Download Chemistry Primer for pH Measurements

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Technical Note
Chemistry Primer for pH Measurements
TrupH
This technical note is a general chemistry primer. First, the structure of the atom and the Bohr
model are described. The period table and molecular bonds are then reviewed, followed by
the definition of ions and ionic dissociation. Finally, the “mole”, a quantity used to describe
molecular concentrations is presented. These basic concepts are presented in the context of
pH measurements.
Atomic Structure
In ancient Greek philosophy, “atomos”, meaning “not divisible”, was the smallest amount of
matter (or particle) that could be conceived.
This fundamental particle was thought to be
indestructible. With the advent of experimental
science in the sixteenth and seventeenth centuries, progress in atomic theory accelerated.
Chemists soon recognised that liquids, gases
and solids could be dissociated into their primary components, called “elements”. These elements, through various types of chemical bonds,
formed the building blocks of molecules.
Atoms are the fundamental form of elements. Atoms can combine in many different ways to form a
multitude of different compounds, whose properties
vary widely based on their atomic composition. Atoms of one hundred and twelve different elements
have been identified to date.
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The Rutherford Model In 1911, Ernest Rutherford formulated a theory of atomic structure that
was the first visualization of the atom as a dense
nucleus surrounded by orbiting electrons, which
was called the “Planetary Model”. Rutherford
established that the mass of the atom is concentrated in its nucleus, which has a positive
electric charge, while the electrons each have
a negative charge. The atom is neutral because
the total electronic and nuclear charges are
equal. Rutherford only identified the positively
charged component of the nucleus, called the
proton. The Rutherford model of an atom was
refined in 1913 by Niels Bohr, who postulated
that electrons are arranged in definite shells (orbits), or quantum levels, at a defined distance
from the nucleus.
Today, it is well-known that the nucleus comprises both neutrons and protons. The neutron, however, was not discovered until 1932,
when James Chadwick realized that the nucleus has another particle having the same
mass as the proton, but without an electric
charge. In any given atom, the number of protons is equal to the number of electrons and
defines the atomic number of the atom. The
atomic number of an element determines its
position in the “Periodic Table”.
The Bohr Model The nuclear atom proposed
by Rutherford was unstable. According to
classical theories, this atom should collapse.
It also failed to explain the discrete spectral
lines of elements. To resolve these issues,
Niels Bohr developed a hypothesis known as
“The Bohr Theory of the Atom”. Bohr’s two
fundamental assumptions were that:
1 There exist steady orbitals for electrons, so
that when electrons orbit a nucleus at any
of these special orbital radii, they do not
radiate energy.
2 Electrons gain and lose energy as they
move from one permitted radius (energy
level) to another. They accept energy during excitation and release radiant energy
during de-excitation. This energy is “quantized” according to Planck’s relationship E
= hf = hc/λ.
Bohr’s model successfully explained the stability of the atom through his concept of “quantization”. His “electron configuration” successfully predicted the spectral lines of hydrogen
(figure 1), which had previously been studied
by Kirchoff, Rydberg, Balmer, and others. The
wavelength of light emitted when an electron
moved from a higher energy level to a lower
energy level was calculated with the formula
λ = hc / ΔE
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where ΔE represents the difference in the two
energy level transitions. Bohr also provided a
formula by which to compute the energy levels
(in electron volts, eV):
Figure 1
Discrete
emission
lines from
Ionization
Second Excited State
hydrogen
atom first
Paschen (IR)
First Excited State
predicted by
Balmer (Visible)
Bohr’s atomic model.
Ground State
Lyman (UV)
Lyman
Balmer
UV Radiation Visible Light
Figure 2:
Paschen
IR Radiation
En = -13.6 Z2 / n2
where Z is the atomic number and n is the energy level. The ground state is n = 1, the first
excited state is n = 2, the second excited state
is n = 3, etc. 1 eV equals 1.6 x 10-19 Joules.
