rhodanometry
KSCN
Mercurimetry
Hg(NO3)2
Fluorimetry
NaF
Complexonometry
EDTA
Solution of HClO4 in acetic acid or nitrometane
Solution of NaOH or CH3ONa in methanol
Titration is a process in which a standard reagent (titrant) is added to a solution of
an analyte until the reaction between the analyte and reagent is judged to be complete.
Titration can be:
1) direct titration – titrant add to an analyte solution and react with determined substrance;
63
2) back-titration – is a process in which the excess of a standard solution used to react with
an analyte is determined by titration with a second standard solution. Back-titrations are
required when the reagent is slow or when the standard solution lacks stability. For
example:
CaCO3 + HCl = CaCl2 + H2O + CO2
surplus (titrant 1)
HCl + NaOH = NaCl + H2O
residue
titrant 2
3) substitute-titration – is a process in which a standard solution used to react with an
additional (substitute) substance, amount of which is equivalent an analyte amount.
Substitute-titrations are required when the analytes are unstable substance or when is
impossible to indicate the equivalent (end) point in direct reaction. For example:
CrCl2 + FeCl3 = CrCl3 + FeCl2
analyte
substitute
5FeCl2 + KMnO4 + HCl = 5FeCl3 + KCl + MnCl2 + 4H2O
Equivalence point is the point where sufficient titrant has been added to be
stoichiometrically equivalent to the amount of analyte. The equivalence point of a titration
is a theoretical point that can not be determined experimentally, but can be determined
experimentally the end point.
End point is the point in a titration when a physical change that is associated with
the condition of chemical equivalence occurs. We can estimate its position by observing
some physical changes with various indicating techniques:
a) without any special means. The visible changes occur in titrated solution – change
of titrant or analyte colour, turbidity arise, precipitation formation;
b) with internal indicator using. The special chemical substances called indicators are
added to the analyte solution. Typical indicator changes include the appearance or
disappearance of a colour, a change in colour, or the appearance or disappearance
of turbidity;
c) with instruments. This instruments respond to certain properties of the solution
that change in a characteristic way during the titration.
The difference in volume between the equivalence point and the end point is the titration
error.
A standard solution (or titrant) is a reagent of exactly known concentration that is
used in a titrimetric analysis. Standard solutions are the main participants in all titrimetric
methods of analysis. The titrant solutions must be of known composition and concentration.
Ideally, we would like to start with a primary standard material.
Primary standard is an highly purified compound that serves as the reference
materials for a titrimetric method of analysis. Important requirements for a primary standard
are:
1. High purity.
2. Stability toward air.
3. Absence of hydrate water so that the composition of the solid does not change with
variations in relative humidity.
4. Ready availability at modest cost.
5. Reasonable solubility in the titration medium.
64
6. Reasonable large molar mass so that the relative error associated with weighing the
standard is minimised.
A secondary standard is compound whose purity has been established by chemical
analysis and serves as the reference material to a titrimetric method of analysis.
The concentration of the standard solutions can be established by two basic methods:
1. Direct method – a carefully weighed quantity of a primary standard is dissolved in a
suitable solvent and diluted to an exactly known volume in a volumetric flask. A made
solution is referred to as a primary standard solution (titrant).
2. Standardisation – concentration of a volumetric solution (titrant) is detrmined by using to
titrate
1) a weighed quantity of a primary standard,
2) a weighed quantity of a secondary standard,
3) a measured volume of another standard solution.
A titrant that is standardised against a secondary standard or against another standard
solution is referred to as a secondary standard solution (titrant).
Units of Concentration of Standard Solutions
The concentration of standard solutions (titrants) are generally expressed in units of
either molarity (CM, or M) or normality (CN, or N).
Molarity (M) – is the number of moles of a material per liter of solution.
Normality (N) – is the number of species equivalents per liter of solution.
Sometime is used also one unite of concentration – titer (T). Titer established the
relationship between volume of titrant and amount of analysed substance present. The most
commonly titer is in units of mg analysed substance per ml of titrant. This system was
developed to assist in doing routine calculations. It reduces the amount of time and training
for technicians.
Equivalents Law
Titrimetry is based on equivalents law:
Na·Va = Ns·Vs,
or number of analyte equivalent present = number of standard reagent added,
or one equivalent of one material will react exactly with one equivalent of another
The weight of one equivalent of a compound depends on reference to a chemical
reaction in which that compound is a participant. Similarly, the normality of a solution can
never be specified without knowledge about how the solution will be used. Equivalent value
is based on the type of reaction and the reactants:
1. One equivalent weight of a substance participating in a neutralisation reaction is that
amount of substance that either react with or supplied one mol of hydrogen ions in that
reaction.
2. One equivalent weight of a participant in an oxidation-reduction reaction is that amount
that directly or indirectly produces or consumer one mol of electrons.
65
3. The equivalent weight of a participant in a precipitation or a complex-formation reaction
is that weight which or provides one mole of the univalent reacting cation.
Calculations in Titrimetric Method of Analysis
T=
mx(is) =
N ⋅ meq
1000
Nt ⋅ Vt ⋅ meqx
px
N=
mx(al) =
m
meq ⋅ V
Nt ⋅ Vt ⋅ meqx ⋅ W
Vs ⋅ px
T – titer (g/ml);
Nt – nomality of used titrant (N);
m – mass of substance (g);
mx(al) – amount of analyte, determined as
aliquot of sample (g);
meqx – mass of one equivalent of analyte
(g);
Vs – aliquot of sample solution (ml);
ax – percentage of substance in sample (%)
m=
ax =
N ⋅ V ⋅ meq
1000
m
⋅100%
px
N – normality (number of equivalents/l);
Vt – volume of used titrant (ml);
meq – mass of one equivalent (g);
mx(is) – amount of analyte, determined as
individual sample (g);
W – dilution of analyte sample (ml);
px – mass of sample (g);
Indicators of Titrimetry Methods
Indicators are the chemical compounds, which give some external effect attached to
concentrations of reactive species according to equivalence point. This external effect can
be accompanied by change, appearance or disappearance of colouring, and formation of
slightly soluble compounds (precipitate formation).
On appliance technique indicators are external and internal.
Internal indicators are introduced into titrated solution. An end point install on
changes of colour of analysed mixture.
The external indicators are used when internal indicators using is impossible.
Reaction with external indicators run out of analysed mixture. Some drops of analysed
solution put on peace of filter paper, impregnated with indicator, or mix with drop of
indicator solution on porcelain plate.
For effect the reactions appearance indicators are reversible and unreversible.
Reversible indicators – changes the colour can be repeated many times as changes
the system state.
Unreversible indicators – colour changes ones with destruction of indicator molecule.
The unreversible indicators are less comfortable and thinly use.
66
ACID-BASIC TITRATION
This is a quick and accurate method for determining acidic or basic substances in
many samples. This method enable to determine some inorganic and hundred of organic
acids and bases of different types; frequently organic compounds are titrated in waterless
environment. The used titrant is typically a strong acid or base. The sample species can be
either a strong or weak acid or base. The neutralisation method based on acid-basic
reactions (exchange reactions by protons), which one can be expressed by general scheme:
HA + BOH = B+ + A– + H2O
Titrations according to the applied titrant are
1) acidimetric (titrants are the acids solutions) – uses for determination of strong and weak
bases, salts of strong bases and weak acids and organic compounds;
2) alkalimetric (titrants are solutions of bases) – uses for titration of strong and weak acids,
sour salts, salts of strong acids and weak bases, organic compounds having acidic
disposition (acids, phenols).
Standard Titrants
I. Bases.
NaOH is the most common although KOH can be serve the same purpose. There are not
primary standards.
Primary standards for bases standardisation are weak acids:
oxalic acid H2C2O4×2H2O, benzoic acid C6H5COOH, succinic acid HOOC(CH2)2COOH,
potassium hydrogen phthalate KHC8H4O4, potassium hydrogen iodate KH(IO3)2,
potassium hydrogen tartrate KHC4H4O6.
II. Acids.
More frequently are used HCl and H2SO4. There are not primary standards too. Primary
standards for acids standardisation are weak bases:
borax Na2B4O7×10H20, TRIS (hydroxymethyl-aminomethane) (HOCH2)2CNH2, sodium
carbonate Na2CO3, mercury oxide HgO, sodium oxalate Na2C2O4, potassium iodate
KIO3.
Titration Curves
Acid-base property of titration system changes accordingly to proportion (ratio) of
protolytes in mixture. Dependency on correlation of protolytes force the equivalence point
can be in neutral, alkaline or acidic environment. Change the pH value during titration
process, or dependence the pH value on concentration of titrated electrolytes, show the
titration curves. A titration curve is a graph of the pH as a function of the amount of titrant
(acid or base) added. This still results in four types of titration for simple acids or bases:
Strong acid vs. strong base
Strong acid vs. weak base
Strong base acid vs. strong acid
Strong base vs. weak base
67
Strong Acid-Strong Base Titrations
Here is an example of a titration curve, produced when a strong base is added to a
strong acid. This curve show how pH varies as 0,100 M NaOH is added to 50,0 ml of 0,100
M HCl.
The equivalence point of the titration is the point at which exactly enough titrant has
been added to react with all of the substance being titrated with no titrant left over. In other
words, at the equivalence point, the number of moles of titrant added so far corresponds
exactly to the number of moles of substance being titrated according to the reaction
stoichiometry. (In an acid-base titration, there is a 1:1 acid:base stoichiometry, so the
equivalence point is the point where the moles of titrant added equals the moles of
substance initially in the solution being titrated.)
Notice that the pH increases slowly at first, then rapidly as it nears the equivalence
point. At the equivalence point, the pH = 7.00 for strong acid-strong base titrations.
However, in other types of titrations, this is not the case.
Titrations Involving a Weak Acid
There are three major differences between this curve (in blue) and the one we saw before
(in black):
1. The weak-acid solution has a higher initial pH.
2. The pH rises more rapidly at the start, but less rapidly near the equivalence point.
3. The pH at the equivalence point does not equal 7.00. The equivalence point for a weak
acid-strong base titration has a pH > 7.00.
For a strong acid-weak base or weak acid-strong base titration, the pH will change
rapidly at the very beginning and then have a gradual slope until near the equivalence point.
The gradual slope results from a buffer solution being produced by the addition of the
strong acid or base, which resists rapid change in pH until the added acid or base exceeds
the buffer's capacity and the rapid pH change occurs near the equivalence point.
Titration curve of a weak acid being titrated by a strong base:
68
Here, 0,100 M NaOH is being added to 50,0 ml of 0,100 M acetic acid.
Titrations Involving a Weak Base
Titration curve of a weak base being titrated by a strong acid:
Here, 0,100 M HCl is being added to 50,0 ml of 0,100 M ammonia solution.
As in the weak acid-strong base titration, there are three major differences between
this curve (in blue) and a strong base-strong acid one (in black): (Note that the strong basestrong acid titration curve is identical to the strong acid-strong base titration, but flipped
vertically.)
