Download Laboratory Practices from Physical Chemistry

SLOVAK UNIVERSITY OF TECHNOLOGY IN BRATISLAVA FACULTY OF CHEMICAL AND FOOD TECHNOLOGY INSTITUTE OF PHYSICAL CHEMISTRY AND CHEMICAL PHYSICS Laboratory Practices from Physical Chemistry REPORT ON TRAINING VISIT In the frame work of the project No. SAMRS 2009/09/02 “Development of human resource capacity of Kabul Polytechnic University” Funded by Bratislava 2011 Mir Hedayatullah Jalaly Contents Introduction ................................................................................................................................ 3 Acknowledgement ...................................................................................................................... 4 3 Polarimetry .............................................................................................................................. 5 4 Determination of molar mass of volatile liquids ..................................................................... 7 5 Surface tension of liquids ...................................................................................................... 11 6 Viscosimetric measurements ................................................................................................. 15 7 Calorimetry – determination of integral solvation enthalpy ................................................. 18 8 Determination of vapor pressure ........................................................................................... 22 11.2 Cryoscopy......................................................................................................................... 25 13 Determination of acidity constant of weak acid using conductivity measurements ........... 28 15.1 Quinhydrone electrode ..................................................................................................... 33 15.2 Fe3+/Fe2+ electrode ........................................................................................................... 36 17 Polarization of electrodes .................................................................................................... 39 18.2 Hydrolysis of ethyl acetoacetate ...................................................................................... 42 20 Kinetics of extinction of phenolphthalein color form in alkaline solution ......................... 45 22 Adsorption – Szyszkowski equation ................................................................................... 48 23 Adsorption on solid phase ................................................................................................... 51 24 Determination of molar absorption coefficient ................................................................... 55 Supplementary material – CD .................................................................................................. 57 References ................................................................................................................................ 58 2
Introduction This report is related to preparation of the instructions for Laboratory Practices from Physical
Chemistry. Prepared texts cover all fundamental parts of Physical Chemistry: states of matter
(perfect gas), thermodynamics, electrochemistry, chemical kinetics, as well as fundamentals
of colloid chemistry and molecular spectroscopy.
The main aim of this study was to become familiar with selected practices and to improve
the knowledge and practical skills on the basis of performed experiments and subsequent data
processing. This effort resulted in the preparation of texts for intended textbook for
Laboratory Practices from Physical Chemistry. This training visit also serves as a reference
for development of Laboratory from Physical Chemistry and its equipment at Kabul
Polytechnic University.
Prepared practices are numbered in accordance with the textbook of Klein et al. employed
at Faculty of Chemical and Food Technology in Bratislava which represents the basis of the
prepared texts.
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Acknowledgement The author would like to express his appreciation for the Training Program to Institute of
Physical Chemistry and Chemical Physics, Faculty of Chemical and Food Technology and
Slovak Aid program for financial support of this project. The author thanks Mr. Štefan Miksai
for helpful discussion about the organization and technical background/equipment inevitable
for laboratory practices. Author also thanks Assoc. Prof. Erik Klein for his guidance and
assistance during preparation of this report and Assoc. Prof. Juma Haydary, the coordinator of
SMARS/2009/09/02 project.
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3 Polarimetry Aim
Determination of specific rotation of optically active substance.
Theoretical part
In stereochemistry, the specific rotation of a chemical compound, [α ]tλ , is defined as the
observed angle of optical rotation α when plane-polarized monochromatic light is passed
through a sample with a optical path length of 1 m and a sample mass concentration, ρ2, of
1 kg m–3. The specific rotation of a substance is an intrinsic property of that substance at a
given wavelength and temperature. Specific rotation values should always be accompanied by
the temperature at which the measurement was performed and the wavelength of employed
monochromatic light. There is a linear relationship between the observed rotation angle, α,
and the concentration of optically active compound in the sample
α = [α ]tλ dρ 2
(1)
where d is the optical path length. This dependence is linear with zero intercept and line slope
b = [α ]tλ d which allows to determine specific rotation Equation 1 can be considered reliable
for diluted solutions.
Equipment and chemicals
Polarimeter; 100 ml volumetric flask; watch glass; 100 ml beaker; 50 ml volumetric flask
(5 pieces); 25 ml graduated pipette; funnel; optically active substance sample.
Experimental part
First, we turn sodium-vapor lamp on. In 100 ml volumetric flask, we prepare the stock
solution of optically active substance with mass concentration 100 kg m–3. Form the stock
solution, we prepare solutions with 80, 60, 40, 30 and 20 % of stock solution concentration at
laboratory temperature, t.
We fill the polarimetric tube with distilled water. No air bubble can be present in the tube.
We place the tube in the polarimeter and find the zero value of rotation angle, α0.
Analogously, we measure rotation angles of prepared solutions. We start form the solution
with the lowest concentration and finish with the stock solution. Firstly, polarimetric tube
should be rinsed with measured solution and then filled with that solution. Each measurement
is performed three-times. Measured values of the angle, α’, as well as their average are
summarized in Table 1.
Processing of the measured data
We correct measured α’ values using obtained α0 value
5
α = α’ – α0
(2)
Table 1. t = .................. °C, α0 = ..................
No.
1
2
3
4
5
6
ρ2/kg m–3
α’/°
α/°
20
30
40
60
80
100
Using linear regression, from α = f(ρ2) dependence, we find the value of specific rotation,
[α ]tλ . We construct α = f(ρ2) plot.
6
4 Determination of molar mass of volatile liquids Aim
To determine molar mass of volatile liquid sample by means of Meyer and Dumas methods.
Theoretical part
In the case of volatile liquid, their behavior can be described in terms of the equation of state
for a perfect gas, if the temperature is at least by 10 °C higher than its boiling point
pV = nRT = mRT/M
(1)
where p is pressure, T temperature, V volume, n amount of substance (number of moles), m
mass, M molar mass of the sample and R gas constant.
From eq. 1, we express the molar mass
M =
mRT
pV
(2)
or
M =
ρRT
(3)
p
where ρ is the density of the sample vapors (ρ = m/V).
Meyer method
Equipment and chemicals
Meyer apparatus; electric power source; syringe; analytic scales; 50 ml beaker.
Experimental part
Measurements are performed using modified Meyer apparatus (Fig. 1), which consists of
housing 1 with evaporation vessel 2. Evaporation vessel is closed with rubber stopper 3,
where syringe 4 can be inserted. Evaporation vessel heated by resistance wire is connected
with burette 6 via two-way cock 5. Water level in burette is equalized with vessel 7.
First, we turn the electric power source on in order to stabilize the temperature in the
evaporation vessel for 20 minutes. Meanwhile, we determine the value of atmospheric
pressure, patm, and the temperature in the laboratory, T. We turn the cock 5 to burette–
surroundings position. Then, we fix the vessel 7 in appropriate height to set the meniscus of
water in burette on zero. We detach the tube leading from the evaporation vessel 2 to burette
6. We attach the balloon to evaporation vessel in order to blow the traces of sample after
previous measurement out. Then, we attach the tube back and close the evaporation vessel
with stopper 3. We turn the cock 5 to burette–Meyer apparatus position. We check the correct
(zero) position of water meniscus in the burette. We add the sample to syringe and determine
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its weight, m1. We insert the syringe in the stopper opening and inject a small amount of
sample, ca 0.05 ml. Syringe remains inserted in stopper to keep the apparatus tight. Sample
evaporates and the water level in the burette is rapidly decreasing. When it stops to decrease,
we equalize the water levels in burette 6 and vessel 7 to eliminate the hydrostatic pressure of
the water in burette. We read the volume of air, V, corresponding to the volume of sample
vapor. Finally, we remove the syringe and determine its weight, m2. Sample weight, m, is
given as follows: m = m1 – m2. We repeat the measurement ten times. After all measurements,
we read the value of atmospheric pressure, patm, and temperature in the laboratory, T, again.
All results we summarize in Table 1.
Fig. 1. Meyer apparatus.
Table 1. T = .................. K, patm = .................. Pa, p(H2O) = .................. Pa
Measurement No.
1
2
⋅⋅⋅
10
m1/g
m2/g
m/g
106 V/m3
M/g mol–1
Processing of the measured data
In experimental data processing, we use average values of atmospheric pressure and
laboratory temperature. In burette, there are air and water vapor present. Therefore,
atmospheric pressure, patm, is the sum of air partial pressure, pa, and water partial pressure,
p(H2O). Thus, for partial pressure of air that is equal to vapor pressure, p, we can write
p = pa = patm – p(H2O)
(4)
8
The value of water vapor pressure we find in physico-chemical tables. Vapor pressure values
for temperatures that are not tabulated, we find by means of linear interpolation.
From eq. 2, we calculate molar masses of liquid for individual measurements and compile
them in Table 1. The molar mass of liquid we find as the average of all found values. We
calculate also the standard deviation of the molar mass.
Dumas method
Dumas method represents pycnometric method for gas-phase samples density determination.
Long narrow necked Dumas flask (with volume ca 100 ml) plays a role of pycnometer.
We set the temperature of the thermostatic bath by 10 °C higher than sample boiling point.
Using analytical scales, we determine the weight, m1, of empty Dumas flask with stopper.