While Bohr’s model is not completely correct,
i.e., it fails to explain why the protons stay together in the nucleus, it had many features
that were approximately correct. The correct
theory of the atom is called quantum mechanics; the Bohr Model is an approximation to
quantum mechanics that has the virtue of being much simpler.
Arrangement
of electrons
in shells
Electron Shells In a multi-electron atom, each
electron has its own orbital according to the
Pauli principle (a law of quantum mechanics),
so that many different kinds of orbitals can be
occupied. A group of orbitals with the same, or
nearly the same energy, is called a shell. The
pattern of filled and unfilled shells is different
for each element. This shell pattern gives the
elements their distinctive characteristics and
chemical reactivity.
The number of electrons equals the atomic number
of the atom: for example, hydrogen has a single orbital electron, oxygen has 8, and uranium has 92.
The electron shells are built up in a regular fashion from a first shell to a maximum of seven shells,
each of which has an upper limit of the number
of electrons that it can accommodate (figure 2).
The shells are named from inner shell to outer
shell: K-shell, L-shell … to Q-shell. The K-shell is
complete with two electrons, the L-shell can hold
up to eight electrons, the M-shell 18 electrons. In
general, the nth shell can hold up to 2n2 electrons.
The electrons in the outer shell determine the
chemical behaviour of the atom. Atomic shells do
not necessarily fill up with electrons in consecutive order. The electrons of the first 18 elements in
the periodic table are added in a regular manner,
with each shell being filled to a designated limit
before a new shell is started.
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Starting with the 19th element, however, the
outermost electron starts a new shell before
the previous shell is completely filled. A pattern
can still be discerned, however, as electrons
fill successive shells in a repetitive, back-andforth pattern. The result is the regular repetition
of chemical properties for atoms of increasing
atomic weight that corresponds to the arrangement of the elements in the periodic table.
The Periodic Table In 1869, Dmitri Mendeleyev arranged all elements known at the
time into a table according to their atomic mass.
By doing so, he discovered that certain properties of the elements repeated themselves in a
periodic way. Therefore, Mendeleyev grouped
elements with similar chemical activities into
vertical columns. This arrangement of the element became known as the Periodic Table. In
the Periodic Table, the name, symbol, atomic
Figure 3 Representation
of elements in the peri-
Electron Orbit
for hydrogen and oxygen
elements.
Electron -
Proton +
Atomic
Number
1
Atomic
Weight
1.0079
H
Symbol
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Neutron -
Proton +
Hydrogen
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Since Mendeleyev’s time, additional elements
have been discovered, so that the periodic table
has been rearranged a few times. The table, as
we know it today, is illustrated in figure 4. The
elements are arranged horizontally from left to
right by ascending atomic number (i.e., number
of protons in the nucleus or orbiting electrons)
in seven rows. Each row represents one of the
seven electronic shells of the atom. Hydrogen,
in position 1 of row 1, is the lightest element.
The last element in the table is, for the time being, the artificial element “ununbium”, taking the
112th position with an atomic mass of 277. The
Periodic Table thus provides for a total of 118 elements. The 18 vertical columns group the elements according to their chemical activities (i.e.
the numbers of electrons in their outer shell).
The Hydrogen Atom
odic table and example
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number, and atomic weight are presented for
each element, as illustrated for hydrogen and
oxygen in figure 3.