The weak-acid solution has a lower initial pH.
1. The pH drops more rapidly at the start, but less rapidly near the equivalence point.
2. The pH at the equivalence point does not equal 7.00. The equivalence point for a weak
base-strong acid titration has a pH < 7.00.
69
Titrations of Polyprotic Acids
An example of a polyprotic acid is H2CO3 which neutralises in two steps:
H2CO3 + OH– ↔ H2O + HCO3–
HCO3– + OH– ↔ H2O + CO32–
The titration curve for these reactions will look like this, with two equivalence points.
Uses of Titrations
Use titration data or a titration curve to calculate reaction quantities such as the
concentration of the substance being titrated.
The most common use of titrations is for measuring unknown concentrations. This is
done by titrating a known volume of the unknown solution with a solution of known
concentration (where the two react in a predictable manner) and finding the volume of
titrant needed to reach the equivalence point using some method appropriate to the
particular reaction. Then, the volume and concentration of titrant can be used to calculate
the moles of titrant added, which, when used with the reaction stoichiometry, gives the
number of moles of substance being titrated. Finally, this quantity, along with the volume of
substance being titrated, gives the unknown concentration.
For acid-base titrations, the equivalence point can be found very easily. A pH meter
is simply placed in the solution being titrated and the pH is measured after various volumes
of titrant have been added to produce a titration curve. The equivalence point can then be
read off the curve.
In the same way, knowing the equivalence point can also be used to calculate other
unknown quantities of interest in acid base reactions, such as concentration of titrant or
volume of solution being titrated, provided that enough other information is known to
perform the calculations.
70
INDICATORS FOR ACID-BASIC TITRATION
Acid-base indicators are highly coloured weak acids or bases. Indicators that use in acidbase titration change its colouring dependency on pH value. Acid-basic indicators change
colour because protons join to or lost the indicator molecule. Protons exchange causes
exchange or appearance new chromophores into indicator molecule. The both forms of
indicator are coloured differently:
HIn (color 1) ↔ In (color 2)
If indicator (HIn) is a weak acid, in water solution becomes equilibrium:
HIn + H2O ↔ In– + H+.
If indicator (HIn) is a weak base, in water solution becomes equilibrium:
HIn + H2O ↔ HIn+ + OH–,
or in general form:
Ina + H2O ↔ Inb + H+.
An equilibrium constant of this process is
[Inb] ⋅ [H + ]
KIn =
.
[Ina ]
Ina – acid form of indicator;
Inb – base form of indicator.
An equilibrium constant of this process (KIn) is called indicator constant.
Colour of solution depends on ratio
[Ina]
and is defined by the pH value. A human eye can
[Inb]
take notice of appearance of new colour on background basic, if concentration correlation of
differently tinted forms is not less 1:10. Is considered, that colour change is visible, when
71
concentration of one form exceeds another more then ten times, or when ratio
[Ina] [ H + ]
=
[Inb]
K In
equal 0,1 or 10,0.
Colour change is visible in range pH = pKIn ± 1, which called indicator transition interval.
The pH value of end point called titration index, pT.
Indicators for pH displaying, which are used in neutralisation titrimetry, can be:
1) with one coloured form. One of the forms may be colourless – phenolphthalein
(colourless to magenta);
2) with two coloured form. They have more than one colour transition – methyl red –
yellow to orange to red;
3) mixed – indicators mixture and to dyestuff (for example, methyl orange and
cyanviolet). Dyestuffs have a lesser colouring transition interval;
4) universal – mixtures of indicators which continuously change colour in wide interval
of pH – from 1 to 14. Used for approximate definition pH of solutions.
On indicators equilibrium in solution influences a row of factors:
1. Amount of indicator in solution. Concentration increasing causes decreasing of contrast
of visible colour exchange.
2. Temperature. It connected with shift of water ion product.
3. Presence of colloid particles in solution – molecules of indicator can be adsorbed.
4. Presence dissolved in water CO2 (from air).
5. Presence of strong neutral electrolytes – salting effect.
6. Nature of solvent – ethylenglycol, methanol change activity of H+ ions in mixtures with
water.
Luminescent indicators change colour and fluorescence intensity in accordance to pH
value. Use for titration of turbid and tinted solutions.
Indicators of turbid use for titration of weak acids. It forms reversible colloid system,
which coagulates at specific pH value.
Amphy-indicators use for determination organic acids and bases at presence of
unmixible with water organic solvents.
To chemical structure indicators of neutralisation method divides on:
1. Phthalein indicators; for example, phenolphthalein.
2. Sulfophthalein indicators; for example, phenol red.
3. Azo indicators; for example, methyl orange, methyl red.
4. Nitro indicators; for example p-nitrophenol.
Concepts of Indicators of Neutralisation Method
In all cases of indicators colour exchange passes a structural transformations in their
molecules. Exists a few indicators theories.
Ionic theory of indicators, that takes beginning from 1894 year and offered by W.
1.
Ostwald. Accordance to ionic theory the indicators are tinted organic compounds with
72
basic, acidic, or amphoteric properties, which can exist in solution in molecular and ionic
forms having a different colour.
The important quantitative description of this process is dissociation constant (KIn) of
indicator. Attached to gradual change of рН the indicator transition from molecular form
into ionic form and colour exchange passes gradually. In strongly-acid environment
practically all of acid-basic indicators are found in molecular form, into strongly-alkaline –
in ionic form.
2.
Chromophoric theory of indicators. An ionic theory supplements the
chromophoric theory, in according which a colouring change is related with indicators
molecules structure change, that touched off by Н+ and OH– ions influence. This is
associated with benzoic-quinolinic tautomery.
A colour of organic compounds accordance to chromophoric theory is conditioned
by chromophores presence: –N=N–, –NO2, –NO, –С=С–, –С=О. Attached to introduction
auxochromes into molecule: –OH, –NH2, –NHR, –NR2, goes over reinforcing of colours.
Colouring change of indicator takes place in that case, when appear chromophores group,
or one chromophores transform into another.
3.
Ionic-chromophoric theory of indicators. In solution of indicator takes place an
equilibrium, conditioned by molecules dissociation, and equilibrium, conditioned by
intermolecular regrouping.
Resonance theory: on which electrons steam of one autochromic group co-operates
4.
with other steam, and this causes to colouring change.
5.
Also exist the still different theories: ionic-co-ordinating and ionic-quinolinic.
Titration Errors Associated with Choice of Indicator
Demands to indicators choice:
1) is necessary to have a sharp colour distinction of indicator in acidic and alkaline
environment;
2) colour transition interval of indicator must lie near equilibrium point;
3) an indicator must be sensible uses 1-2 drops. If to add richly up indicator, the titrant
expends on titration of indicator itself;
4) always necessary titrate to appearance of one hue of solution, making the same
volumes of titrated solution;
5) get such indicator, that рТ is coincided with titration interval.
As a rule, the end point do not coincided with equivalence point. Because of analysed
solution is over or short titrated. Or, another words, the analysed solution have any surplus
of acid or base.
If pT value is less then pH in equivalence point, titration error is caused H+ ions surplus and
called hydrogen error.
If pT value is more then pH in equivalence point, titration error is caused OH– ions surplus
and arise hydroxyl error.
An example of these errors arising:
73
10− pT ⋅ V2
[H ] error =
⋅ 100%
N ⋅ V1
+
10 − (14− pT) ⋅ V2
[OH ] error =
⋅ 100%
N ⋅ V1
–
N – normality of titrant;
V1 – volume of used titrant, ml;
V2 – volume of sample after titration, ml.
When is titrated weak acids or weak bases, in solution present unionised electrolytes. In
these cases arise acidic error or alkaline error.
An example of these errors arising:
acidic error = 10 pKa − pT
pKa = –logKa
alkaline error = 10 pKb+ pT −14
pKb = –logKb
pKa and pKb – dissociation constant of weak acid and weak base respectively.
74
REDOX TITRATIONS
Redox titration – A titration in which the reaction between the analyte and titrant is
an oxidation/reduction reaction. Oxidation-reduction titration is a volumetric analysis that
relies on a net change in the oxidation number of one or more species. The titrant is a
commonly an oxidising agent although reducing titrants can be used.
Redox titrations were introduced shortly after the development of acid–base
titrimetry. The earliest methods took advantage of the oxidizing power of chlorine. In 1787,
Claude Berthollet introduced a method for the quantitative analysis of chlorine water (a
mixture of Cl2, HCl, and HOCl) based on its ability to oxidize solutions of the dye indigo
(indigo is colorless in its oxidized state). In 1814, Joseph Louis Gay-Lussac (1778–1850),
developed a similar method for chlorine in bleaching powder. In both methods the end point
was signaled visually. Before the equivalence point, the solution remains clear due to the
oxidation of indigo. After the equivalence point, however, unreacted indigo imparts a
permanent color to the solution.
The number of redox titrimetric methods increased in the mid-1800s with the
introduction of MnO4–, Cr2O72– and I2 as oxidizing titrants, and Fe2+ and S2O32– as reducing
titrants. Even with the availability of these new titrants, however, the routine application of
redox titrimetry to a wide range of samples was limited by the lack of suitable indicators.
Titrants whose oxidized and reduced forms differ significantly in color could be used as
their own indicator. For example, the intensely purple MnO4– ion serves as its own indicator
since its reduced form, Mn2+, is almost colorless. The utility of other titrants, however,
required a visual indicator that could be added to the solution. The first such indicator was
diphenylamine, which was introduced in the 1920s. Other redox indicators soon followed,
increasing the applicability of redox titrimetry.
The equivalent weight of a participant in an oxidation reaction is that amount that directly or
indirectly produces or consumes 1 mole of electrons.
The Nernst expression for electrode potential of redox reaction (aA + bB ↔ cC + dD)
participants is
E = E0 +
RT [A]a ⋅ [B]b
0,0592 [A]a ⋅ [B]b
0
ln
=
E
−
lg
nF [C]c ⋅ [D]d
n
[C]c ⋅ [D]d
n - total number of electrons gained in the reaction
This expression is valid for simple redox expressions.
n A ⋅ E 0A + n B ⋅ E 0B
At equilibrium the redox potential of system is Eeq =
.
nA + n B
n(E 0B − E 0A )
The equilibrium constant is determined from lgKeq =
.
0,0592
As another titration methods, we can get either to the following types of curves, based on
the type of reaction:
75
The vertical axis on oxidation/reduction titration curves is generally an electrode potential
instead logarithmic p-functions that were used for all titration methods curves (precipitation,
complex-formation, neutralisation). There is a logarithmic relationship between electrode
potential and concentration of the analyte or titrant.
For equivalence point determination in redox methods can be used coloured titrants itself.
Such titrants appear, disappears, or change specific colour.
Also two types of chemical indicators are used to detect equivalence point (end point) for
oxidation/reduction titration:
1. General redox indicators are substances that change colour upon being oxidised or
reduced. The colour changes of the redox indicators are largely independent of the
chemical nature of the analyte and titrant and depend instead upon the changes in the
electrode potential of the system that occur at the titration processes.