We add ca 1–2 ml of sample to Dumas flask and we place it in the thermostatic bath with
temperature Tk. Only the end of the flask neck (1–2 cm) has to project from the bath. During
sample evaporation, all air from the flask escapes and the flask contains just sample vapor.
Sample evaporation process can be monitored using a small piece of filter paper set to the
flask neck. When vapor stops to escape from the flask, we close it with stopper. Then we
determine the weight of the dry flask with (condensed) vapor, m2. Laboratory temperature, t1,
has to be recorded, too. Since this part of experiment is crucial, we repeat it once again. We
place the flask back to the thermostatic bath. After a minute, we remove stopper and add ca
1 ml of liquid sample. When sample evaporation ends, we repeat the determination of the
weight of Dumas flask containing vapor. The two m2 values should be within 0.002 g. When
the difference is larger, we repeat m2 determination once again. Finally, we immerse the flask
into the vessel with distilled water (with temperature t2) and below the surface we remove the
stopper. Underpressure occurring after vapor condensation sucks the water into the flask
quickly. We determine the weight of dry flask filled with water, m3. In physico-chemical
tables we find density of air, ρa, at temperature t1 and water density ρ(H2O) at temperature
t2We record all data in Table 2.
Tale 2
m1/g m2/g m3/g
Tk/K
t1/°C ρa/kg m–3 t2/°C ρ(H2O)/kg m–3 patm/Pa
Processing of the measured data
Sample vapor density at Tk we calculate as follows
ρ=
m2 − m1
( ρ (H 2O) − ρa ) + ρ a
m3 − m1
(5)
where ρa and ρ(H2O) are densities of air and water, respectively. Using atmospheric pressure,
patm, value, we calculate the molar mass of the sample from eq. 3.
9
Table 3. Density of water, ρ, at various temperatures.
t/°C
ρ/kg m–3
0 999,868
1 999,927
2 999,968
3 999,992
4 1000,000
5 999,992
6 999,968
7 999,929
8 999,876
9 999,808
10 999,727
11 999,632
12 999,525
t/°C
13
14
15
16
17
18
19
20
21
22
23
24
25
ρ/kg m–3
t/°C
26
27
28
29
30
40
50
60
70
80
90
100
999,404
999,271
999,126
998,970
998,801
998,622
998,432
998,230
998,019
997,797
997,565
997,323
997,071
Table 4. Density of dry air, ρ, at various temperatures and pressures.
ρ/kg m–3 pri tlaku p/kPa
t/°C 94,659 95,992 97,325 98,568 99,992 101,325
0
1,208 1,225 1,242 1,259 1,276 1,293
2
1,199 1,216 1,233 1,250 1,267 1,284
4
1,191 1,207 1,224 1,241 1,258 1,274
6
1,182 1,199 1,215 1,232 1,249 1,265
8
1,174 1,190 1,207 1,223 1,240 1,256
10
1,165 1,182 1,198 1,215 1,231 1,247
11
1,161 1,178 1,194 1,210 1,227 1,243
12
1,157 1,173 1,190 1,206 1,222 1,239
13
1,153 1,169 1,186 1,202 1,218 1,234
14
1,149 1,165 1,181 1,198 1,214 1,230
15
1,145 1,161 1,177 1,193 1,210 1,226
16
1,141 1,157 1,173 1,189 1,205 1,221
17
1,137 1,153 1,169 1,185 1,201 1,217
18
1,133 1,149 1,165 1,181 1,197 1,213
19
1,129 1,145 1,161 1,177 1,193 1,209
20
1,126 1,141 1,157 1,173 1,189 1,205
21
1,122 1,137 1,153 1,169 1,185 1,201
22
1,118 1,134 1,149 1,165 1,181 1,197
23
1,114 1,130 1,145 1,161 1,177 1,193
24
1,110 1,126 1,142 1,157 1,173 1,189
25
1,107 1,122 1,138 1,153 1,169 1,185
26
1,103 1,118 1,134 1,149 1,165 1,181
27
1,099 1,115 1,130 1,146 1,161 1,177
28
1,096 1,111 1,126 1,142 1,157 1,173
29
1,092 1,107 1,123 1,138 1,153 1,169
30
1,088 1,104 1,119 1,134 1,150 1,165
10
ρ/kg m–3
996,810
995,539
995,259
995,971
995,673
992,240
988,070
977,810
988,070
971,530
965,340
955,380
5 Surface tension of liquids Aim
To determine the surface tension of liquid samples using bubble pressure method.
Theoretical part
In the bulk of the liquid, each molecule is in a force field of neighboring liquid molecules.
These forces are equal in every direction, therefore the net force is zero. Due to the
imbalanced forces (the forces between liquid molecules and gas are negligible), the molecules
in the surface layer are pulled inwards (Fig. 1). Thus, molecules in the surface layer have
higher potential energy in comparison to the molecules in the bulk. This forces liquid surfaces
to contract to the minimal area. The tension occurring in the surface is characterized by
surface tension, γ (unit N m–1).
Fig. 1. Intermolecular attractive forces in the vicinity of surface.
A growth of the surface of liquid is accompanied with transfer of molecules from bulk to
the surface formed. This needs to overcome attractive forces between molecules. Required
work is converted to surface potential energy that we call surface energy, σ (unit J m–2).
Fig. 2. Illustration of surface tension action.
Capillary action, often observed in nature, is a consequence of surface tension. In
laboratory, we can observe the capillary action when capillary tube is immersed in the liquid
(see Fig. 3). This phenomenon can be used for surface tension measurement.
For surface tension measurements, we employ bubble pressure method. Here, we have to
reach a pressure, p, to overcome capillary pressure, pγ (that keeps the liquid level in capillary
above its level in the vessel) and hydrostatic pressure, ph which depends on the depth of
capillary tube submersion, h (Fig. 3)
p = p γ + ph
(1)
11
Fig. 3. Determination of depth of capillary submersion.
For hydrostatic pressure, ph, of liquid column with a height h, we can write
ph = hgρ
(2)
where ρ is liquid density and g is standard acceleration of free fall.
Capillary pressure can be expressed as follows
p=
2πrγ 2γ
=
r
πr 2
(3)
where r is the diameter of the capillary.
Using eq. 2 and 3, eq.1 can be rewritten in this form
p=
2γ
+ h ρg
r
(4)
Pressure p is measured with water gauge. If the difference of water levels in the U-tube of the
gauge is h1, for the pressure p we obtain
p = h1ρ1g
(5)
where ρ1 is density of water. Then, eq. 4 can be expressed as
h1 ρ1 g =
2γ
+ hρg
r
(6)
This enables to find the following formula for surface tension
r
2
γ = ( h1 ρ1 − hρ ) g
(7)
Equipment and chemicals
Apparatus for surface tension measurement; laboratory stand; capillary (2 pieces), 25 ml
beaker; 150 ml beaker; 10 ml pycnometer.
12
Experimental part
First, we determine the capillary radius, r, by means of water surface tension measurement.
Temperature dependence of water surface tension can expressed as follows
γ1 = (75,872 – 0,154t – 0,00022t2)⋅10–3 N m–1
(8)
where t is temperature in °C. All measurements are performed at ambient temperature.
We clean the capillary K, rinse it with distilled water and ethanol and dry with compressed
air. Then we fix the capillary to apparatus (Fig. 4) and immerse it to beaker with water. We
fill the funnel A with water. Then we open the cock T to increase the pressure in the
apparatus. We find the maximum difference of water levels in U-tube of water gauge M, h1
(just before the first bubble escapes). Measurement is performed 10-times. In the same
manner, we determine the radius of second capillary.
Fig. 4. Apparatus for surface tension measurement.
Then, we employ dry capillaries in the measurements of studied liquid samples. We add the
liquid in the beaker and measure its surface tension at ambient temperature using above
described procedure. All results we compile in tables according Table 1.
Water density, ρ1, we find in physico-chemical tables; sample density, ρ, we determine by
means of pycnometry.
Processing of the measured data
Capillary radius, r, for all measurements we calculate on the basis of eq. 6
r=
2γ 1
(h1 − h) ρ1 g
(9)
since in the case of water, ρ = ρ1. Determined value of capillary radius is the average of
individual calculated values. Then, we use the obtained value of radius for sample surface
tension calculations according eq. 7.
13
We summarize all measured and calculated data in table and find average values of r and γ,
as well as their standard deviations.
For the second capillary, we construct analogous table.
Table 1. Results for the first capillary. t = .................. °C, water: ρ1 = .................. kg m–3,
sample 1: ρ = .................. kg m–3, sample 2: ρ = .................. kg m–3
No.
1
2
⋅⋅⋅
10
Average
water, h/m =
h1/m
rI/m
—
sample 1, h/m =
h1/m
γ1,I/N m–1
—
sample 2, h/m =
h1/m
γ2,I/N m–1
—
Finally, we compare determined surface tension values obtained for the first and the second
capillary and discuss possible differences.
14
6 Viscosimetric measurements Aim
Measurement of intrinsic viscosity of a liquid and the study of dependence of viscosity on
temperature.
Theoretical part
When a fluid flows, for example in a tube, the flow rate is not constant in each point. In the
vicinity of walls, liquid flows with lower speed, in the centre of the tube cross-section the
maximum speed is observed. We can imagine it as the series of layers moving past one
another.