8
Element
Name
15.9994
O
Oxygen
The Oxygen Atom
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Periodic Table of the Elements
Group
IA
1
VIIIE
2
H
Hydrogen
Li
Lithium
6.941
11
Na
Sodium
22.989770
19
K
Potassium
39.0983
37
Rb
Rubidium
85.4678
55
Cs
Cesium
132.90545
87
Fr
Francium
Symbol
Be
Beryllium
12
5
Gases
Noble Gases
Liquids
Solids
Synthetically
Prepared
Ce
Cerium
140.116
Atomic
†
Weight
Mg
Boron
13
Al
Aluminum
24.3050
20
Ca
Calcium
40.078
38
Sr
26.981538
IIIA
21
Sc
Scandium
44.955910
39
Strontium
87.62
Yttrium
88.90585
47.867
Zirconium
91.224
Hf
Barium
Hafnium
178.49
88
104
Ra
Rf
Radium
Rutherfordium
(226)
(261)
Actinides
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Titanium
72
137.327
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Ti
Zr
Ba
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IVA
22
40
Y
56
the Elements
B
10.811
Magnesium
Figure 4 Periodic Table of
P04
IIIB
58
Name
9.012182
Lanthanides
(223)
4
4.002602
Atomic
Number
IIA
3
He
Helium
1.00794
57
La
Lanthanum
138.9055
89
Ac
Actinium
(227)
VA
23
V
Vanadium
50.9415
41
Nb
Niobium
92.90638
73
Ta
Tantalum
180.9479
105
Db
Dubnium
(262)
58
Ce
Cerium
140.116
90
Th
Thorium
232.0381
VIA
24
Cr
Chromium
51.9961
VIIA
25
Mn
Manganese
54.938049
42
43
Molybdenum
Technetium
74
75
Mo
95.94
W
Tungsten
183.84
106
Sg
Seaborgium
(266)
59
Pr
Tc
(98)
Re
Rhenium
186.207
107
Bh
Bohrium
(264)
60
91
Pa
Protactinium
231.03588
Fe
Iron
55.845
44
Ru
Ruthenium
101.07
76
Os
Osmium
190.23
108
Hs
Hassium
(277)
61
Co
Ni
58.933200
58.6934
Cobalt
45
Rh
Rhodium
102.90550
77
Ir
Iridium
192.217
109
144.24
92
U
Uranium
238.02891
Promethium
(145)
93
Np
Neptunium
(237)
Nickel
46
Pd
Palladium
106.42
78
Pt
Platinum
195.078
110
IB
29
Cu
Copper
63.546
47
Ag
Silver
107.8682
79
Au
Gold
196.96655
111
IIB
30
Zn
Zinc
65.409
48
Cd
Cadmium
112.411
80
Hg
Mercury
200.59
31
Ga
Gallium
69.723
49
In
Indium
114.818
81
Tl
Thallium
204.3833
112
Mt Uun Uuu Uub
Meitnerium
Ununnilium Unununium
(268)
62
Nd Pm Sm
Praseodymium Neodymium
140.90765
26
VIIIA
27
28
Samarium
150.36
94
(281)
63
Eu
Europium
151.964
95
(272)
64
Gd
Gadolinium
157.25
96
(285)
Tb
Terbium
158.92534
97
Pu Am Cm Bk
Plutonium
(244)
Americium
(243)
Curium
(247)
Berkelium
(247)
C
Carbon
12.0107
14
Si
Silicon
28.0855
32
Ge
Germanium
72.64
50
Sn
Tin
118.710
82
Pb
Lead
207.2
VB
7
N
Nitrogen
14.0067
15
P
Phosphorus
30.973761
33
As
Arsenic
74.92160
51
Sb
Antimony
121.760
83
Bi
Bismuth
208.98038
Dy
Dysprosium
162.500
98
Cf
Californium
(251)
O
Oxygen
15.9994
16
S
Sulfur
32.065
34
Se
Selenium
78.96
52
Te
Tellurium
127.60
84
Po
Polonium
(209)
116
Ununquadium
Ununhexium
67
Ho
Holmium
164.93032
99
Es
Einsteinium
(252)
VIIB
9
F
Fluorine
18.9984032
17
Cl
Chlorine
35.453
35
Br
Bromine
79.904
53
I
Iodine
126.90447
85
At
Astatine
(210)
10
Ne
Neon
20.1797
18
Ar
Argon
39.948
36
Kr
Krypton
83.798
54
Xe
Xenon
131.293
86
Rn
Radon
(222)
Uuh
(289)
66
VIB
8
114
Uuq
Ununbium
65
IVB
6
(292)
68
Er
Erbium
167.259
100
69
Tm
Thulium
168.93421
101
Fm Md
Fermium
(257)
Mendelevium
(258)
70
Yb
Ytterbium
173.04
102
No
Nobelium
(259)
71
Lu
Lutetium
174.967
103
Lr
Lawrencium
(262)
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The Molecule – Covalent Bonds
TrupH
The molecule is the smallest unit of a chemical
compound having the unique chemical properties
of that compound. A molecule is comprised of atoms that are joined by an electrical force called a
chemical bond. In the 1770s, Joseph Priestly and
Antoine Lavoisier proved that water was not a basic element, as the ancient philosophers thought,
but a compound of one atom of oxygen and two
atoms of hydrogen – as expressed by the present-day formula H2O.