Typically, a change from the colour of the oxidised form of the indicator (colour 1) to the
colour of the reduced form (colour 2) requires a change of about 100 in the ratio of reactants
concentrations:
(colour 1) InOx + ne ↔ InRed (colour 2)
[In Red ] 1
0,0592 1
0,0592
=
⇒ E Red = E 0 −
lg = E 0 +
[In Ox ] 10
n
10
n
[In ox ] 10
0,0592 10
0,0592
=
⇒ E Ox = E 0 −
lg = E 0 −
[In Red ] 1
n
1
n
Therefore, the redox indicators transition interval (pT) is
pT = E 0 ±
0,0592
n
Protons involved in the reduction of the many indicators, so the range of potential over
which a colour change occurs (the transition potential) is often pH dependent.
Classes of Redox Indicators:
1) Metal [more frequently – iron(II)] complexes of o-phenanthrolines;
76
2) Diphenylamine and its derivatives.
2. Specific indicators are used only in one specific redox titration method. These indicators
react with a specific chemical species involved in the titration;
1) Starch – forms a dark blue complex with iodine.
2) Potassium thiocyanate – forms a red complex with iron(III) ion.
Redox reactions have some peculiarities, which impede its titrimetry using:
1) reactions reversibility and
2) different rates of various resctions.
There are some techniques of redox reaction rate rising:
1. Temperature increasing.
2. The pH value and reactants concentration change.
3. Catalyst addition.
4. Inducted reactions running.
The redox titration divides on titration with reducing agents – for oxidisers determination,
and titration with oxidisers – for reducing agents determination. Common standard titrants
are named below:
Standard titrants
E0 , V
+ 1,51
Standardised with
Oxidants
Na2C2O4, Fe, As2O3
+ 1,45
is primary standard
+ 1,44
Na2C2O4, Fe, As2O3
+ 1,33
is primary standard
Sodium nitrite, NaNO2
+ 1,20
sulphanilic acid, KMnO4
Ammonium vanadate,
(NH4)VO3
+ 1,02
K2Cr2O7, Mohr salt
Iron(II) solutions,
Fe(NH4)2(SO4)2
Iodine, I2
Sodium thiosulphate,
Na2S2O3
Titanium sulphate,
Ti2(SO4)3
+ 0,77
Reductants
is primary standard
Potassium
permanganate, KMnO4
Potassium bromate,
KBrO3
Cerium(IV) sulphate,
Ce(SO4)2
Potassium dichromate,
K2Cr2O7
+ 0,54
+ 0,08
+ 0,04
Na2S2O3, BaS2O3
K2Cr2O7, KIO3, KBrO3,
K3[Fe(CN)6]
K2Cr2O7, KMnO4,
Fe2(SO4)3
Indicator
pink colour disappearance
methyl orange, methyl red,
starch
ferroin
diphenylamine, starch,
yellow colour
disappearance
starch (internal indicator),
tropeoline 00
diphenylamine,
phenylanthranilic acid
KSCN
starch
starch
diphenylamine, violet
colour disappearance
77
PRECIPITATION TITRIMETRY
Precipitation titrimetry is based upon reactions that yield ionic compounds of limited
solubility. The slow rate of precipitate formation limits the number of precipitating agents
that can be used in titrimetry to a handful.
A reaction in which the analyte and titrant form an insoluble precipitate also can form
the basis for a titration. We call this type of titration a precipitation titration.
One of the earliest precipitation titrations, developed at the end of the eighteenth
century, was for the analysis of K2CO3 and K2SO4 in potash. Calcium nitrate, Ca(NO3)2,
was used as a titrant, forming a precipitate of CaCO3 and CaSO4. The end point was
signalled by noting when the addition of titrant ceased to generate additional precipitate.
The importance of precipitation titrimetry as an analytical method reached its zenith in the
nineteenth century when several methods were developed for determining Ag+ and halide
ions.
Titration Curves
Titration curves for a single anion are derived in a way completely analogous to
another titration methods. The only difference is that the solubility product of the precipitate
is substituted to for the ion-product constant for water.
The change in p-function value at the equivalence point becomes grater as the
solubility products become smaller – that is, as the reaction between the analyte and
precipitant becomes more complete. Ions forming precipitates with solubility products much
larger than about 10-10 do not yield satisfactory end point.
The titration curve for a precipitation titration follows the change in either the
analyte’s or titrant’s concentration as a function of the volume of titrant. For example, in an
analysis for I– using Ag+ as a titrant
Ag+ + I– → AgI↓
the titration curve may be a plot of pAg or pI as a function of the titrant’s volume.
As we have done with previous titrations, we first show how to calculate the titration curve
and then demonstrate how to quickly sketch the titration curve.
Calculating the Titration Curve. As an example, let’s calculate the titration curve
for the titration of 50.0 mL of 0.0500 M Cl– with 0.100 M Ag+. The reaction in this case is
Ag+ + Cl– → AgCl↓
The equilibrium constant for the reaction is
K = (Ksp)–1 = (1.8 ×10–10)–1 = 5.6 ×109
Since the equilibrium constant is large, we may assume that Ag+ and Cl– react completely.
By now you are familiar with our approach to calculating titration curves. The first
task is to calculate the volume of Ag+ needed to reach the equivalence point. The
stoichiometry of the reaction requires that
78
Moles Ag+ = Moles Cl–
or
MAgVAg = MClVCl
Solving for the volume of Ag+
shows that we need 25.0 mL of Ag+ to reach the equivalence point.
Before the equivalence point Cl– is in excess. The concentration of unreacted Cl–
after adding 10.0 mL of Ag+, for example, is
If the titration curve follows the change in concentration for Cl–, then we calculate pCl as
pCl = –log[Cl–] = –log(2.50 ×10–2) = 1.60
However, if we wish to follow the change in concentration for Ag+ then we must first
calculate its concentration. To do so we use the Ksp expression for AgCl
Ksp = [Ag+][Cl–] = 1.8 ×10–10
Solving for the concentration of Ag+
gives a pAg of 8.14.
At the equivalence point, we know that the concentrations of Ag+ and Cl– are equal.
Using the solubility product expression
Ksp = [Ag+][Cl–] = [Ag+]2 = 1.8 ×10–10
gives
[Ag+] = [Cl–] = 1.3 ×10–5 M.
At the equivalence point, therefore, pAg and pCl are both 4.89.
79
After the equivalence point, the titration mixture contains excess Ag+. The
concentration of Ag+ after adding 35.0 mL of titrant is
or a pAg of 1.93. The concentration of Cl– is
or a pCl of 7.82.
Additional results for the titration curve are shown in Table and Figure.
Data for Titration of 50.0 mL of 0.0500 M Cl– with 0.100 M Ag
Volume AgNO3(mL)
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
50.00
pCl
1.30
1.44
1.60
1.81
2.15
4.89
7.54
7.82
7.97
8.07
8.14
pAg
—
8.31
8.14
7.93
7.60
4.89
2.20
1.93
1.78
1.68
1.60
Precipitation titration curve for
50.0 mL of 0.0500 M Cl– with
0.100 M Ag+. (a) pCl versus
volume of titrant; (b) pAg versus
volume of titrant.
Precipitation titration methods are classified accordance to applied titrants:
1. Argentometry – AgNO3, KSCN.
80
2. Mercurometry – Hg2(NO3)2.
3. Seldom using methods for specific purposes.
Selecting and Evaluating the End Point
Initial attempts at developing precipitation titration methods were limited by a poor
end point signal. Finding the end point by looking for the first addition of titrant that does
not yield additional precipitate is cumbersome at best. Two types of end points are
encountered in titration with precipitants:
1) chemical,
2) instrumental: potentiometric and amperometric.
Chemical indicators for precipitation titration
The end point produced by a chemical indicator usually consists of a colour change or,
occasionally, the appearance or disappearance of turbidity in the solution being titrated. The
requirements for an indicator for a precipitation titration are analogous to those for an
indicator for a neutralisation titration:
1) the colour change should occur over the reagent limited range in p-function of the
reagent or the analyte and
2) the colour change should take place within the steep portion of the titration curve for
the analyte.
Argentometry
Argentometry used for halide-like anions (Hal–, CN–, SCN–) determination, which
forms slightly soluble compounds with Ag+ ion. Standard titration solution is AgNO3. For
back-titration uses standard solution of NaCl, that titrated AgNO3 surplus. The silver nitrate
solution can be standardised against primary-standard-grade sodium chloride.
Four indicators have found extensive use for argentometric titration:
1. Chromate ion. The Mohr method.
The first important visual indicator to be developed was the Mohr method for Cl–
using Ag+ as a titrant. By adding a small amount of K2CrO4 to the solution containing the
analyte, the formation of a precipitate of reddish-brown Ag2CrO4 signals the end point.
Because K2CrO4 imparts a yellow colour to the solution, obscuring the end point, the
amount of CrO42– added is small enough that the end point is always later than the
equivalence point. To compensate for this positive determinate error an analyte-free reagent
blank is analyzed to determine the volume of titrant needed to effect a change in the
indicator’s colour. The volume for the reagent blank is subsequently subtracted from the
experimental end point to give the true end point. Because CrO42– is a weak base, the
solution usually is maintained at a slightly alkaline pH. If the pH is too acidic, chromate is
present as HCrO4–, and the Ag2CrO4 end point will be in significant error. The pH also must
be kept below a level of 10 to avoid precipitating silver hydroxide.
81
Sodium chromate serves as indicator for the argentometric detrmination of chloride,
bromide, and cyanide ions by reacting with silver cation to form a brick-red silver chromate
(Ag2CrO4) precipitate in the equivalence point region:
AgNO3 + NaCl = AgCl↓ + NaNO3
white
AgNO3 + Na2CrO4 = Ag2CrO4↓ + NaNO3
red
The Mohr titration must be carried out at a pH between 7 and 10, because chromate
ion is the conjugate base of the weak chromic acid. In more acidic solutions the chromate
ion concentration is too low to produce the precipitate at the equivalence point. A suitable
pH is achieved with sodium hydrogen carbonate.
The Mohr titration can not be used for iodide and thiocyanate determination, because
these ions form colloid solutions with silver ion.
2. Iron(III) ion. The Volhard method.
A second end point is the Volhard method in which Ag+ is titrated with SCN– in the
presence of Fe3+. Silver ions are titrated with a standard solution of potassium or ammonium
thiocyanate:
AgNO3 + NaCl = AgCl↓ + NaNO3
white
AgNO3 + KSCN = AgSCN↓ + KNO3
white
Iron(III) ion serve as the indicator. The end point for the titration reaction
Ag+ + SCN– → AgSCN↓
is the formation of the reddish coloured Fe(SCN)3 complex:
SCN– + Fe3+ → Fe(SCN)3
The solution turns red with the first slight excess of thiocyanate ion:
2NH4Fe(SO4)2 + 6KSCN = 2Fe(SCN)3 + 3K2SO4 + (NH4)2SO4
red
The titration must be carried out in distinct acidic solution
1) to prevent precipitation of iron(III) as the hydrated oxide,
2) and such ions as carbonate, oxalate, and arsenate not interfere with silver ion.