If a force, F, affects such a layer with area S in direction parallel with layers, other layers
start to move, too. Neighboring layers move with lower speed and speed profile will be
formed in the liquid. Force between two layers with unit area is called tangential tension and
it is proportional to negative gradient of moving layers speed
τ =
F
dv
= −η
S
dx
(1)
where η is intrinsic viscosity (unit Pa s). Eq. 1 represents Newton law. All liquids and gases
that obey this equation are called Newtonian. The flow described by eq. 1 is laminar. Under
certain circumstances, for example when the flow speed is high enough, the layers start to tear
and mix – flow is then called turbulent.
In practice, kinematic viscosity, ν (units m2 s–1), is also used. It is defined as the ratio of
intrinsic viscosity and density of the liquid
ν=
η
ρ
(2)
Motion of the solid body in liquid
By free fall of the sphere-shaped solid body (ball) in liquid, gravity force, Fg, is oriented
downwards
4
FG = ms g = πr 3 ρ s g
3
(3)
where ms is the mass, ρs is density of the ball, r is ball radius and g is standard acceleration of
free fall. Friction force, Ffric, is oriented in opposite direction (upwards) and it can be
expressed in terms of Stokes equation
Ffric = 6πrηv
(4)
where v is the speed of the ball. In the same direction buoyancy force, Fb occurs
15
Fb = mg =
4 3
πr ρg
3
(5)
where m is the mass of liquid with the volume of the ball and ρ is liquid density.
When the sphere speed is constant, the sum of the three forces zero
FG – Ffric – Fb = 0
(6)
Using eqs. 3–5 and 6, we can express the viscosity as
η=
2 r2g
(ρs − ρ )
9 v
(7)
For speed, we can write v = s/t, then
η=
2 r 2 gt
( ρs − ρ )
9 s
(8)
where s is the distance passed by ball and it corresponds to time t.
In viscosity determination by means of falling ball (Höppler) viscometer, we measure time,
t, required for the passing the distance, s. In eq. 8, the constant term
2 r2g
9 s
(9)
represents a ball constant, K. Therefore, we can rewrite eq. 8
η = K ( ρ s − ρ )t
(10)
Ball constant as a characteristic of employed ball and it is provided by viscometer producer.
This constant depends on sphere radius, r, and distance, s, marked in viscometer.
Dependence of viscosity on temperature
In general, the viscosity decreases with temperature. This can be described using following
equation
1
η
= Ae
−
Evis
RT
(11)
where Evis (in J mol–1) is molar activation energy of viscous flow. It represents an energy
barrier of elementary flow process. Pre-exponential factor, A, represents a limiting value of
eq. 11, for T → ∞.
Equipment and chemicals
Falling ball viscometer (Höppler viscometer); stop-watch; densimeter; thermostatic bath; 25
ml beaker; studied liquid.
16
Experimental part
Measured sample is pre-heated to initial temperature. We turn the viscometer by 180° in order
to let the ball fall to bottom end of the tube. Then, we turn the viscometer to the working
position and fix it with the lock. When the bottom part of the ball passes upper mark, we start
to measure the time. When the bottom part of the ball passes by bottom mark, we stop the
time measurement. We perform three measurements (t1, t2, t3, see Table 1).
After the temperature increase, we wait at least 7 minutes (until temperature in viscometer
stabilizes) and then we perform three measurements for the new temperature. This procedure
is repeated up to maximum allowed temperature (usually 50 °C).
For all measurements, we read also the density of the studied liquid at the given
temperature. All data are compiled in Table 1.
Table 1. K = .................. m2 s–2, ball density ρs = .................. kg m–3
No. T/K
1
⋅⋅⋅
t1/s
t2/s
t3/s
t/s
ρ/kg m–3
η/Pa s
T–1/K–1
–ln(η/Pa–1 s–1)
Processing of the measured data
Using the values of ball constant K, ball density ρs, measured densities of studied liquid ρ,
and time t (average of t1, t2 and t3), we obtain viscosities from eq. 10. We construct η = f(T)
plot.
From linearized form of eq. 11
− lnη = ln A −
E vis
RT
(12)
we find parameters A and Evis using least squares fit. We construct –ln η = f(T–1) plot with
regression line, too.
17
7 Calorimetry – determination of integral solvation enthalpy Aim
Calorimetric determination of integral solvation enthalpies of studied salts.
Theoretical part
When a process is exothermic, energy has been transferred from a system to surroundings as
heat, q < 0. When system receives the energy as heat from surroundings, the heat has positive
sign, q > 0. Calorimetry enables the study of thermal effects of various chemical or physicochemical processes, e.g. reactions, dilution, solvation, adsorption. In calorimetric
measurements, which are at constant pressure, transferred heat is identical to the enthalpy
change, ΔH, of the system
q = ΔH
(dp = 0)
(1)
In calorimetry, we observe temperature changes accompanying the studied process. The
simplest form of calorimeter consists of a thermally insulated vessel with a precise
thermometer and stirrer.
Heat transferred between the system and surroundings is
q = –Cp(Tf–Ti) = –CpΔTcal
(dp = 0)
(2)
where Cp is heat capacity of the calorimeter at constant pressure – the amount of heat needed
to transfer to calorimeter in order to increase its temperature by 1 K. Ti and Tf are initial and
final temperatures of water (or solution) in calorimeter, respectively. Minus sign in eq. 2
means that heat transferred to/from system is expressed in terms of heat transferred from/to
surroundings (calorimeter), when temperature change ΔTcal occurs. In endothermic processes,
the system obtains the energy from calorimeter, therefore ΔTcal < 0 and q > 0. On the contrary,
if a process is exothermic, ΔTcal > 0 and q < 0. In eq. 2, it is supposed that heat capacity of the
calorimeter is constant, Cp≠f(T).
Heat capacity of the calorimeter is often determined by dissolving a substance with known
integral solvation enthalpy in water.
Equipment and chemicals
Calorimeter; stirrer; laboratory system CoachLab with temperature sensor; glass tube with
stopper; stick; watch glass (2 pieces); 500 ml graduated cylinder; KNO3; samples for
determination of solvation enthalpy.
A
Determination of heat capacity of the calorimeter, Cp
Experimental part
Heat capacity of the calorimeter, Cp, can be determined from dissolving the substance with
known value of integral molar solvation enthalpy, Δ sol H o . Here, we will employ KNO3 with
18
Δ sol H o (KNO3) = 36 008 J mol–1 (the value was determined for T = 291,15 K and molar ratio
of KNO3 and H2O 1 : 400).
Calorimeter (Fig. 1) consists of Dewar vessel D with lid Z, where temperature sensor T is
fixed, glass tube S containing KNO3 and electric stirrer M. Calorimeter contains distilled
water.
Fig. 1. Scheme of the calorimeter.
In calorimeter, we add 600 ml of distilled water. In glass tube S with the stopper on the
bottom end, we add such amount of KNO3 to obtain the molar ratio 1 : 400 (first, we have to
calculate its mass and then we weigh out required amount on analytic scales). We insert
temperature sensor in the lid Z of Dewar vessel and switch the stirrer M on. After ca 3 min of
temperature equilibration, we set 10 min measurement time with 1 reading per second
frequency in Measurement settings window of laboratory measurement system Coach
software (Fig. 2). Finally, we start the time-based measurement.
(a)
(b)
Fig. 2. Settings icon (a) and Measurement Settings window (b). Default value is Time-based.
When the temperature of the systems remains constants or it is linearly changing at least
3 min, using the stick, we push the stopper from the tube S. KNO3 starts to dissolve in water.
19
This is the end of Preliminary period and Main period starts (see Fig. 3). Due to rapid KNO3
dissolving, temperature change is fast, too.
Fig. 3. Tcal = f(t) dependence and determination of ΔTcal.
When the change in temperature is negligible, Main period ends and Final period starts. We
finish the measurement, when the temperature remains 3 min constant. During the
experiment, we follow temperature changes on monitor, where Tcal = f(t) curve is being
drawn.
Processing of the measured data
From Tcal = f(t) dependence (see Fig. 3), we find ΔTcal value as the temperature difference in
points B and C
ΔTcal = TC – TB
(3)
Heat capacity of the calorimeter, Cp, we obtain from following equation
Cp = −
Δ sol H o (KNO3 )m(KNO3 )
ΔTcal M (KNO3 )
(4)
where m(KNO3) is the mass and M(KNO3) is molar mass of KNO3.
B
Determination of standard integral solvation enthalpy of a sample
Experimental part
We add 600 ml of distilled water in calorimeter. In the glass tube S we add such amount of
sample – with mass m(X), to fulfill 1 : 400 molar ratio. Then, we perform measurement the
same way as in the heat capacity of the calorimeter determination.
20
Processing of the measured data
First, we find ΔTcal value (see part A). Then, we calculate the standard solvation enthalpy of
the sample, Δ sol H o (X)
Δ sol H o (X) = −
C p ΔTcal M (X)
(5)
m(X)
where M(X) is molar mass of the sample.
21
8 Determination of vapor pressure Aim
Determination of molar vaporization enthalpy.
Theoretical part
Vaporization is phase transition, where a substance changes its phase from liquid to gas.
Chemical potential of a substance by the phase transition at constant temperature and pressure
remains constant in the two phases.