Figure 5
Electron
Configuration of Noble
Gases
In molecules, atoms are held together by sharing
electrons (covalent bonds). In order to maximize
these bonds, the atoms adopt specific positions
relative to each other, i.e. each molecule has its
own definite geometric structure. For instance in
the water molecule, the two hydrogen atoms are
bonded to the oxygen atom at an angle of 104.5°.
As a consequence, there is a slight charge separation of the electronic clouds of the atoms so that
water molecules have a dipole moment: specifically, the hydrogen atom electrons are attracted
slightly towards the nucleus of the larger oxygen
atom. In contrast, the CO2 molecule is has a linear
geometry (the O=C=O atoms form a straight line),
and has therefore no dipole moment.
Not all elements can form molecules, however. If
the outer shell of an atom is completely full, then
the atom cannot normally form a bond (figure 5).
Noble gases have atoms that contain either 2 electrons (He) or 8 electrons (Ne and Ar) in their outer
shell. These lighter noble gases are non-reactive
and cannot form molecules. However, this is not the
case for the heavier noble gases. Since 1962, scientists have succeeded in producing compounds
involving Kr, Xe and Rn. Any other element having
an incomplete outer shell will more or less readily
form a bond with other “non-noble” elements.
The number of bonds that an atom can form is
called its valence. Oxygen has a valence of 2 as
it needs another 2 electrons in order to fill its outer
shell. Hydrogen has a valence of 1 because it has
only one electron in its outer shell; it requires another electron to fill its shell, or it can give an electron to an atom which is one electron short. Two
hydrogen atoms fulfil the needs of the oxygen
atom and thereby form a molecule of water.
Salts – Ionic Bonds
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The word “ion” derives from a Greek word
meaning “traveller”. An ion is formed when a
neutral atom gains or loses one or more electrons. An atom that loses an electron forms a
positively charged ion called a cation, whereas an atom that gains an electron forms a
negatively charged ion, called an anion.
When the elements sodium (Na) and chlorine
(Cl) combine to form the molecule sodium chloride (NaCl), better known as table salt, they
form an ionic bond (figure 6). The neutral sodium atom, having a single electron in its outer
shell, will share this electron with the chlorine
atom, which has 7 electrons in its outer shell.
Again, the outer shell of each atom become, by
this electron transfer, filled with 8 electrons.
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In sodium chloride, the sodium atom becomes
positively charged (by the loss of one electron
to form a sodium ion Na+), while the chlorine
atom becomes a negatively charged (by the
gain of one electron to form a chlorine ion (Cl-).
The new shell-structure of the sodium ion resembles that of a neon atom, and the new shellstructure of the chlorine ion resembles that of
an argon atom. The two ions are held together
by their electrostatic attraction.
TrupH
If the ionic bond of a NaCl molecule is broken either through high temperature or through dissolution in water (see figure 7), the chlorine atom will
keep its gained electron, and stays a negatively
charged ion. The sodium atom will stay a positively charged ion. Under the influence of an electric field, ions will migrate (travel) to their opposite
pole, and thereby create electrical conductivity in
gases and liquids.