The most important application of the Volhard method is for the indirect
determination of halide ions. Sometime the indirect Volhard method called thiocyanometry.
A measurement excess of standard silver nitrate solution is added to the sample, and the
excess silver ion is determined by back-titration with a standard thiocyanate solution. At
chloride determination occurs titration error, because silver chloride is more soluble than
silver thiocyanate.
82
3. Adsorption indicators. The Fajans method.
A third end point is evaluated with Fajans’ method, which uses an adsorption
indicator whose colour when adsorbed to the precipitate is different from that when it is in
solution. The adsorption indicator is an organic compound that tends to be adsorbed onto
the surface of the solid in a precipitation titration. The adsorption occurs near the
equivalence point and colour transfers from the solution to the solid.
For example, when titrating Cl– with Ag+ the anionic dye dichlorofluoroscein is used
as the indicator. Before the end point, the precipitate of AgCl has a negative surface charge
due to the adsorption of excess Cl–. The anionic indicator is repelled by the precipitate and
remains in solution where it has a greenish yellow colour. After the end point, the
precipitate has a positive surface charge due to the adsorption of excess Ag+. The anionic
indicator now adsorbs to the precipitate’s surface where its colour is pink. This change in
colour signals the end point.
COOH
COOH
Br
Br
O
O
Br
OH
O
O
OH
Br
Tetrabromofluorescein (eosine)
Fluoresceine
Fluorescein is a typical adsorption indicator that is useful for the titration of chloride
ion with silver nitrate. In aqueous solution, fluorescein partially dissociates into hydronium
ions and negatively charged fluoresceinate ions that are yellow-green. The fluoresceinate
ion forms an intensively red silver salt at equivalence point. For bromide, iodide, and
thiocyanate titration as an indicator is used tetrabromfluorescein, named eosin.
Titration involving adsorption indicators are rapid, accurate, and reliable, but their
application is limited to the relatively few precipitation reactions in which a colloidal
precipitate is formed rapidly.
4. Iodide ion. The Liebig-Deniges method.
Can be used for cyanide determination:
AgNO3 + KCN = AgCN + KNO3
At the equivalence point forms non soluble complex compound, which occurs turbidity
appearance:
Ag NO3 + AgCN = Ag[Ag(CN)2]↓
white
Or can be applied potassium iodide at ammonium solution:
AgNO3 + NH4OH = [Ag(NH3)2]OH
83
[Ag(NH3)2]OH + KI + H2O = AgI↓ + KOH + 2NH4OH
yellow
There are also so called the Gay-Lussac argentometric titration method without indicators.
At equivalence point the titrated halide solution clears up because occurs coagulation of
precipitate.
Mercurometry
For mercurometric titration is using mercury(I) salts for halide ion determination.
Hg2(NO3)2 + 2NaCl = Hg2Cl2↓+ 2NaNO3
white
Indicator is iron(III) thiocyanate, which disappearance at equivalence point:
3Hg2(NO3)2 + 2Fe(SCN)3 = 3Hg2(SCN)2↓+ 2Fe(NO3)3
red solution
white
Also as an indicator can be used diphenylcarbazon, which is an adsorption indicator and at
equivalence point change colour of precipitate from white to blue.
NH
O=C
N= N
NH
C6H5
C6H5
Superiority of mercurometry:
1. Not required expensive silver salts.
2. Mercury(I) precipitates are less soluble than analogous silver salts. Therefore,
equivalence point is clearly marked.
3. Mercurometric determination are carried out with direct titration in acidic solution.
4. Chloride ion can be determined with reducers (S2–, SO32–) and oxidisers (MnO4–, Cr2O7–)
presence.
5. Titration can be carried out in turbid and coloured solutions.
Another Precipitation Titration Methods
1. Barium determination with sulphate:
BaCl2 + H2SO4 = BaSO4↓ + 2HCl
Indicator is sodium rhodizonate, which disappearance red colour of solution.
2. Lead determination with chromate:
84
Pb(NO3)2 + K2CrO4 = PbCrO4↓ + 2KNO3
Indicator is AgNO3 solution. At equivalence point forms red precipitate.
3. Zinc determination with K4[Fe(CN)6]:
3ZnCl2 + K4[Fe(CN)6] = Zn3K2[Fe(CN)6] ↓ + 2KCl
Indicator is UO2(NO3)2, which forms brown precipitate with K4[Fe(CN)6].
Finding the End Point Potentiometrically
Another method for locating the end point of a precipitation titration is to monitor the
change in concentration for the analyte or titrant using an ion-selective electrode. The end
point can then be found from a visual inspection of the titration curve.
Quantitative Applications
Precipitation titrimetry is rarely listed as a standard method of analysis, but may still
be useful as a secondary analytical method for verifying results obtained by other methods.
Most precipitation titrations involve Ag+ as either an analyte or titrant. Those titrations in
which Ag+ is the titrant are called argentometric titrations. Table provides a list of several
typical precipitation titrations.
Representative Examples of Precipitation Titrations
Analyte
AsO4
Br–
3–
Cl–
CO32–
C2O42–
CrO42–
I–
PO43–
S2–
SCN–
Titranta
AgNO3, KSCN
AgNO3
AgNO3, KSCN
AgNO3
AgNO3, KSCN
AgNO3, KSCN
AgNO3, KSCN
AgNO3, KSCN
AgNO3
AgNO3, KSCN
AgNO3, KSCN
AgNO3, KSCN
AgNO3, KSCN
End Pointb
Volhard
Mohr or Fajans
Volhard
Mohr or Fajans
Volhard*
Volhard*
Volhard*
Volhard*
Fajans
Volhard
Volhard*
Volhard*
Volhard
a)
When two reagents are listed, the analysis is by a back titration. The first reagent is added
in excess, and the second reagent is used to back titrate the excess.
b)
For Volhard methods identified by an asterisk (*) the precipitated silver salt must be
removed before carrying out the back titration.
85
Quantitative Calculations
The stoichiometry of a precipitation reaction is given by the conservation of charge
between the titrant and analyte thus
86
TITRATIONS BASED ON COMPLEXATION REACTIONS
The earliest titrimetric applications involving metal–ligand complexation were the
determinations of cyanide and chloride using, respectively, Ag+ and Hg2+ as titrants. Both
methods were developed by Justus Liebig (1803–1873) in the 1850s. The use of
monodentate ligand, such as Cl– and CN–, however, limited the utility of complexation
titrations to those metals that formed only a single stable complex, such as Ag(CN)2– and
HgCl2. Other potential metal–ligand complexes, such as CdI42–, were not analytically useful
because the stepwise formation of a series of metal–ligand complexes (CdI+, CdI2, CdI3–,
and CdI42–) resulted in a poorly defined end point.
The utility of complexation titrations improved following the introduction by
Schwarzenbach, in 1945, of aminocarboxylic acids as multidentate ligands capable of
forming stable 1:1 complexes with metal ions. The most widely used of these new ligands
was ethylenediaminetetraacetic acid, EDTA, which forms strong 1:1 complexes with many
metal ions. The first use of EDTA as a titrant occurred in 1946, when Schwarzenbach
introduced metallochromic dyes as visual indicators for signalling the end point of a
complexation titration.
Chemistry and Properties of EDTA
Ethylenediaminetetraacetic acid, or EDTA, is an aminocarboxylic acid. The structure
of EDTA is shown
HOOCH2C
N
N
HOOCH2C
CH2COOH
CH2COOH
EDTA, which is a Lewis acid, has six binding sites (the four carboxylate groups and the two
amino groups), providing six pairs of electrons. The resulting metal–ligand complex, in
which EDTA forms a cage-like structure around the metal ion, is very stable.
O
O
O
O
O
O
N
M
O
N
O
The actual number of coordination sites depends on the size of the metal ion; however, all
metal–EDTA complexes have a 1:1 stoichiometry.
Metal–EDTA Formation Constants. To illustrate the formation of a metal–EDTA
complex consider the reaction between Cd2+ and EDTA
CdCl2 + H4Y → CdH2Y + 2HCl
87
where H4Y is a shorthand notation for the chemical form of EDTA. The formation constant
for this reaction
Kf =
[CdY 2− ]
= 2,9 × 1016
2+
4−
[Cd ][Y ]
quite large, suggesting that the reaction’s equilibrium position lies far to the right.
EDTA Is a Weak Acid. Besides its properties as a ligand, EDTA is also a weak
acid. The fully protonated form of EDTA, H6Y2+, is a hexaprotic weak acid with successive
pKa values of
pKa1 = 0.0; pKa2 = 1.5; pKa3 = 2.0; pKa4 = 2.68; pKa5 = 6.11; pKa6 = 10.17.
The first four values are for the carboxyl protons, and the remaining two values are for the
ammonium protons. A ladder diagram for EDTA is shown
The species Y4– becomes the predominate form of EDTA at pH levels greater than 10.17. It
is only for pH levels greater than 12 that Y4– becomes the only significant form of EDTA.
Conditional Metal–Ligand Formation Constants. Recognizing EDTA’s acid–base
properties is important. The formation constant for CdY2– assumes that EDTA is present as
Y4–. If we restrict the pH to levels greater than 12, then equation provides an adequate
description of the formation of CdY2–. For pH levels less than 12, however, Kf overestimates
the stability of the CdY2– complex.
At any pH a mass balance requires that the total concentration of unbound EDTA
equal the combined concentrations of each of its forms.
CEDTA = [H6Y2+] + [H5Y+] + [H4Y] + [H3Y–] + [H2Y2–] + [HY3–] + [Y4–]
To correct the formation constant for EDTA’s acid–base properties, we must account for the
fraction, α Y , of EDTA present as Y4–.
4−
αY =
4−
[Y 4− ]
C EDTA
88
If we fix the pH using a buffer, then α Y
4−
is a constant. Combining α Y
K ′f = α Y 4 − × K f =
4−
with Kf gives
[CdY 2− ]
[Cd 2 + ]C EDTA
where Kf´ is a conditional formation constant* whose value depends on the pH. As shown
in Table 9.13 for CdY2–, the conditional formation constant becomes smaller, and the
complex becomes less stable at lower pH levels.
EDTA Must Compete with Other Ligands. To maintain a constant pH, we must
add a buffering agent. If one of the buffer’s components forms a metal–ligand complex with
Cd2+, then EDTA must compete with the ligand for Cd2+. For example, an ammonia buffer
(NH4Cl/NH3OH) includes the ligand NH3, which forms several stable Cd2+–NH3 complexes.
EDTA forms a stronger complex with Cd2+ and will displace NH3. The presence of NH3,
however, decreases the stability of the Cd2+–EDTA complex.