Standard molar vaporization enthalpy Δ vap H o represents the energy required for
evaporation of 1 mol of a liquid at constant temperature and constant pressure equal to vapor
pressure at this temperature. Molar vaporization enthalpy (unit J mol–1) is positive and with an
increase in temperature it decreases.
Temperature vs pressure dependence by equilibrium phase transition can be described in
terms of Clapeyron equation. If the vaporization runs at constant temperature T (significantly
lower than critical temperature Tc) and constant pressure p and the vapor behaves as the
perfect gas ( Vm∗ (g) >> Vm∗ (l) ), Clapeyron equation can be rewritten as follows
o
d ln p ∗ Δ vap H
=
dT
RT 2
(1)
Eq. 1 is Clausius-Clapeyron equation for liquid-gas phase transition and it represents
dependence of vapor pressure of pure liquid, p*, on temperature, T.
After eq. 1 integration, assuming that standard molar vaporization enthalpy is not
temperature dependent, we obtain
ln p ∗ = −
Δ vap H o
RT
+I
(2)
where I is an integration constant. Dependence of ln p* = f(T–1) is linear with the intercept
a = I and slope b = −Δ vap H o / R . On the other hand, p* = f(T) dependence is exponential and
describes liquid-gas equilibrium curve in p-T phase diagram of pure substance.
Equipment and chemicals
Apparatus according Scheme 1; 25 ml beaker; laboratory measurement system CoachLab
with gas-pressure and temperature sensors.
22
Scheme 1. Apparatus for vapor pressure determination.
Experimental part
In isoteniscope 1, we add studied liquid. Isoteniscope is U-shaped tube connected to a vessel
of liquid on one side and a pressure gauge on the other. The vessel should be filled up to 2/3
and U-tube to 1/3 of their heights. We set the initial temperature on the thermostatic bath. We
place the isoteniscope 1 to the bath 2 and fix the reflux condenser 3. After ten minutes of
temperature equilibration, we start to decrease the pressure in the system using vacuum air
pump (air ejector) 4 in order to reach the boiling of the sample. First, we turn the air vacuum
pump on and turn the cock 6 into apparatus–pump position. We decrease the pressure until
sample vapor bubbles pass through the U-tube even the cock 6 is already closed. After ca 15–
20 seconds of sample evaporation, we adjust the pressure using the cock 7 until the liquid
level on both ends of the U are at the same level. This is the vapor pressure of the liquid – in
the manual measurements mode of CoachLab system we read the pressure, p*, and
temperature, T, values from sensors (9 and 10). For each temperature, we perform three
measurements. Then, using the cock 7, through the capillary 8, we slowly increase the
pressure in the apparatus, until atmospheric pressure is reached.
Now, we increase the temperature of the thermostatic bath by 4 °C. After 10 min
equilibration, we start the new vapor pressure measurement. This way, we measure the vapor
pressure values for 5–7 temperatures. All measured data, we compile in Table 1
Table 1
T/K
p*/Pa
T–1/K–1
ln (p*/Pa)
⋅⋅⋅
⋅⋅⋅
⋅⋅⋅
⋅⋅⋅
23
After all measurements, we close the cock 6. Using the cock 7, through the capillary 8, we
slowly increase the pressure in the apparatus, until atmospheric pressure is reached. Then we
turn the air ejector off. Never turn the air ejector off, if the pressure in the apparatus is lower
than atmospheric, otherwise water can contaminate the apparatus.
Processing of the measured data
We calculate T–1 and ln p* values required in Table 1. Then, we construct ln p* = f(T–1) and
p* = f(T) plots. Parameters a and b of ln p* = f(T–1) linear dependence (eq. 2) we find from
linear regression. From line slope b, we calculate molar vaporization enthalpy, Δ vap H o ,
value.
24
11.2 Cryoscopy Aim
Cryoscopic determination of molar mass of nonelectrolyte.
Theoretical part
The depression of freezing point arising from presence of a solute represents one of
colligative properties. In dilute solutions, these properties depend only on the number of
solute particles present, not their identity. We will assume that the solute does not dissolve in
the solid solvent, i.e. the pure solid solvent separates when the solution is frozen.
In the case of diluted solutions, for depression of freezing point, ΔTc, we can derive the
equation
ΔTc = Ecb2
(b2 → 0)
(1)
where b2 is the molality of the solute and Ec is empirical cryoscopic constant of solvent. Its
value depends only on the solvent properties
Ec =
RTc2 M1
Δ fus H1*
(2)
where Tc is solvent freezing point, M1 is molar mass of the solvent, and Δ fus H1* is the
enthalpy of fusion of the solvent.
For the molality b2 we can write
b2 = n2 / m1 = (m2 / M 2 ) / m1
(3)
where m2 is mass of the solute in solution, M2 is its molar mass and m1 is the mass of the
solvent. For M2, from eqs. 1 and 3 we obtain
M 2 = (m2 / ΔTc )( Ec / m1 )
(4)
Here, one should keep in mind that all above mentioned equations are valid for infinitely
diluted solution (b2 → 0). Therefore, in real measurements, the results have to be extrapolated
to infinitely diluted solution
Ee = lim (ΔTe / b2 )
(5)
M 2 = ( Ec / m1 ) lim (m2 / ΔTc )
(6)
b2 →0
or
m2 → 0
Equipment and chemicals
25
Device for cryoscopic measurements; laboratory system CoachLab with temperature sensor;
10 ml weighing bottles (3 pieces); 25 ml graduated pipette; 250 ml beaker; NaCl; crushed ice.
Experimental part
For the cryoscopic determination of the sample molar mass, we employ device depicted in
Fig. 1. In vessel 1, we prepare cooling mixture (5 : 1 crushed ice and NaCl). Cooling bath
temperature, we monitor by auxiliary thermometer and the appropriate temperature is
controlled by adding ice or salt and its stirring. During the measurement, cooling mixture
temperature should be 3–5 °C bellow the solvent freezing point.
Fig. 1. Device for cryoscopy.
In each of three clean weighing bottles, we add ca 0.5 g of the sample. The mass of the
sample has to be determined with 0.001 g precision. We clean the cryoscopic tube 2
thoroughly. In dry cryoscopic tube, we add 25 ml of distilled water and close the tube with the
stopper 3 equipped with the stirrer. In stopper, we insert temperature sensor. The sensor
should not be in contact with tube wall or stirrer. We place the prepared tube in cooling
mixture. We stir the distilled water in tube until ice starts to form. This way we find an
approximate value of water freezing point. Then, we remove the tube from the cooling
mixture and elevate the temperature of the sample holding the tube in the hand to melt all ice
in the tube. Then, we place the tube back to cooling mixture and stir it slowly (1 lift in 2
seconds). We let the temperature fall ca 0.2–0.3 °C bellow the found freezing point. When
lower temperature drop is observed, we induce the fusion by means of intensive stirring. Due
to evolved heat of fusion, the temperature rises to freezing point. We keep on stirring and
follow the temperature. Maximum temperature, which remains at least one minute constant, is
the freezing point of solvent, T0. Again, we remove the tube from the cooling mixture and
warm it in the hand up to temperature 2–3 °C above freezing point. We determine T0 value
three-times and in data processing we use the average value.
Freezing point of the solution is found same way. We add the solute in the tube. When it
dissolves, we determine the solution freezing point. The freezing point of the solution is the
maximum temperature reached after under-cooling the solution. We perform three
measurements for every molality. We measure the solutions with three molality values to
obtain T1, T2 and T3 freezing points as the average values from three measurements for each
molality. The molality of solution is the sum of added amounts of the solute.
26
Processing of the measured data
Measured values are compiled in Tables 1 and 2. We calculate average freezing point of the
solvent, T0. For each addition of the solute, we determine average freezing point, Ti,
depression of freezing point ΔTci = T0 –Ti, and m2i/ΔTci ratio.
Table 1. Freezing point of the solvent,
m1 = .................., Ec = ..................
T01/K
T02/K
T03/K
T0/K
Table 2.
Solute amount
No.
Net m2i/g
1
2
3
Ti1/K
Ti2/K
Ti3/K
Ti/K
ΔTci/K
(m2i/ΔTki)/(g K–1)
lim (m2i / ΔTci ) = ..................
m 2i → 0
We construct m2i/ΔTci = f(m2i), where i = 1, 2, 3, plot for the solute. From extrapolation to
m2i → 0, we find limiting value of this ratio. Then, using eq. 6, we calculate sample molar
mass. Water cryoscopic constant we find in Table 3.
Table 3. Freezing point and cryoscopic constants for selected solvents
at 101 325 Pa.
Solvent
water
benzene
cyclohexane
cyclohexanol
camphor
acetic acid
nitrobenzene
naphthalene
Ec/K kg mol–1
1.859
5.10
20.2
38.3
40.0
3.90
6.90
6.80
t/°C
0.00
5.53
6.55
20.0
178.0
16.60
5.70
80.2
27
13 Determination of acidity constant of weak acid using conductivity measurements Aim
Conductometric determination of acidity constant of acetic acid, CH3COOH.