Figure 6 Ionic Bond of
Sodium and Chlorine
Figure 7 Dissociation of
Sodium Chloride
Water: The Universal Solvent
Figure 8 Formation of an
Figure 9 Measurement
electrolyte solution.
of current in electrolytic
solution.
Water, by its polar nature, is an excellent solvent
for three major groups of chemical compounds:
salts, acids and bases. When dissolved in water,
these chemicals separate into their underlying
ions, namely, they dissociate. For example, when
sodium chloride (NaCl) is placed into water, the
polar forces of the water molecules will reduce the
electrostatic attraction between the sodium and
chlorine ions and cause them to dissociate (figure
7). The ions become surrounded by water molecules (hydrated) and can no longer recombine.
Hydrochloric acid (HCl) will dissociate into H+ and
Cl- ions and sodium hydroxide (NaOH) will dissociate into Na+ and OH- ions. The dissociation of
salts, acids and bases in water causes the water
to become an excellent conductor. The resulting
solutions are called electrolytes (figure 8).
If two electrodes are immersed into an electrolytic solution, and a potential difference is
applied to these electrodes, the anions will be
attracted by the positively charged electrode
(anode). When the anions reach the anode,
they lose their charge (i.e., they loose their electrons). Similarly the positively cations will move
towards the negatively charged electrode (cathode) and lose their charge by gaining electrons.
The result is that a current can be measured in
the electric circuit (figure 9).
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Technical Note
Acids – Bases – Salts
TrupH
In chemistry, there are three basic types of electrolytes: acids, bases, and dissolved salts.
g
Litmus is the oldest and most commonly used
indicator of whether a solution is an acid or a
base. It is a pink dye derived from lichen (a
symbiotic association of a fungus and algae)
and absorbed into paper. Litmus paper cannot
be used to identify salts.
g
Acids are chemical compounds that, when dissolved in water, produce a concentration of
hydrogen ions, (H+ or protons) exceeding that
of pure water. An acid is therefore a proton donor. Acids taste sour and turn Litmus paper red.
Common acids include: g
Hydrochloric acid HCl
Component of gastric juices
g
Nitric acid
HNO3
Dyes and explosives
g
Acetic acid
Vinegar
CH3COOH
g
Formic acid
HCOOH
Dyeing and tanning
g
Sulphuric acid
Batteries
H2SO4
g
Phosphoric acid
H3PO4
Dental cement, fertilizer
Bases are chemical compounds that, when dissolved in water, produce an concentration of hydroxyl ions (OH¯) exceeding that of pure water.
A base is therefore a proton acceptor. Bases
feel slimy, taste bitter and turn Litmus paper
blue. The most common bases are:
Sodium hydroxide NaOH
Drain and oven cleaner
Calcium hydroxide Ca(OH)2
Slated lime (mortar for construction)
g
Aluminium hydroxideAl(OH)3
Raw material for aluminium compounds
g
Potassium hydroxideKOH
Soft soap
g
Magnesium hydroxideMg(OH)2
Milk of magnesia
g
Ammonia
NH3
Household cleaners
When an acid and a base are combined, a neutralization reaction occurs. This reaction takes
place very rapidly and generally produces water
and a salt. For example, sulphuric acid (H2SO4)
and sodium hydroxide (NaOH), yield water and
sodium sulphate (Na2SO4): H2SO4 + 2NaOH =
2H2O + Na2SO4.
Salts are produced from acids or bases by
substituting the H+ ion with a base part or by
substituting the OH- ion with an acid part. The
resulting cations and anions combine to form an
electrically neutral compound called a salt. For
example:
g
Sodium nitrate
NaNO3= Na++NO3g
Aluminium sulphate
Al2(SO4) = 2Al3++3SO42g
Calcium phosphate
Ca3(PO4)2 = 3Ca2++2PO43-
The Mole: Measuring Quantities of Molecules
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“The mole is the SI unit of an amount of substance equal to the quantity containing as many
elementary units as there are atoms in 0.012 kg
(12g) of carbon-12. The elementary entities must
be specified and may be atoms, molecules, ions,
electrons or other particles. The unit was established in 1971 for international use.”