We can account for the effect of an auxiliary complexing agent**, such as NH3, in
the same way we accounted for the effect of pH. Before adding EDTA, a mass balance on
Cd2+ requires that the total concentration of Cd2+, CCd, be
CCd = [Cd2+] + [Cd(NH3)2+] + [Cd(NH3)22+] + [Cd(NH3)32+] + [Cd(NH3)42+]
* Conditional formation constant is the equilibrium formation constant for a metal–ligand
complex for a specific setof solution conditions, such as pH.
** Auxiliary complexing agent is a second ligand in a complexation titration that initially
binds with the analyte but is displaced by the titrant.
Complexometric EDTA Titration Curves
The complexometric EDTA titration curve shows the change in pM, where M is the
metal ion, as a function of the volume of EDTA.
Calculating the Titration Curve. As an example, let’s calculate the titration curve
for 50.0 mL of 5.00 ×10–3 M Cd2+ with 0.0100 M EDTA at a pH of 10 and in the presence
of 0.0100 M NH3. The formation constant for Cd2+–EDTA is 2.9 ×1016.
Since the titration is carried out at a pH of 10, some of the EDTA is present in forms
other than Y4–. In addition, the presence of NH3 means that the EDTA must compete for the
Cd2+. To evaluate the titration curve, therefore, we must use the appropriate conditional
formation constant
Kf ˝ = α Y
4−
× α Cd × Kf = (0.35)(0.0881)(2.9 × 1016) = 8.9 × 1014
2+
Because Kf˝ is so large, we treat the titration reaction as though it proceeds to completion.
The first task in calculating the titration curve is to determine the volume of EDTA
needed to reach the equivalence point. At the equivalence point we know that
Moles EDTA = Moles Cd2+
or
89
MEDTAVEDTA = MCdVCd
Solving for the volume of EDTA
shows us that 25.0 mL of EDTA is needed to reach the equivalence point.
Before the equivalence point, Cd2+ is in excess, and pCd is determined by the
concentration of free Cd2+ remaining in solution. Not all the untitrated Cd2+ is free (some is
complexed with NH3), so we will have to account for the presence of NH3. For example,
after adding 5.0 mL of EDTA, the total concentration of Cd2+ is
To calculate the concentration of free Cd2+ we use equation
[Cd2+] = α Cd ×CCd = (0.0881)(3.64 ×10–3 M) = 3.21 ×10–4 M
2+
Thus, pCd is
pCd = –log[Cd2+] = –log(3.21 ×10–4) = 3.49
At the equivalence point, all the Cd2+ initially present is now present as CdY2–. The
concentration of Cd2+, therefore, is determined by the dissociation of the CdY2– complex. To
find pCd we must first calculate the concentration of the complex.
Letting the variable x represent the concentration of Cd2+ due to the dissociation of the
CdY2– complex, we have
Once again, to find the [Cd2+] we must account for the presence of NH3; thus
[Cd2+] = αCd2+ ×CCd = (0.0881)(1.93 ×10–9 M) = 1.70 ×10–10 M
giving pCd as 9.77.
After the equivalence point, EDTA is in excess, and the concentration of Cd2+ is
determined by the dissociation of the CdY2– complex. Examining the equation for the
90
complex’s conditional formation constant, we see that to calculate CCd we must first
calculate [CdY2–] and CEDTA. After adding 30.0 mL of EDTA, these concentrations are
Substituting these concentrations into equation and solving for CCd gives
Thus,
[Cd2+] = α Cd ×CCd = (0.0881)(5.60 ×10–15 M) = 4.93 ×10–16 M
2+
and pCd is 15.31. Figure and Table show additional results for this titration.
Complexometric titration curve for 50.0
mL of 5.00 ×10–3 M Cd2+ with 0.0100 M
EDTA at a pH of 10.0 in the presence of
0.0100 M NH3
.
Data for Titration of 5.00 × 10–3 M Cd2+
with 0.0100 M EDTA
at a pH of 10.0 and in the Presence of
0.0100 M NH3
Volume of EDTA
(mL) pCd
0.00
3.36
5.00
3.49
10.00
3.66
15.00
3.87
20.00
4.20
23.00
4.62
25.00
9.77
27.00
14.91
30.00
15.31
35.00
15.61
40.00
15.78
45.00
15.91
50.00
16.01
91
Selecting and Evaluating the End Point
The equivalence point of a complexation titration occurs when stoichiometrically
equivalent amounts of analyte and titrant have reacted. For titrations involving metal ions
and EDTA, the equivalence point occurs when CM and CEDTA are equal and may be located
visually by looking for the titration curve’s inflection point.
As with acid–base titrations, the equivalence point of a complexation titration
estimated by an experimental end point. A variety of methods have been used to find the
end point, including visual indicators and sensors that respond to a change in the solution
conditions. Typical examples of sensors include
1) recording a potentiometric titration curve using an ion-selective electrode
(analogous to measuring pH with a pH electrode),
2) monitoring the temperature of the titration mixture,
3) and monitoring the absorbance of electromagnetic radiation by the titration
mixture.
Finding the End Point with a Visual Indicator. Most indicators for complexation
titrations are organic dyes that form stable complexes with metal ions. These dyes are
known as metallochromic indicators. To function as an indicator for an EDTA titration,
the metal–indicator complex must possess a colour different from that of the uncomplexed
indicator. Furthermore, the formation constant for the metal–indicator complex must be less
favourable than that for the metal–EDTA complex. The complex are often intensely
coloured and are discernible to the eye at concentrations in the range at 10–6 to 10–7 M.
The indicator, Inm–, is added to the solution of analyte, forming a coloured metal–
indicator complex, MInn-m. As EDTA is added, it reacts first with the free analyte, and then
displaces the analyte from the metal–indicator complex, affecting a change in the solution’s
colour. The accuracy of the end point depends on the strength of the metal–indicator
complex relative to that of the metal–EDTA complex. If the metal–indicator complex is too
strong, the colour change occurs after the equivalence point. If the metal–indicator complex
is too weak, however, the end point is signalled before reaching the equivalence point.
Eriochrome Black T is a typical metal-ion indicator that is used in the titration of
several common cations. Eriochrome Black T forms red complexes with more than two
twenty metal ions, but the formation constant of only a few are appropriate for end-point
detection. Except, Eriochrome Black T behaves as an acid-base indicator as well as metal
ion indicator:
The metal complexes of Eriochrome Black T are generally red. Until the equivalence
point in a titration, the indicator complexes the excess metal ion, so the solution is red.
When EDTA becomes present in slight excess, the solution turns blue as a consequence of
the reaction:
MIn– + HY3– ↔ HIn2– + MY2–
red
(Yn– – EDTA ions)
blue
92
A limitation of Eriochrome Black T is that its solutions decompose slowly with standing.
Most metallochromic indicators also are weak acids or bases. The conditional
formation constant for the metal–indicator complex, therefore, depends on the solution’s
pH. This provides some control over the indicator’s titration error. The apparent strength of
a metal–indicator complex can be adjusted by controlling the pH at which the titration is
carried out. Unfortunately, because they also are acid–base indicators, the colour of the
uncomplexed indicator changes with pH. For example, calmagite, which we may represent
as H3In, undergoes a change in colour from the red of H2In– to the blue of HIn2– at a pH of
approximately 8.1, and from the blue of HIn2– to the red-orange of In3– at a pH of
approximately 12.4. Since the colour of calmagite’s metal–indicator complexes are red, it is
only useful as a metallochromic indicator in the pH range of 9–11, at which almost all the
indicator is present as HIn2–.
A partial list of metallochromic indicators, and the metal ions and pH conditions for
which they are useful, is given in Table. Even when a suitable indicator does not exist, it is
often possible to conduct an EDTA titration by introducing a small amount of a secondary
metal–EDTA complex, provided that the secondary metal ion forms a stronger complex
with the indicator and a weaker complex with EDTA than the analyte. For example,
calmagite can be used in the determination of Ca2+ if a small amount of Mg2+–EDTA is
added to the solution containing the analyte. The Mg2+ is displaced from the EDTA by Ca2+,
freeing the Mg2+ to form the red Mg2+–indicator complex. After all the Ca2+ has been
titrated, Mg2+ is displaced from the Mg2+–indicator complex by EDTA, signaling the end
point by the presence of the uncomplexed indicator’s blue form.
Selected Metallochromic Indicators
Indicator
Calmagite
Eriochrome Black T
Eriochrome Blue Black R
Murexide
PAN
Salicylic acid
Useful pH Range
9–11
7.5–10.5
8–12
6–13
2–11
2–3
Useful for
Ba, Ca, Mg, Zn
Ba, Ca, Mg, Zn
Ca, Mg, Zn, Cu
Ca, Ni, Cu
Cd, Cu, Zn
Fe
Quantitative Applications
With a few exceptions, most quantitative applications of complexation titrimetry
have been replaced by other analytical methods.
Selection and Standardization of Titrants. EDTA is a versatile titrant that can be
used for the analysis of virtually all metal ions. Although EDTA is the most commonly
employed titrant for complexation titrations involving metal ions, it cannot be used for the
direct analysis of anions or neutral ligands. In the latter case, standard solutions of Ag+ or
Hg2+ are used as the titrant.
Solutions of EDTA are prepared from the soluble disodium salt, Na2H2Y × 2H2O.
Concentrations can be determined directly from the known mass of EDTA; however, for
more accurate work, standardization is accomplished by titrating against a solution made
from the primary standard CaCO3. Solutions of Ag+ and Hg2+ are prepared from AgNO3 and
93
Hg(NO3)2, both of which are secondary standards. Standardization is accomplished by
titrating against a solution prepared from primary standard grade NaCl.
Inorganic Analysis. Complexation titrimetry continues to be listed as a standard
method for the determination of hardness, Ca2+, CN–, and Cl– in water and wastewater
analysis. The determination of Ca2+ is complicated by the presence of Mg2+, which also
reacts with EDTA. To prevent an interference from Mg2+, the pH is adjusted to 12–13,
precipitating any Mg2+ as Mg(OH)2. Titrating with EDTA using murexide or Eriochrome
Blue Black R as a visual indicator gives the concentration of Ca2+.
Titration with inorganic complexing agents. Complexometric titrations with
inorganic reagents are among the oldest volumetric methods.
Cyanide is determined at concentrations greater than 1 ppm by making the sample
alkaline with NaOH and titrating with a standard solution of AgNO3, forming the soluble
Ag(CN)2– complex. The end point is determined using p-dimethylaminobenzalrhodamine as
a visual indicator, with the solution turning from yellow to a salmon colour in the presence
of excess Ag+.
Now sometime is used the titration of halide ions with mercury(II) ions, called
mercurimetry. Chloride is determined by titrating with Hg(NO3)2, forming soluble HgCl2:
Hg(NO3)3 + 2NaCl = HgCl2 + 2NaNO3
The sample is acidified to within the pH range of 2.3–3.8 where diphenylcarbazone,
O
N
N
N
H
H
N
which forms a coloured complex with excess Hg2+, serves as the visual indicator, or sodium
nitroprousside Na3[FeNO(CN)5]. Xylene cyanol FF is added as a pH indicator to ensure that
the pH is within the desired range. The initial solution is a greenish blue, and the titration is
carried out to a purple end point.