Theoretical part
Dissociation of weak acid, HA, runs according the equation
HA + H2O = H3O+ + A–
with acidity constant, KHA
K HA =
aH + aA −
(1)
aH2O aHA
where aH+ = aH3O+. Since activities are dependent on standard state definition, acidity constant,
KHA, also depends on the standard states of solution constituents. Here, activities will be
expressed using this formula
ai =
ci f i
co
where fi is molar activity coefficient and standard molar concentration is co = 1 mol dm–3. In
diluted solutions, the activity of water can be considered aH2O = 1. Therefore
K HA =
cH + cA − f H + f A −
cHA
f HA
= kHA
fH+ fA−
( a H 2O = 1 )
f HA
(2)
where kHA is the concentration equilibrium quotient. For the sake of simplicity, in further
equations, standard concentration, co , will be omitted. However, one should keep in mind that
activities are dimensionless and all concentrations have to be expressed in the units of
standard concentration.
When dissociation of water molecules is neglected, for concentrations of H+ and A– ions
can be written
cA − = cH + , cHA = c0 − cH +
where c0 represents the acid concentration. Because weak acids are ionized only partially,
above mentioned concentrations may be expressed in terms of ionization degree, αHA
α HA = cA / c0 ⇒ cA = cH = α HA c0 , cHA = c0 (1 − α HA )
−
−
+
Then, for acidity constant, KHA, we obtain
28
K HA = c0
2
2
α HA
α HA
f ±2 = k HA f ±2 , k HA = c0
1 − α HA
1 − α HA
( aH 2O = 1 , fHA = 1)
(3)
Here, activity coefficients of ions were replaced by mean activity coefficient, f±, f± = (f+f–)1/2.
In very diluted solutions, limiting Debye-Hückel equation
(Ic → 0)
log f ± = − Ac z + z − I c
(4)
may be used for mean activity coefficients calculations. Constant, Ac, has the value of
0.5115 dm3/2 mol–1/2 for 25 °C, z+ and z– are charges of ions and Ic is the ionic strength of
solution
Ic =
1
ci zi2
∑
2 i
where ci is concentration of i-th ion with zi charge. Ionic strength of solution expresses overall
effect of electrostatic forces between ions in the solution. For uni-univalent electrolyte,
following expressions can be written: z+ = 1, z– = –1, Ic = (c+×12 + c–×(–1)2)/2 = (c+ + c–)/2.
For the weak acid we get
I c = (cH + + cA− ) / 2 = (α HA c0 + α HA c0 ) / 2 = α HA c0
From eq. 3, we obtain log KHA = log kHA + 2log f±. Then, using eq. 4, we can write
log K HA = log k HA − 2 Ac α HA c0
(5)
While the acidity constant, KHA, depends only on the temperature, the pressure and the solvent
properties, concentration equilibrium quotient, kHA, also depends on the solution composition.
Therefore, in eq. 5, log kHA, is the dependent variable and KHA is a constant. After the
rearrangement of the eq. 5, we can write
log k HA = log K HA + 2 Ac α HA c0
(6)
This dependence is linear (y = a + bx) with a = log KHA intercept and b = 2Ac line slope.
Acidity constant, KHA, will be determined from the conductivity measurements.
Conductance, G, of the prepared solutions with various HA concentrations will be measured.
Conductance of a conductor − solution with the constant cross-section, S, and the length, l, is
G=
S
1
=κ
R
l
(7)
where κ is conductivity and R is resistance of the solution. Conductivity of the solution, κ,
represents the sum of conductivities of individual constituents of the solution, κi, and
conductivity of the solvent, κsolv
29
κ = κ solv + ∑ κ i
i
In this experiment, conductivity of solution is the sum of conductivities of weak acid HA and
water, κ = κHA + κH2O. From known conductivities of the solution and the water, conductivity
of the acid HA, κHA, can be calculated as follows
κHA = κ – κH2O
(8)
Both, the conductance (unit Siemens, S) and the conductivity (unit S m–1) of a solution
depend on temperature.
Conductance of an electrolyte solution is measured in the conductometric cell using
alternating current with the sufficiently high frequency to prevent the electrolysis of the
solution. However, measured value of the conductance depends on the geometry of the cell
(cross-section of the electrodes and their distance, see eq. 7). Therefore, conductometric cell
constant, C, serves to characterize the employed cell
C =κ /G =
l
S
(9)
Cell constant, C (unit m–1), can be determined from the measurement of the conductance of
the solution with known conductivity.
In the case of weak electrolytes, ionization degree, α, can be find on the basis of molar
conductivity, λ, and limiting molar conductivity, λ∞i (molar conductivity in the infinitely
diluted solution), of an electrolyte
α = λ / λ∞
(10)
Molar conductivity, λ (unit S m2 mol–1), of an electrolyte depends on its conductivity and its
concentration
λ =κ /c
(11)
where c is molar concentration of the electrolyte. According Kohlrausch law, for limiting
molar conductivity, λ∞i , we can write
λ∞ = λ∞+ + λ∞−
(ci → 0)
(12)
where λ∞+ and λ∞− are limiting molar conductivities of the cation and the anion. In an infinitely
diluted solution, weak electrolyte can be considered fully ionized (α = 1). Besides, ions are
not interacting together and their movements are independent. For the ionization degree of the
weak acid, αHA, and the concentration equilibrium quotient calculations, kHA we will employ
following equations
α HA = λHA / λ∞HA
λHA = κ HA / c0
(13)
30
λ∞HA = λ∞H + λ∞A
+
−
Equipment and chemicals
Conductometer or laboratory system CoachLab with conductometric sensor; volumetric flasks
100 cm3 (6 pieces); pipette 50 ml; beaker 25 ml; thermometer; CH3COOH stock solution with
0,125 mol L–1 concentration; KCl solution, 0,1 mol L–1 concentration.
Experimental part
From the CH3COOH stock solution, diluted solutions with the concentrations according
Table 1 are prepared. The solution with higher concentration is always diluted with the
distilled water in 1:2 ratio in volumetric flasks. Every solution has to be mixed thoroughly.
Before measurements, conductometric cell and the beaker used for measurements have to
be carefully rinsed with distilled water (at least five times). First, conductance of the distilled
water, GH2O, has to be measured. Then, CH3COOH solutions, in order of increasing
concentrations, are measured. Before each measurement, the cell and the beaker have to be
thoroughly rinsed with the corresponding solution. Conductance of each solution is measured
three times, for the calculations average value is used. Finally, the conductance of 0.1 mol L–1
KCl solution, GKCl, is measured (again, three times). All measured data, together with the
value of the temperature in laboratory, t, are compiled in Table 1.
Table 1. t = .................., GKCl = .................., C = .................., GH2O = .................., κH2O = ..................
No.
c0
mol dm −3
1
2
3
4
5
6
7
1/8
1/16
1/32
1/64
1/128
1/256
1/512
G
S
κ HA
κ
Sm
−1
Sm
−1
λHA
2
S m mol
−1
αHA
kHA
log kHA
(α HA c0 )1 / 2
(mol dm −3 )1 / 2
Processing of the measured data
First, we calculate the conductometric cell constant, C, using the conductance of KCl solution.
Its conductivity can be found in Table 2. From the average value of measured GKCl and κKCl,
we can get the cell constant, C, from eq. 9. This equation allows also the calculations of the
conductivities of CH3COOH solutions,κ, and the conductivity of distilled water, κH2O. For the
calculations of molar conductivities of CH3COOH, λHA, using eq. 13, we need to know the
conductivity of CH3COOH,κHA, which we obtain from eq. 8.
31
Table 2. Conductivity of 0.1 mol L–1 KCl for various
temperatures.
t/°C
18
19
20
21
22
23
24
25
κ/S m–1
1.113
1.143
1.167
1.191
1.215
1.239
1.264
1.269
Limiting molar conductivity of CH3COOH, λ∞HA , represents the sum of limiting molar
conductivities of H+ cation and A– anion (eq. 13). Their values are summarized in Table 3.
For other temperatures within 18–25 °C range, limiting molar conductivities have to be
calculated using linear interpolation.
Table 3. Limiting molar conductivities of ions.
Ion
+
H
CH3COO–
λ∞i /S m2 mol–1
t = 18 °C
0.0314
0.00346
t = 25 °C
0.0350
0.00408
Ionization degree of the acid, αHA, can be obtained from eq. 13 and the value of concentration
equilibrium quotient, kHA, from eq. 3. Then, we calculate values of log kHA and (αHAc0)1/2. All
results are compiled in Table 1.
Finally, we plot log kHA= f(αHAc0)1/2 dependence (eq. 6). Using the linear regression (least
squares fit) we find the acidity constant, K ( co = 1 mol L–1), value.
HA
32
15.1 Quinhydrone electrode Aim
Determination of the standard electrode potential of quinhydrone electrode.
Theoretical part
Quinhydrone electrode consists of a inert metal (gold or platinum) immersed in saturated
water solution of quinhydrone (ChH), which represents equimolecular complex of quinone
(Ch) and hydroquinone (ChH2)
C6H4O2⋅C6H4(OH)2 = C6H4O2 + C6H4(OH)2
or
ChH = Ch + ChH2
On this electrode, redox reaction
C6H4O2 + 2H+ + 2e– = C6H4(OH)2
takes place. For the potential of quinhydrone electrode we can write
E (Ch/ChH 2 ) = E o (Ch/ChH 2 ) −
a(ChH 2 )
RT
ln
2 F a (Ch )a 2 (H + )
(1)
where E o (Ch/ChH2) is the standard potential of quinhydrone electrode.