(The Oxford Dictionary)
The number of elementary particles contained in
12g of carbon-12 (the standard reference atom)
is 6.0221367 x 1023. This number is known as
the Avogadro’s number in honour of the Italian
physicist Amedeo Avogadro, who postulated
in 1811 that equal volumes of gases, at equal
temperatures and pressures, contain the same
number of molecules.
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Technical Note
TrupH
A mole, therefore, is an amount of any substance
that weighs, in grams, as much as the numerically equivalent atomic weight of that substance.
1 mole H2
=2g
1 mole H2O
= 18 g
1 mole
1 mole
1 mole
1 mole
Cl2
Rn
HCl
NaOH
= 71 g
= 222 g
= 36.5 g
= 40 g
Hydrogen Ion Concentration in Aqueous Solutions
Not only does water dissolve and dissociate
electrolytes, but water itself disassociates. Specifically, water molecules can dissociate into hydrogen ions (H+) and hydroxyl ions (OH-) through
the reaction: H2O ⇔ H+ + OH-. These hydrogen
ions have the following charateristics:
By dissolving a base in neutral water, the OH- concentration is increased by the OH- ions which are
produced by the dissociation of that base (figure
10). There, the relative amount of the H+ ions will
be reduced. The water will again change its properties, i.e. it tastes bitter and feels slimy like wet soap.
H+ = Positive charge and associated
with acidity
In both cases, the water becomes an aqueous solution. All aqueous solutions of acid and bases owe
their chemical activity to their relative hydrogen ion
(H+) and hydroxyl ion (OH-) concentration.
OH- = Negative charge and associated alkalinity
If the amount of hydrogen ions equals the amount
of hydroxyl ions, then the water is neutral. In
clean, neutral water only one out of 10 000 000
(107) water molecules will dissociate.
In reality, hydrogen ions do not exist freely in solution but are associated with water molecules. The
ionization of water should thus be written more correctly as: 2HOH ⇔ H3O+ + OH-. H3O+ is called the
hydronium ion and is, in aqueous solutions, the
ion responsible for acidic properties. For simplicity,
equations are normally written using H+.
By dissolving an acid in neutral water, the H+ concentration is increased by the H+ ions, which are
produced by the dissociation of that acid (figure
10). As a result, the water changes its properties, i.e. it tastes sour like vinegar or lemon juice,
and becomes corrosive and dissolves metals.
Figure 10 Formation of
an acid and base aqueous solution.
The hydrogen ion concentration in an aqueous
solution is expressed by the amount of non-dissociated water molecules in relation to one hydrogen ion, i.e.
g
if one H+ is found in 100 water molecules
we write 1:100 or 1/102 or 10-2
g
if one H+ is found in 10,000,000 water
molecules we write 1:10,000,000 or 1/107
or 10-7, and
g
if one H+ ion is found in 1,000,000,000
water molecules we write 1:1,000,000,000
or 1/109 or 10-9.
The ion product of dissociated H+ ions and dissociated OH- ions in water has been found to
be a constant of 10-14 (mole/liter) at 22°C. Thus,
when the concentration of H+ ions and OH- ions
in pure water are equal, the H+ ion concentration must be 10-7 and, of course, the OH- ion
concentration must be 10-7 as well.
This automatically leads to the definition of pH value, which is expressed as the negative base 10
logarithm of the active hydrogen ion concentration
in an aqueous solution, or in mathematical terms:
pH = - log[H+].
Acid solution
P08
Alkaline solution
Acknowledgements: We would like to thank
Erich K. Springer for his contributions to this
technical note.