Quantitative Calculations. The stoichiometry of complexation reactions is given by
the conservation of electron pairs between the ligand, which is an electron-pair donor, and
the metal, which is an electron-pair acceptor; thus
This is simplified for titrations involving EDTA where the stoichiometry is always 1:1
regardless of how many electron pairs are involved in the formation of the metal–ligand
complex.
94
NONAQUEOUS TITRATIONS
Nonaqueous titration is the special technique of the acid-base titration. Acids with
dissociation constant value less than 1⋅10–7 (pKa > 7) and bases with dissociation constant
value more than 1⋅10–7 (pKb < 7) can not be titrated in water solutions. The ionisation
degree of such weak acid and weak bases is comparable with indicator ionisation degree.
During titration of aqueous solutions of these compounds can not be indicated equivalent
point.
For titration of weak acid and weak bases are used waterless (nonaqueous) solvents,
which intensify its acidic/basic properties. Indeed, water is the most common solvent in
acid–base titrimetry. When considering the utility of a titration, however, the solvent’s
influence cannot be ignored.
Autoprotolysis of Solvents
Many solvents autoprotolysise like as water:
2C2H5OH ↔ C2H5OH2+ + C2H5O–
2H2N–(CH2)2–NH2 ↔ R–NH3+ + R–NH–
2(CH3)2SO ↔ (CH3)2SOH+ + CH3–SO–CH2–
The dissociation, or autoprotolysis constant for a solvent, SH, relates the
concentration of the protonated solvent, SH2+, to that of the deprotonated solvent, S–. For
amphoteric solvents, which can act as both proton donors and proton acceptors, the
autoprotolysis reaction is
2SH ↔ SH2+ + S–
with an equilibrium constant of
KS = [SH2+][S–]
Remember, that water autoprolysis constant KS = KW = 1⋅10–14.
You should recognize that KW is just the specific form of KS for water. The pH of a solution
is now seen to be a general statement about the relative abundance of protonated solvent
pH = –log[SH2+]
where the pH of a neutral solvent is given as
pH neut =
1
pK S
2
Perhaps the most obvious limitation imposed by KS is the change in pH during a
titration. To see why this is so, let’s consider the titration of a 50 mL solution of 10–4 M
95
strong acid with equimolar strong base. Before the equivalence point, the pH is determined
by the untitrated strong acid, whereas after the equivalence point the concentration of excess
strong base determines the pH. In an aqueous solution the concentration of H+ when the
titration is 90% complete is
[H + ] =
M a Va − M b Vb
= 5.3×10–6 M
Va + Vb
corresponding to a pH of 5.3. When the titration is 110% complete, the concentration of
OH– is
[OH − ] =
M b Vb − M a Va
Va + Vb
or a pOH of 5.3. The pH, therefore, is
pH = pKW – pOH = 14.0 – 5.3 = 8.7
The change in pH when the titration passes from 90% to 110% completion is
∆pH = 8.7 – 5.3 = 3.4
If the same titration is carried out in a nonaqueous solvent with a KS of 1.0×10–20, the pH
when the titration is 90% complete is still 5.3. However, the pH when the titration is 110%
complete is now
pH = pKS – pOH = 20.0 – 5.3 = 14.7
In this case the change in pH of
∆pH = 14.7 – 5.3 = 9.4
is significantly greater than that obtained when the titration is carried out in water. Figure 1
shows the titration curves in both the aqueous and nonaqueous solvents. Nonaqueous
solvents also may be used to increase the change in pH when titrating weak acids or bases
(Figure 2).
Figure 1. Titration curves for 50.00 mL of
10–4 M HCl with 10–4 M NaOH in
(a) water, KW = l×10–14, and
(b) nonaqueous solvent, KS = 1×10–20.
96
Figure 2. Titration curves for 50.00 mL of
0.100 M weak acid (pKa = 11) with 0.100 M
NaOH in
(a) water, Kw = 1×10–14; and
(b) nonaqueous solvent, KS = 1×10–20.
The titration curve in (b) assumes that
the change in solvent has no effect on
the acid dissociation constant of the
weak acid.
If autoprolysis constant (KS) of solvent is low, we have great titration jump. Solvent with
KSH less than water (CH3COOH, C2H5OH) used for the charged acid titration – for example,
NH4+.
Classification of Solvents for Nonaqueous Titration
Accordance to donator-acceptor interaction (or acid-base properties) with protons and
accordance to chemical nature of participants all solvents are divided on protonic
(protolytic) and aprotonic (nonprotolytic). There are three groups of protolytic solvents:
1) acidic, or protogenic,
2) basic, or protophylic,
3) amphiprotic, or amphoteric.
Protogenic solvent (HF, H2SO4, HCOOH, CH3COOH) is acidic substance that can give
protons. Molecules of protogenic solvent can join protons only from strong acids. For
example, acetic acid as week acid joins protons from H2SO4 (or HCl, HClO4):
CH3COOH + H2SO4 ↔ CH3COOH2+ + HSO4–,
base
acid
but: (CH3)3N + CH3COOH ↔ (CH3)3NH+ + CH3COO–
base
acid
Protophylic solvent (NH3, N2H4, (CH3)2NH2, dioxane) is basic substances that have
attraction to protons. Tears off the protons from molecule can only very strong bases. There
are no strong bases, that can interrupt (divert) proton from ammonia molecule. For example,
acetamide interaction in liquid ammonium:
CH2CONH2 + NH3 ↔ NH4+ + CH3CONH–
weak base
strong base
H2N–(CH2)2–NH2 +NH2– ↔ H2N–(CH2)2–NH– + NH3
Amphiprotic solvent (H2O, CH3OH, C2H5OH) is amphoteric species which can exhibit as
acid that basic properties. These solvents can accept or donate protons accordance to
dissolved substances nature: water gives protons to NH3, N2H4, CH3NH2 and takes protons
from HCl, H2SO4, CH3COOH.
97
H2SO4 + H2S2O7 ↔ H3SO4+ + HS2O7–
H2SO4 + HSO3F ↔ H3SO4+ + SO3F–
Aprotonic solvent (C6H6, C6H5Cl, CH3Cl) is neutral substance that can not accept neither
donate protons. Molecules of aprotonic solvent not ionised.
Interaction the Solute with Solvents
Another parameter affecting the feasibility of a titration is the dissociation constant
of the acid or base being titrated. For titration of weak acids are using proton-accepting
solvents (ethylenediamine, dimethylformamide). For titration of weak bases are using
proton-donating solvents (glacial acetic acid, formic acid).
Again, the solvent plays an important role. Acidic (basic) solvents have
differentiating action, because in its environment can be titrated consecutively few acids
(bases) in mixture.
The tendency of the solvent to accept or donate protons determines the strength of a
solute acid or base dissolved in it. In the Brшnsted–Lowry view of acid–base behavior, the
strength of an acid or base is a relative measure of the ease with which a proton is
transferred from the acid to the solvent, or from the solvent to the base. For example, the
strongest acid that can exist in water is H+. The acids HCl and HNO3 are considered strong
because they are better proton donors than H+. Or another example, perchloric acid and
hydrochloric acid are strong acids in water.
When acetic acid, which is a weak acid, is placed in water, the dissociation reaction
CH3COOH + H2O ↔ H3O+ + CH3COO–
does not proceed to a significant extent because acetate is a stronger base than water and the
hydronium ion is a stronger acid than acetic acid. If acetic acid is placed in a solvent that is
a stronger base than water, such as ammonia, then the reaction
CH3COOH + NH3 ↔ NH4+ + CH3COO–
proceeds to a greater extent. In fact, HCl and CH3COOH are both strong acids in ammonia.
If anhydrous acetic acid, a weaker proton acceptor than water, is substituted as the
solvent, neither of this acid undergoes complete dissociation. Instead the equilibrium such
as the following are established
CH3COOH + HClO4 ↔ CH3COOH2+ + ClO4–
base
acid
conjugated base conjugated acid
Perchloric acid is, considerably stronger than hydrochloric acid in this solvent, its
dissociation being about 5000 times greater. Acetic acid thus acts as a differentiating solvent
toward the two acids by revealing the inherent differences in their acidities. Strong acids
essentially donate all their protons to H2O, “leveling” their acid strength to that of H+. In a
different solvent HCl and HNO3 may not behave as strong acids. Water, on the other hand,
is a levelling solvent for perchloric, hydrochloric, nitric, and sulphuric acids because all four
are completely ionised in this solvent and thus exhibit no differences in strength.
Differentiating and levelling solvents also exist for bases.
98
All other things being equal, the strength of a weak acid increases if it is placed in a
solvent that is more basic than water, whereas the strength of a weak base increases if it is
placed in a solvent that is more acidic than water. In some cases, however, the opposite
effect is observed. For example, the pKb for ammonia is 4.76 in water and 6.40 in the more
acidic glacial acetic acid. In contradiction to our expectations, ammonia is a weaker base in
the more acidic solvent.
Indicators for Nonaqueous Titrations
N+(CH3)2Cl-
(CH3)2N
CH(CH3)2
CH(CH3)2
O
HO
C
C
CH3
CH3
SO3H
N(CH3)2
Thymol blue
Crystal violet
(CH3)2 N
N
CH3
N
NH2
.HCl
Neutral red
99
SPECTROMETRIC METHODS OF ANALYSIS
Characteristics of Ultraviolet Radiation
The term spectroscopy referred to a branch of science, which include studies with all
types of electromagnetic radiation. Electromagnetic spectra are the plots of some function
radiant intensity versus wavelength of frequency.
Spectrochemical methods have provided perhaps the most widely used tools for the
elucidation of the structure of molecular species as well as the quantitative and qualitative
determination of both inorganic and organic compounds.
An important thing to know is that ultraviolet (UV) is not a single entity, but is a
wide band of wavelengths. The chief natural source of UV is the sun. In fact, about 9 % of
all energy emitted by the sun are UV. Most which is in the region between 300-400 nm.
Artificial sources of UV include incandescent, gas discharge, low-pressure mercury,
medium pressure mercury metal halide, electrodeless and xenon lamps.
UV radiation is electromagnetic radiation in the part of the spectrum between x-rays
and visible light. It differs from visible light only in that the UV wavelengths are too short
to be seen by the human eye. The boundary between visible light and UV is a wavelength of
400 nm (4000 Angstroms).
Medical literature divides UV into three ranges: UVA (315-400 nm) where the
filtered (BLB) is used for fluorescence blacklight effects while unfiltered UVA is used in
UV curing and photochemical reactions. UVB (280-315 nm) is used in scientific
applications such as genetic visualisation. UVC (200-280 nm) unfiltered UV is used in
germicidal and crosslinking applications and when properly filtered, for mineral
fluorescence. This is a small sampling of applications.