Quinhydrone is weak dibasic acid and in acid solutions it is dissociated in very small
extent. Therefore, concentrations of quinone (Ch) and hydroquinone (ChH2) can be
considered equal and activities of Ch and ChH2 can be considered equal, too. Then, eq. 1 can
be written this form
E (Ch/ChH 2 ) = E o (Ch/ChH 2 ) +
RT
ln a(H + )
F
(2)
Proton activity, a(H+), we determine as the product of proton concentration, c(H+), and the
activity coefficient, f(H+). Activity coefficient, f(H+), can be calculated using extended DebyeHückel law
log f i = −
0,5115 zi2 I c
(3)
1 + Ic
where Ic is the ionic strength of the solution
Ic =
1
ci zi2
∑
2 i
(4)
33
Equipment and chemicals
Vessel for the galvanic cell construction; voltmeter suitable for cell potential measurement;
platinum electrode; calomel electrode; cords; 0.5 mol L–1 HCl; quinhydrone; volumetric
flasks 50 ml (4 pieces); beaker 50 ml; beaker 250 ml, pipette 10 ml.
Experimental part
First, we construct the galvanic cell using quinhydrone and calomel electrode
(–) Hg, Hg2Cl2 | KCl(aq. sat.) || H+(aq), ChH | Pt (+)
Then, we prepare HCl solutions with 0.10, 0.02, 0.004 a 0.0008 mol L–1 by means of sequent
dilution (1 : 5) of the 0.5 mol L–1 HCl stock solution. HCl solution with given concentration is
then placed into the beaker and small amount of quinhydrone is added. After 2 minutes
stirring, we place the solution into the galvanic cell compartment with platinum electrode in
order to measure cell potential, E. It should be stabilized within 2 minutes.
Processing of the measured data
From eq. 4, we obtain the ionic strengths of individual HCl solutions. Then, using eq. 3, we
calculate activity coefficients of the solutions. The potential of quinhydrone electrode,
E(Ch/ChH2), can be calculated from the equation defining the cell potential
E = E(Ch/ChH2) – E(Hg2Cl2/Cl–)
(5)
Potential of the saturated (sat.) calomel electrode for the given temperature, t, we find from
the following equation
E(Hg2Cl2/KCl, aq. sat.)/V = [0.244 – 7.6×10–4(t/°C – 25)]
(6)
Activities of H+ ions are calculated from the concentrations and activity coefficients
a(H+) = c(H+)f(H+)
Finally, ln a(H+) values (for co = 1 mol L–1) are calculated. All measured and calculated
quantities we summarize in Table 1.
Table 1. t = ..................
No.
1
2
3
4
5
c(H+)/mol L–1
0.5
0.1
0.02
0.04
0.008
E/V
Ic/mol L–1
f(H+)
34
a(H+)
ln a(H+)
E(Ch/ChH2)/V
Using linear regression, from E(ChH) = f(ln a(H+)) dependence we obtain an intercept, a, and
a line slope, b, where a = E o (Ch/ChH2) and b = RT/F. E o (Ch/ChH2) represents the standard
electrode potential of quinhydrone electrode. From the line slope, b, we calculate the value of
Faraday constant, F. We compare obtained value with the tabulated one: 96485 C mol–1.
35
15.2 Fe3+/Fe2+ electrode Aim
Determination of the standard electrode potential of Fe3+/Fe2+ electrode.
Theoretical part
Fe3+/Fe2+ electrode consists of a inert metal (platinum) immersed in the solution of Fe3+ and
Fe2+ ions. The electrode reaction is as follows
Fe3+(aq) + e– = Fe2+(aq)
For the potential of the electrode, we can write
E (Fe 3+ /Fe 2+ ) = E o ( Fe 3+ /Fe 2+ ) −
RT a ( Fe 2+ )
ln
F
a (Fe 3+ )
(1)
where E o (Fe3+/Fe2+) is the standard potential of Fe3+/Fe2+ redox system, a(Fe3+) and a(Fe2+)
represent activities of Fe3+ and Fe2+ ions in solution, respectively. Activities can be expressed
in the terms of concentrations and activity coefficients (a = c f , co = 1 mol L–1), therefore
i
E (Fe3+ /Fe 2+ ) −
i i
RT c(Fe 2+ )
2,303RT
Δ (log f ) = E o (Fe3+ /Fe 2+ ) −
ln
F
F
c(Fe3+ )
(2)
where
Δ(log f) = log f(Fe3+) – log f(Fe2+)
(3)
Using the extended Debye-Hückel law, for Δ(log f), we can write
Δ(log f ) = −
0,5115 ⋅ 32 I c
1 + Ic
+
0,5115 ⋅ 2 2 I c
1 + Ic
=−
0,5115 ⋅ 5 I c
1 + Ic
(4)
Equipment and chemicals
Vessel for the galvanic cell construction; voltmeter suitable for cell potential measurement;
platinum electrode; calomel electrode; cords; KI (solid); 0.5 mol L–1 HCl; diluted H2SO4
(1 : 1); 0.05 mol L–1 Na2S2O3; 0.01 mol L–1 KMnO4; 0.1 mol L–1 (NH4)2Fe(SO4)2; 0.1 mol L–1
NH4Fe(SO4)2; starch indicator solution; Erlenmayer flasks 100 ml (5 pieces); Erlenmayer
flasks 100 ml with stoppers (3 pieces); titration flasks 250 ml (2 pieces); pipettes 25 ml;
funnels (2 pieces); plastic spoon; beakers 100 ml (2 pieces); beaker 250 ml; burettes 25 ml
(2 pieces).
36
Experimental part
First, we construct the galvanic cell with the platinum electrode immersed in Fe3+/Fe2+ ions
solution and the calomel electrode
(–) Hg, Hg2Cl2 | KCl(aq, nas.) || Fe3+/Fe2+(aq) | Pt (+)
From (NH4)2Fe(SO4)2 and NH4Fe(SO4)2 stock solutions we prepare calibration solutions
according Table 1.
Table 1
V(Fe3+) : V(Fe2+)
V(Fe3+)/ml
V(Fe2+)/ml
10 : 1
40.0
4.0
5:1
35.0
7.0
1:1
20.0
20.0
1:5
7.0
35.0
1 : 10
4.0
40.0
Actual concentrations of Fe3+ and Fe2+ ions in prepared calibration solutions are determined
by means of titration.
Fe3+
10 ml of the solution, 1 ml of diluted HCl and approximately 2 g of KI (one spoon) are added
to Erlenmayer flask. We close the flask with stopper. After 10 min, formed iodine is titrated
using Na2S2O3 solution until the solution color turns to light yellow. After adding 1 ml of
starch indicator solution (solution color turns to dark) we continue the titration until the
extinction of blue color. In Fe3+ concentration determination, following reactions take place
2Fe3+ + 2I– = 2Fe2+ + I2
I2 + 2 SO 32− = 2 I– + S4 O 62−
Fe2+
10 ml of the solution and 3 ml of diluted H2SO4 (1 : 1) are added to the titration flask. The
solution is titrated by KMnO4 solution until the solution turns to light rosy
5Fe2+ + MnO −4 + 8 H+ = 5Fe3+ + Mn2+ + 4H2O
Now, we add individual calibration solutions into Pt electrode compartment in order to
measure the cell potential, E. We summarize all measured values in Table 2.
Table 2
No.
1
2
3
4
5
V(Fe3+) : V(Fe2+)
10 : 1
5:1
1:1
1:5
1 : 10
V(Na2S2O3)/ml
37
V(KMnO4)/ml
E/V
Processing of the measured data
From the titration results, we find concentrations of Fe3+ and Fe2+ ions required for the ionic
strengths of calibration solutions
Ic = 7c(Fe2+) + 9c(Fe3+)
(5)
From eq. 4, we obtain Δ(log f). Cell potential is given by
E = E(Fe3+/Fe2+) – E(Hg2Cl2/Cl–)
(6)
where the potential of the saturated (sat.) calomel electrode for the given temperature, t, we
find from the following equation
E(Hg2Cl2/KCl, aq. sat.)/V = [0.244 – 7.6×10–4(t/°C – 25)]
(7)
Using eq. 6, we obtain E(Fe3+/Fe2+) potentials. Finally, for all solutions we calculate
quantities x and y as follows
x = ln
2,303RT
c(Fe3+ )
, y = E (Fe3+ /Fe 2+ ) −
Δ(log f )
2+
F
c(Fe )
(8)
All calculation results are compiled in Table 3.
Table 3. t = ..................
No.
c(Fe3+)/
mol L–1
c(Fe2+)/
mol L–1
Ic/mol dm–3
Δ(log f)
E(Fe3+/Fe2+)/V
x
y/V
1
⋅⋅⋅
Dependence of y = f(x) is linear with the intercept a = E o (Fe3+/Fe2+) and the line slope b =
RT/F. From linear regression (least squares fit) we determine standard potential E o (Fe3+/Fe2+)
corresponding to the intercept, a (see eq. 2). Finally, we construct the plot of the above
mentioned linear dependence.
38
17 Polarization of electrodes Aim
Observation of changes occurring on the electrodes that result from the application of
potential difference.
Theoretical part
When two identical electrodes (e.g. platinum) are immersed in a solution, the two electrodes
gain identical potentials (E1 = E2). After connecting the external source of unidirectional
voltage, U, electrolysis begins. On the cathode and anode, products of electrolysis are
different and the electrodes gain different potentials (E1 ≠ E2). After turning off the external
voltage source, formed cell has potential
Ep = E2 – E1
(1)
Potential Ep represents the polarization potential. It has inverse polarity in comparison to the
external source of potential (Le Chatelier’s principle). Applied potential, U, and polarization
potential of formed electrolytic cell, Ep, are compensated (U – Ep ≈ 0). A low electric current,
I, observed in the cell is caused by diffusion of certain amounts of the gas products from the
electrode surface (see Fig. 1, AB part).
Fig. 1. I vs U dependence for a cell with two polarizable electrodes.
Increase in the potential U causes the increase in polarization potential of the cell. However,
the polarization potential, Ep, reaches a limit denoted as the maximum polarization potential,
Ep,max. Further increase in potential U does not lead to a higher value of the polarization
potential. Through the circuit flows an electric current according Ohm’s and Kirchhoff’s law
I=
U − E p ,max
(2)
R
where R is the resistance of the system.
39
When hydrochloric acid is used as the electrolyte, applied potential induces polarization of
platinum electrodes. On the surface of positive electrode, gaseous chlorine is formed
2Cl–(aq) – 2e– = Cl2(g)
On the surface of negative electrode, gaseous hydrogen is formed
2H+(aq) + 2e– = H2(g)
Therefore, we obtain chlorine and hydrogen electrodes with potentials
E (H + / H 2 ) =
RT a 2 (H + )
ln
2F
a (H 2 )
E (Cl 2 / Cl − ) = E o (Cl 2 / Cl − ) −
(3)
RT a 2 (Cl − )
ln
2F
a(Cl 2 )
(4)
When we employ a(Cl2) = p(Cl2) / p o , a(H2) = p(H2) / p o , and a(H+) = a(Cl–) = a±(HCl), then
for the polarization potential, we can write
Ep = E(Cl2/Cl–) – E(H+/H2)
E p = E o (Cl 2 / Cl − ) −
RT
RT
( po ) 2
ln a±4 ( HCl) −
ln
2F
2 F p (Cl 2 ) p ( H 2 )
(5)
From eq. 5, it follows that the cell potential of secondary formed galvanic cell (polarization
potential) is proportional to the partial pressures of formed H2 and Cl2 if the concentration of
HCl remains constant (a±(HCl) = const.). Maximum value of the polarization potential is
reached when the partial pressures p(H2) and p(Cl2) are equal to atmospheric pressure (patm =
p o ). For different concentrations of HCl solutions, different values of maximum polarization
potential are obtained. If p o is equal to the atmospheric pressure (101 325 Pa) and a±(HCl) =
1, Ep = | E o (Cl2/Cl–)| = 1,3593 V (for 25 °C).
Usually, maximum polarization potential, Ep,max, is determined from I = f(U) curve. Its shape
is depicted in Fig. 1. Maximum polarization potential value can be found from the point of
intersection of the linear parts of I = f(U) curve – as shown in Fig. 1.
Equipment and chemicals
Source of unidirectional voltage; voltmeter; mili-ammeter; rheostat; electrolytic cell (Fig. 2a);
cords; pipette 50 ml; volumetric flasks 100 ml (2 pieces); beaker 150 ml; beaker 50 ml;
funnel; HCl stock solution, c = 1 mol L–1.
40
Fig. 2. (a) Electrolytic cell: 1 – Pt electrodes, 2 – electrolyte, 3 – clamps. (b) Scheme of polarization potential
measurements apparatus.
Experimental part
We add the HCl stock solution to the electrolytic cell. Next, we switch the external source of
potential on. Using the rheostat R, we change the voltage from 0 V to 1.8 V with ca 0.1 V
step. For each potential, we read corresponding value of the flowing current. After the
increase in external potential, it is required to wait ca half a minute and then the value of the
current can be read.
External potential values and the corresponding currents are compiled in the Table 1. We
repeat this procedure also for 0.5, 0.25 a 0.125 mol L–1 HCl solutions. Results are compiled in
the tables constructed as Table 1.
Table 1. t = .................., c = ..................
No.
1
⋅⋅⋅
U/V
I/mA
Processing of the measured data
For individual concentrations, we plot measured I = f(U) dependences. Then, we find the
maximum polarization potential values, Ep,max (see the method described above). Found Ep,max
values are then compiled in Table 2 and Ep,max = f(c) plot is constructed.
41
18.2 Hydrolysis of ethyl acetoacetate Aim
Study of kinetics of hydrolysis of ethyl acetoacetate and the determination of the reaction rate
constant.
Theoretical part
In acidic environment, hydrolysis of ethyl acetoacetate occurs. Acetic acid and ethanol are
reaction products
+
CH 3COOC 2 H 5 + H 2 O ⎯H⎯→ CH 3COOH + C 2 H 5 OH
(1)
Because water is in the reaction mixture in a large excess, the reaction rate depends only on
the ethyl acetoacetate concentration. The kinetics of reaction therefore can be described using
first order rate law
−
dcA
= kcA cA
dt
(dT = dV = 0)
(2)
with integrated rate law
⎛c ⎞
k cA t = ln⎜⎜ 0 A ⎟⎟
⎝ cA ⎠
(3)
where c0A is the concentration of ethyl acetoacetate in time t = 0, cA is its concentration in
time t and kcA is the first-order rate constant of reaction 1.
In the course of the reaction, the acidity of reaction mixture grows. Therefore, the process
of the hydrolysis of ethyl acetoacetate can be monitored titrimetrically – by means of titration
with sodium hydroxide, NaOH. The consumption of NaOH solution represents an additive
property of the system and we can write
c0A V∞ − V0
=
cA V∞ − Vt
(4)
where V0 is the consumption of NaOH solution used for H+ ions in t = 0 (at the beginning of
reaction), Vt is the consumption of NaOH solution used in time t (during the reaction) and V∞
is the consumption of NaOH solution corresponding to time t = ∞ (the end of the reaction).
From eqs. 3 and 4, it follows
ln
V∞ − V0
= k cA t
V∞ − Vt
(5)
or
42
ln (V∞ – Vt) = ln (V∞ – V0) – kcAt
(6)
Eq. 6 shows that ln(V∞ – Vt) = f(t) dependence is linear with intercept a and line slope b
a = ln (V∞ – V0), b = –kcA
(7)
Equipment and chemicals
Thermostatic bath; cooling vessel with crushed ice/water mixture; Erlenmayer flasks 250 ml
(2 pieces); stopper; graduated cylinder 250 ml; graduated cylinder 10 ml; titration flasks (2
pieces); pipettes 5 ml (2 pieces); reflux condenser; beaker 250 ml; ethyl acetoacetate; HCl
(c = 1 mol L–1); NaOH (c = 0.2 mol L–1); phenolphthalein.
Experimental part
200 ml of 1 mol L–1 HCl solution (measured using graduated cylinder) are added to 250 ml
Erlenmayer flask. The flask is then placed to the thermostatic bath with chosen temperature
set. After 15 minutes, we add 10 ml of ethyl acetoacetate. After short, but thorough, stirring,
we take 5 ml of reaction mixture using dry pipette to perform its titration immediately (t = 0)
in order to determine the consumption of NaOH, V0. Erlenmayer flask with the stopper is
placed back to the thermostatic bath.
Next samples are taken in t = 20, 40, 60, 80, 100 and 120 minutes. All samples are handled
following way: we add 50 ml of distilled water to titration flask and place the flask to vessel
with the crushed ice to decrease the temperature of the water (optimum 0–5 °C). Using dry
clean pipette, we take 5 ml sample from the reaction mixture and add it to the cooled water.
Decrease in the temperature and the dilution of the sample results in the reaction slowdown.
This way prepared sample is immediately titrated using NaOH solution. For t = 0 we get the
consumption V0 and for the rest of titrations (in time t) Vt consumptions.
We add approximately 100 ml of the reaction mixture to the second Erlenmayer flask.
After fixing the reflux condenser on the flask, the mixture is heated 2 hours at 80–90 °C.
Under these conditions, reaction 1 will be terminated. When the mixture cools down, we take
5 ml sample to determine V∞ consumption using the procedure described above.
During the experiment, temperature in the bath has to be constant. Recommended
temperature range is 20–30 °C. All measured values are summarized in Table 1.
Table 1. V0 = .................., V∞ = ..................
t/min
Vt/ml
ln [(V∞ – Vt)/ml]
20
40
60
80
100
120
Processing of the measured data
From the titrant consumptions, we calculate ln (V∞ – Vt) values required in Table 1. From
ln (V∞ – Vt) = f(t) dependence (eq. 6) we obtain the rate constant, kcA, and the initial titrant
43
consumption, V0, (see eq. 7) using linear regression. We compare found value of V0 with the
experimentally determined one. Finally, we construct Vt = f(t) and ln (V∞ – Vt) = f(t) plots.
44
20 Kinetics of extinction of phenolphthalein color form in alkaline solution Aim
Study of kinetics of phenolphthalein reaction in alkaline solution, reaction order and rate
constant determination.