An interesting characteristic of UV radiation occurs when it falls upon certain
substances known as phosphors, where it causes the phosphors to emit specific radiation.
This phenomenon is known as fluorescence. Everyday fluorescent lighting is basically a UV
lamp constructed of a type of glass bulb that blocks UV rays. The inside of the bulb is
coated with a thin layer of fluorescent material that receives UV generated by the lamp and
in return emits a visible light.
100
One effect of ultraviolet energy upon certain substances is a phenomenon that takes
place at the atomic level. High frequency UV photons collide with atoms and part of the
photon's energy is transferred to the atoms by boosting electrons to the high energy states.
Upon de-excitation, as electrons fall back to lower energy states, energy is released as
photons of light. Since only a portion of the incoming photon's energy was transferred to an
electron, these emitted photons have less energy than the incoming UV photons so their
wavelengths are longer than the excitation photons. This process is called fluorescence.
In some materials, the fluorescence lingers and disappears, slowing after the UV
source is removed. Here, the electron returns slowly to its original state, and this delayed
fluorescence is called phosphorescence.
Origin of Absorbance Spectrum
For ultraviolet and visible radiation, excitation involves promotion an electron
residing in a low-energy molecular atomic orbital to a higher-energy orbital. The transition
of an electron between two orbitals is called an electronic transition, and the absorption
process is called electronic absorption.
Molecular absorption in the ultraviolet and visible region consists of absorption
bands made up of closely spaced lines. In a solution the absorbing species are surrounded by
solvent and the band nature of molecular absorption often becomes blurred because
collisions tend to spread the energies of the quantum states, thus giving smooth and
continuous absorption peaks.
The absorbing characteristics of a species are conveniently described by means of an
absorbance spectrum. Absorbance spectrum is a plot of some function of the attenuation of
a beam of radiation versus wavelength, frequency, or wavenumber. Two terms are
commonly employed as quantitative measures of beam attenuation:
– the transmittance, or transmission (T) of a solution – is the fraction of the incident
electromagnetic radiation that is transmitted by a sample,
– and the absorbance (A), or optical density (D) of a solution – is lg(1/T). The absorbance
increases in attenuation of the beam or decreasing transmittance.
As a consequence of interaction between the photons and absorbing particles, the beam is
attenuated from radiation power (P) or radiation intensity (I):
A = –lgT = lg
P0
I
= lg 0 .
P
I
There are special terms for definition of analytical methods using electromagnetic radiation:
Spectroscopy – obtaining of electromagnetic spectra and establishing relationships between
structure of substance and it absorptive properties at various wavelength,
Photometry – measuring the intensity of absorbed or emitted radiation of given frequency
and establishing relationships between amount of substance and intensity of absorbed or
emitted radiation.
101
Molecular Spectroscopy
Absorption of radiation by organic molecules in the wavelength region from 180 nm to 780
nm results from interaction between photons and those electrons that either participate
directly in bond formation (and are thus associated with more then one atom) or are
localised about such atoms as oxygen, sulphur, nitrogen, and the halogens.
Electrons involved in double and triple bonds of organic molecules are not as strongly held
and are therefore more easily excited by the radiation. Unsaturated organic functional
groups that absorb in the ultraviolet or visible regions are known as chromophores.
The common organic chromophores are:
alkene
–CH=CH– ;
conjugated alkene
–C=C–C=C– ;
alkyne
carbonyl
–CO–
;
–C≡C– ;
carboxyle
–COOH ;
amido
–CO–NH2 ;
nitro
–NO2 ;
nitroso
–N=O ;
azo
–N=N– ;
and aromatic groups.
The ions and complexes of elements in the first two transition series (d-elements) absorb
broad bands of visible radiation in at least one of their oxidation states and are, as a
consequence, coloured.
The electrons responsible for absorption by the lanthanide and actinide transition series (felements) are shielded from external influences by electrons that occupy orbitals with larger
principal quantum numbers.
Few atom groups in molecules of organic compounds not absorb ultraviolet or visible
radiation. But these groups, called auxochromes, change the absorption peculiarity of the
chromophres in the same organic molecules containing.
When absorption band (peak) under the auxochrome influence displacements to region with
longer wavelengths, this change called batochromic displacement. The reverse effect called
hypsochromic displacement.
When auxochrome increases the chromophore absorption intensity, we talk about
hyperchromic effect. And decreasing of the absorption intensity at auxochrome influence
called hypochromic effect.
Beer’s Law
For monochromatic radiation, absorbance is directly proportional to the path length l
through the medium and the concentration c of the absorbing species. Beer's law gives these
relationships:
A = k⋅l⋅c,
where k is a proportionality coefficient called the absorptivity. The magnitude and
dimensions of k will clearly depend upon the units used for l and c.
For solutions of an absorbing species, l is often given in terms of centimetres.
102
If c is given in percents, the k is called specific extinction (absorption) coefficient –
E . Specific absorption coefficient used for calculation of analyte concentration at routine
quantitative determinations.
If c is given in moles per litre, the k is called molar extinction (absorption)
coefficient – ε. Molar absorption coefficient is absorptivity constant for given species
because it depends only on nature (structure) of the substance.
Absorbance is additive value. Provided there is no interaction among the various
species, the total absorbance for a multicomponent system is given by
1%
1cm
Atotal = A1 + A2 + ... + AN = ε1⋅l⋅c1 + ε2⋅l⋅c2 + ... + εN⋅l⋅cN.
Limitation to Beer’s Law
Few if any exceptions are found to the generalisation that absorbance is linearly
related to path length. But deviations from the direct proportionality between the measured
absorbance and concentration when l is constant are frequently encountered. Some of these
deviations are fundamental and represent real limitations of the law, and others are
instrumental deviations and chemical deviations.
1. Real limitations to Beer’s law are encountered only in relatively concentrated solutions of
the analyte or in concentrated electrolytes.
At high concentrations, the average distance between the species responsible for
absorption is diminished to the point each affects the charge distribution of its
neighbours. This interaction, in turn, can alter their ability to absorb a given wavelength
of radiation.
A similar effect is sometimes encountered in media containing high concentration of
electrolytes. The close proximity of ions to the absorber alters the absorptivity of the
latter as a result of electrolytic interactions.
2. Apparent deviations from Beer’s law arise when an analyte dissociates, associates, or
reacts with solvent to generate a product that has a different absorption spectrum from
that of the analyte.
3. Deviations from Beer's law occur when polychromatic radiation is used to measure
absorbance.
4. Instrumental deviation occurs in the presence of stray radiation. Stay radiation is the
result of scattering phenomena off surfaces of prism, lenses, filters, and cuvettes.
Qualitative Applications of Ultraviolet and Visible Spectroscopy
Spectrophotometric measurements with ultraviolet radiation are useful for detection
chromophoric groups. The most organic molecules are transparent to radiation longer than
180 nm, the appearance of one or more absorption peaks in the region from 200 nm to 400
nm is clear indication of the presence of unsaturated groups. An idea as to the identity of the
absorbing groups can be gained by comparing the spectrum of an analyte with those of
single molecules containing various chromophoric groups.
103
Ultraviolet and visible absorption spectra are usually obtained on a gaseous sample
of the analyte or on a dilute solution of the analyte in transparent solvents. Solvents for
ultraviolet and visible spectroscopy must be not only transparent throughout this region, but
should dissolve a sufficient quantity of the sample to give well-defined peaks.
Absorption spectroscopy in ultraviolet and visible region of electromagnetic radiation
is the most useful tools for quantitative analysis. The important characteristics of
spectrophotometric and photometric methods are:
1) wide applicability,
2) high sensitivity,
3) moderate to high selectivity,
4) good accuracy,
5) easy and convenience.
A first step in any photometric or spectrophotometric analysis is the development of
conditions that yield a reproducible relationship (referable linear) between absorbance and
analyte concentration:
1. Wavelength selection. In order to realise maximum sensitivity, spectrophotometric
absorbance measurements are ordinarily made at a wavelength corresponding to an
absorption peak because the change in absorbance per unit of concentration is greatest at
this point.
2. Variables that influence absorbance. Common variables that influence the absorption
spectrum of a substance include
1) the nature of the solvent,
2) the pH of the solution,
3) the temperature,
4) high electrolyte concentration,
5) and the presence of interfering substances.
3. Choice of cuvettes. Cuvettes material must be transparent in the spectral region of
interest. Can be used cuvettes with path length from 0,1 cm to 10 cm for achievement
(obtaining) the highest sensitivity.
4. Determination of the relationship between absorbance and concentration. The calibration
standards for a photometric or a spectrophotometric analysis should approximate as
closely as possible the overall composition of the actual samples, and should encompass
a resonable range of analyte concentration.
5. Concntration calculation method. Ideally, calibration standards approximate the
composition of the samples to be analysed not only with respect to the analyte
concentration, but also with regard to the concentrations of the other species in the
sample matrix in order to minimise the effects of various components of the sample of
the measured absorbance. There are such techniques:
– calibration plot building,
– definition of extinction coefficient (molar or specific),
– comparison with standard solution,
– standard-addition method.
104
OPTICAL METHODS OF ANALYSIS
Electromagnetic radiation is a type of energy takes numerous forms. For many
purposes, electromagnetic radiation is conveniently represented as electric and magnetic
fields that undergo in-phase, sinusoidal oscillations as right angels to each other and to the
direction of propagation. A beam of monochromatic light has plane-polarised radiation.
Plane-polarised implies that all oscillations of either the electric or the magnetic fields lie
within a single plane. The electric field is responsible for most of the phenomena that are of
interest to analytical assays including transmission, reflection, refraction, and adsorption.
Refractometry
Refractometry is the analytical method based on measuring of relative refractive
index (n) of light rays of investigated substances.
The light ray changes during transition from one transparent environment into
another. This phenomenon is named refraction. An environment can be more or less
optically solid, and the light pass through the environment with different rate. When the ray
transits from environment with less optically solid into environment with higher optical
solid the angle of ray incidence is more than refraction angle.
In a vacuum, the velocity of radiation becomes independent of wavelength and is at
its maximum. In any medium containing matter, propagation of radiation is slowed by the
interaction between the electromagnetic field of the radiation and the bound electrons is the
atoms or molecules present. Since the radiant frequency is invariant and fixed by the source,
the wavelength must decrease as radiation passed from a vacuum to some other medium.
The refractive index n of a medium is the ratio of the speed of light in a vacuum to
the speed in the medium. That is,
ni = c/vi = 3,00⋅1010/v,
vi – the velocity of radiation of wavelength i.
Both ni and vi are wavelength dependent.
Relations of incidence angle sine to refraction angle sine is called relative refractive
index of the second environment in point to the first:
nrel = sin α ,
sin β
α – incidence angle of light ray;
β – refraction angle of light ray.
Relative refractive index for two environments is:
105
n
n = sin α = 2 ,
sin β n1
n1 – refractive index of the first environment;
n2 – refractive index of the second environment (are implied the refraction
indexes n1 and n2 in point of air).
This correlation allows to calculate the relative refractive indexes for various combinations
of environments. For example, relative refraction index of «glass-water» border is: nrel =
nglass/nwater = 1,50/1,33=1,13.
If light ray incidences from air, n is the refraction index of given environment in
point of air. Usually the refraction indexes of and liquids solids determine on attitude to air
and name simply refractive indexes and mark by letter n:
n = sin α .
sin β
Ratio of light speed or incidence angle sine of light ray in vacuum to light speed or
refraction angle sine in given environment is called absolute refractive index and mark by
letter N. Practically matter refraction index in point of air can be equal to his absolute
refraction index.
A refractive index depends on:
– substance nature and it phase state;
– polarisation of light;
– wave-length of light, that passes through the substance;
– temperature and pressure (for gases).
As a rule, the refractometric measuring take attached to temperature 20 °С and to
wave-length of line D in sodium atom spectrum (λ = 589,3 nm). A refractive index definite
at this condition marks n 20
D .
For example, a water refractive index diminishes with augmentation of temperature.
Because an exact measuring is necessary taking at constant temperature. In tables puts the
refractive indexes definite attached at 20 °С and mark n20.
The important description of matter optical properties there is dispersion. The light
speed depends on its wavelength, and a refractive index also depends on wavelength light,
that passes over matter. At passage of white light through a prism there is its decomposition
on a spectrum. The colour beams differently refract by a prism: least deviation from
elementary direction have the red rays, most – violet rays. Accordingly, with augmentation
of wavelength a refraction index diminishes.
A measuring of refractive index is necessary to participate in source radiating with
determined waves lengths (hydrogen lamps, mercurial lamps, sodium lamps).
Quantitatively a dispersion value is D = nλ2–nλ1 difference, where nλ1 – refractive
index at λ1, nλ2 refractive index at λ2. The most frequently the dispersion value is the
difference of the refractive indexes for lengths of waves at С and F lines. The C line is the
emission red line in spectrum of hydrogen (C = 656,3 nm). The F line is dark blue line in
spectrum of hydrogen (F= 486 nm). A difference nF–nC named by middle dispersion.
For majority of solutions a refractive index depends on solutions concentration. For
diluted solutions n = no + KC, where no – solvent refractive index, С – matter concentration
106
in solution, a K – empirical coefficient which determines on solutions with known
concentration (standards). If all of factors influencing on refractive index value is constant,
then n in solutions depends on solvent nature and concentration of dissolved substance.
The refractive index is additive value. In multicomponent mixtures this property can
be described as:
n = no + F1C1+ F2C2 +...+ FnCn,
where no – solvent refractive index;
C1, C2, ... Cn – concentrations of dissolved substances expressed in mass or
volumetric percentages;
F1, F2, ... Fn – empirical coefficients, which name by refractive indexes factors. These
factors show a part of each component in total refractive index of solution.
Application in analysis
A refractive index adapts for identification of liquids and for establishing of their
purity. An individual substance has a determined refractive index, admixtures change a
matter refraction index value.
Refractive index dependence on concentration of solution and uses for:
– quality control of medicines solutions,
– quantitative determination of ingredients in multicomponent mixtures,
– clinical analysis of body fluids.
Polarimetry
Polarimetric method of analysis is based on determination the concentrations of
optically-active substances applying the polarisation angle measurement.
If oscillation of light ray occurs only in one plane it light is called polarised. And
perpendicular to oscillation plane is called the plane of its polarisation. Polarised light
receive passing the through the anisotropic matters, or polarisation crystals (for example,
Icelandic spar, tourmaline etc.).
If on polarised light way were put analyser (also one polarisation prism), the beam
can pass through the analyser or fades on it. When the plane of light polarisation coincided
(is parallel) with the polarisation plane of analyser, then light will get through the analyser.
If analyser to rotate on 90° around polarisation axis, then plane of light oscillation will
perpendicular and lightly will not get through analyser.
Optical activity of substances is caused two factors:
– structure asymmetry of crystalline matters lattice. This type of activity loses after
crystalline lattice destruction (dissolution, melting) – NaCl, CaF;
– molecules asymmetry. This type of activity display only the matters in dissolved or
gaseous state. These are the main the organic compounds, which have a chiral centre.
In matters displaying optical activity in solutions, optical activity is caused by
molecules asymmetry. Such molecules do not have nor centre, nor symmetry plane.
Molecules with two or three atoms always symmetric, because throughout two or three
points can be lined symmetry. But most molecules are asymmetric and are optically active.
These molecules have two optical isomers: right- and left- rotate, which are its mirror
reflection.
Dependency on nature of matter the plane of polarisation rotation can have different
direction and value. Under this if from observer, to which light directed, which passes over
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optically active matter a polarisation plane rotate to right (clockwise) then matter name
right-rotating and in front of it name write D or sign «+», if rotation of polarisation plane
passes left (against the sun) then matters name left-rotating and in front of it name write R
or sign «–».
The optically active substances are: sugar, albumen, nucleic acids, morphine, and
nicotine, win acid, etc. As a rule during synthesis receive racemic mixtures, which are
mixtures of right- and left- rotating antipodes.
The polarised light passed through the optically active matter rotate from elementary
direction to any angle, which named the polarisation plane rotation angle. This angle
expresses in angle degrees and marks by Greek letter α. Its value depends on:
– matter nature,
– thickness of solution layer,
– solution concentration,
– wavelength of light, and
– temperature.
If rotation angle to measure in special cuvettes at constant temperature and wavelength, then
his value depends on concentration only.
Optical matter activity characterise by the specific rotation, which calculate as
polarisation plane rotation angle into right or left side the passed polarised light over
solution with layer 1 dm and with concentration 1 kg/dm3. A value of specific rotation
depends on matter nature, wavelength of polarised light, and temperature. The standard
specific rotation are determined at 20 °С and wavelength 589,3 nm of sodium spectrum and
20
sign [α] 20
D . Specific rotation value [α] D is constant for every substance.
Value of specific rotation for liquids calculates with equation:
[α] 20
D =
α
,
ρ⋅l
α – rotation angle in degrees;
l – thickness of liquid layer, dm;
ρ – specific density of liquid, kg/dm3.
For solutions a specific rotation depends on solvent nature and concentration of
optically-active matter and calculates with equation:
[α] 20
D =
α ⋅ 100
l
,
α – rotation angle in degrees;
l – thickness of liquid layer, dm;
С – concentration of solution, %.
Polarimetry are used:
20
– for identification of optically-active substances (by [α] D )
– and for determination of glucose, ascorbic acid, camphor, etc. in pharmaceuticals quality
control.
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THE ERRORS OF ANALYSIS AND THEIR STATISTICAL TREATMENT
There is no simple and widely applicable method for determining the reliability of
data with absolute certainly. The true value of a measurement is never known exactly.
Common Terms of Statistic Random
Replicates are samples of about the same size that are carried through an analysis
exactly the same way.
The median is the middle value in a set of data that has been arranged in order of
size. The median is used advantageously when a set of data contains an outlier – that is, a
result that differs significantly from the rest of the data in the set. An outlier can have a
significant effect on the mean of the set but have a lesser effect on the median:
n
x=
∑ xi
i =1
n
,
where xi represents the individual values of x making up a set of n replicate
measurements.
Precision is the closeness of data to other data that have been obtained in exactly the
same way.
Accuracy is the closeness of a result to its true or accepted value.
The absolute error of a measurement is the difference between the measured value
and the true value. It bears a sign:
E a = xi – xt,
where xi is the true, or accepted, value of the quantity.
The relative error of a measurement is the absolute error divided by the true value:
Er =
xi − xt
⋅ 100% .
xt
Types of Errors in Experimental Data
The precision of a measurement is readily determined by comparing data from
carefully replicated experiments.
1. Random, or indeterminate, errors are errors that affect the precision of measurement.
2. Systematic, or determinate, errors affect the accuracy of results.
3. Gross error, or an outlier is an occasional result in replicate measurements that
obviously differ significantly from the rest of the results.
Systematic errors lead to bias in measurement technique. There are tree types of
systematic errors:
1) instrumental errors are caused by imperfection in measuring devices and
instabilities in their power supplies;
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2) method errors arise from nonideal chemical or physical behaviour of analytical
systems;
3) personal errors result from the carelessness, inattention, or personal limitations of
the experimenter.
Systematic errors may be either constant or proportional.
Constant errors are independent of the size of the sample being analysed.
Proportional errors decrease or increase in proportion to the size of the sample.
The spread, or range, of a set of replicate measurements is the difference between
the highest and lowest result. Experimental data are distributed symmetrically around the
mean of an infinite set of data. Such distribution of experimental data is described by Gauss’
law, or law of normal errors.
The random, or indeterminate, errors in the results of an analysis can be evaluated by
the methods of statistics. In statistics, a finite number of experimental observations are
called a sample of data. The sample is treated as a tiny fraction of an infinite number of
observations that could in principle be made given infinite time. Statisticians call the
theoretical infinite number of data a population, or a universe, of data.
The sample standard deviation s is given by the equation:
n
∑ (xi − x) 2
i =1
s=
n −1
,
where (n–1) is number of degrees of freedom.
The number of degrees of freedom indicates the number of independent data that go
into the computation of a standard deviation. Only n–1 deviations provide an independent
measure of the precision of the set.
The standard error of a mean is the standard deviation of the set of data divided by
the square root of the number of data in the set:
sm =
s
.
m
The variance is simply the square of the standard deviation:
n
∑ (xi − x) 2
s2 =
i =1
n−1
.
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TABLE OF CONTENTS
Analytical chemistry and chemical analysis
Law of mass action and its application to various types of ions equilibrium in
analytical chemistry
Theory of electrolytes, strong and weak electrolytes. Analytical
concentration and ions activity, dependence between its, coefficient of
activity
Protolytic balance in electrolytes solutions
Solutions of amphoteric compounds. Solutions of complex compounds.
Organic reagents and their application in analysis.
Using law of mass action du to redox processes
Using law of mass action to equilibrium in heterogeneous system precipitate–
saturated solution
Colloid systems, their importance for chemical analysis
Methods of separation and concentrating of substances
Extraction in analytical chemistry
Separation and concentrating techniques on analysis
Chromatographic methods of analysis
Theory of chromatographic separation
Various chromatographic techniques
Plate chromatographic techniques
Gas chromatography
Liquid chromatography
Ion exchange chromatography
Sedimentary chromatography
Gel chromatography
Affinity chromatography
Gravimetric method of analysis
Titrimetric methods of analysis
Acid-basic titration
Indicators for acid-basic titration
Redox titrations
Precipitation titrimetry
Titrations based on complexation reactions
Nonaqueous titrations
Spectrometric methods of analysis
Optical methods of analysis
The errors of analysis and their statistical treatment
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47
49
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56
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57
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63
67
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87
95
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