Theoretical part
Phenolphthalein represents one of the most common acid-base indicators. It does not form
only a simple HIn–In– pair. Structures of individual phenolphthalein forms are depicted in
Fig. 1. Its H2f structure is colorless at pH < 8. When pH is growing from 8 to 10, the two
phenolic protons are splitting-off and the lactone ring opens. This results in well-known rosered colored structure f2–. At higher pH, the slowly color extinction takes place because of
formation of the colorless fOH3– structure. All color changes are reversible. H2f
transformation to f2– is very fast and it is finished at pH = 11. On the other hand, at
sufficiently high pH, f2– → fOH3– process is relatively slow and the corresponding reaction
rate can be measured conveniently.
OH
HO
O
O
H2f
O
O
O
O
C
C
O
O
C
C
f2−
O
O
O
O
C
OH
O
C
O
fOH3−
Fig. 1. Phenolphthalein structures.
Due to intensive color of f2– structure, f2– → fOH3– reaction can be monitored using
photocolorimetry. The reaction of phenolphthalein in alkaline solution can be described using
following equation
45
f2– + OH– → fOH3–
and the rate of f2– concentration can be expressed as
⎛ dc 2−
− ⎜⎜ f
⎝ dt
⎞
⎟ = k (c 2 − ) a (c − ) b
f
OH
⎟
⎠
(1)
In this practice, strong alkaline solution with traces of phenolphthalein is used. Therefore,
concentration of OH– anions exceeds the f2– concentration minimum 104-times. During each
measurement, the concentration of OH– anions can be considered constant and for the rate law
we can write
⎛ d c 2−
− ⎜⎜ f
⎝ dt
⎞
⎟ = k1 (c 2− ) a
f
⎟
⎠
(2)
where
k1 = k (cOH–)b
(3)
The order of the reaction with respect f2– is a. If we suppose that it is the first-order reaction in
f2–, a = 1, then ln cf2– = f(t) is linear with the line slope equal to –k1
ln cf2– = ln c0f2– – k1t
(4)
Eq. 4 was obtained from the integration of eq. 2 using a = 1.
On the basis of Lambert-Beer law, we can write
Aλ = ελdcf2–
(5)
where Aλ is absorbance at given wavelength λ, ελ is molar absorption coefficient and d is the
thickness of the cuvette. Since absorbance, Aλ, is directly proportional to concentration, cf2–,
from eqs. 4 and 5 we obtain
ln Aλ = ln Aλ0 – k1t
(6)
Rate order b (order with respect to OH– anions) and rate constant, k, can be found from
logarithmic form of eq. 3
ln k1 = ln k + b ln cOH–
(7)
We will follow the extinction of f2– form in NaOH solutions with 0.05–0.30 mol L–1
concentration range. For a given NaOH concentration, reaction rate grows with the increase in
ionic strength of the solution, because the studied reaction requires bringing two negatively
charged ions nearer. Their mutual repulsion decreases in the environment containing inert
ions. In order to keep the ionic strength constant in all measurements, we need stock solutions
of NaOH and NaCl with concentrations 0.30 mol L–1. NaOH solutions with lower
concentrations are prepared by means of dilution of the NaOH stock solution with NaCl
solution. Absorbance is measured using photocolorimeter at λ = 565 nm (or with green filter).
46
Equipment and chemicals
Water solutions of NaOH a NaCl (0,30 mol L–1), 1 % phenolphthalein solution in ethanol,
burette 5 ml (2 pieces), beaker 25 ml (3 pieces); colorimeter with color filters or laboratory
system CoachLab with colorimeter 03581; cuvette; stopwatch.
Experimental part
Using NaOH and NaCl stock solutions, NaOH solutions with 0.05, 0.10, 0.15, 0.20 and
0,25 mol L–1 concentrations and 6 ml volume are prepared. To the solution in 25 ml beaker 3
drops of phenolphthalein solution are added. The mixture is then carefully stirred and
transferred to the cuvette. Cuvette is placed in colorimeter and the absorbance, Aλ, of the
solution is measured as the function of time. The absorbance of the solutions with
0.25 and 0.30 mol L–1 concentration is measured every 30 seconds; solutions with 0.15 a
0.20 mol L–1 are measured in 1 minute intervals. Solutions with 0.05 and 0.10 mol L–1 are
measured in two-minute intervals. In each case 10 absorbance readings are performed.
Measurements are carried out at room temperature. Measured results are compiled in tables
according Table 1.
Table 1. cNaOH = ..................
No.
1
⋅⋅⋅
10
t/min
Aλ
ln Aλ
Processing of the measured data
From eq. 6, we calculate rate constant, k1, values for individual measurements using linear
regression (least squares fit). Obtained values are then compiled in Table 2. Using eq. 7, from
linear regression, we determine rate constant k a reaction order b (related to OH– anions).
Reaction order n is n = 1 + b. (If b = 1, k can be obtained from k1 = k⋅cOH– equation).
Table 2
cOH–/mol L–1
0.30
0.25
0.20
0.15
0.10
0.05
k1/min–1
ln (cOH–/mol L–1)
ln (k1/min–1)
47
22 Adsorption – Szyszkowski equation Aim
Determination of surface tensions of surfactant solutions, construction of Gibbs isotherm.
Theoretical part
Adsorption means an increase in molecules concentration in the surface layer. This
phenomenon is the consequence of non-balanced forces in the surface.
Surface tensions of pure solvent and solutions of two liquids can be significantly different.
These differences stem from distinct cohesive and adhesive forces. If adhesive forces
dominate, solute molecules are retracted into the bulk and the solute concentration in surface
is low. Surface tension of such solution is approximately identical to the pure solvent surface
tension. This is a negative adsorption.
When cohesive forces dominate, solute molecules are accumulated in surface. This may
cause a considerable lowering of the solution surface tension. Substances able to decrease
surface tension are called surfactants and this phenomenon is called positive adsorption.
The stalagmometric method is one of the methods for surface tension measurements. The
weight of the drops of the fluid falling from the capillary glass tube is measured. The drop of
the fluid falls from the capillary when its gravity force (mg) is equal to surface tension force
(2πrγ) for the capillary with radius r
mg = 2πrγΦ
(1)
where m is the mass of the drop, g is standard acceleration of free fall and Φ is an empiric
correction depending on the drop volume and capillary radius. In this method, surface tension
of a sample, γ, is obtained on the basis of known surface tension of the pure solvent, γ0. We
determine the mass of a given number of the solution drops, m, and of the solvent, m0.
According eq. 1, we can write
γ=
m g
mg
, γ0 = 0
2πrΦ
2πrΦ0
(2)
Assuming Φ = Φ0, for the γ/γ0 ratio we obtain
γ
m
≈
γ 0 m0
(3)
Gibbs adsorption, Γ, is given by Gibbs adsorption isotherm
Γ =−
c dσ
RT dc
(dT = 0)
(4)
And it represents a measure of the surface activity of surfactant. In eq. 4, c is concentration of
the solution, dσ/dc is change in the surface energy with the concentration. In general, surface
48
energy values, σ, are expressed in terms of surface tension, γ, because their values are
identical. Instead of complicated direct determination of dγ/dc, for water solutions of fatty
acids and alcohols, empiric equation found by B. Szyszkowski can be employed
γ = γ 0 − a log(1 + bc)
(5)
where γ0 and γ are surface tensions of solvent and solution, respectively. Empiric constants
depend on the solute structure.
For constants a and b in Szyszkowski equation, we will use experimentally found γ = f(c)
dependence from stalagmometric method measurements using non-linear least squares fit.
From eq. 5 derivative and eq. 4, we obtain
Γ=
a
bc
2,303 RT 1 + bc
(6)
For high concentrations (c → ∞), we can write bc >> 1. Then, from eq. 6 maximum adsorbed
amount of the surfactant in unit surface, Γmax, can be found. This is related to the surface, s,
covered by the single surfactant molecule, when monomolecular layer is formed. One mole of
surfactant covers sNA surface (NA is Avogadro constant). This surface is equal to
multiplicative inverse of Γmax
Γ max =
a
1
=
2,303 RT sN A
(7)
Equipment and chemicals
Traube’s stalagmometer; analytic scales; small plastic test tubes (10 pieces); 200 ml
volumetric flask; 50 ml volumetric flask (5 pieces); 50 ml burette; ethanol, 1-propanol or
acetic acid; water.
Experimental part
Traube stalagmometer (Fig. 1) is a glass vial with a ground end capillary. From the capillary,
studied fluid drops down. Using the balloon, we take in the solution. Then we close the tap
and place under the stalagmometer clean test tube with known weight. Then we turn the tap to
allow the air pass through the upper capillary and start to count drops. It is advised to
determine the weight of at least 20 drops.
From the given sample, we prepare solutions with concentrations as follows: 1, 0.8, 0.6,
0.4, 0.2, and 0.1 mol L–1. Using analytic scales, we weigh amount of the sample required for
the preparation of 1 mol L–1 stock solution in 200 ml volumetric flask. In 50 ml volumetric
flasks, we prepare the rest of solutions (these are prepared from the stock solution employing
the burette). Solutions have to be stirred thoroughly. First, we determine the weight of chosen
number of solvent (water) drops, m0. Then, we determine the weight of the same number of
drops for individual solutions. Each measurement should be performed three-times and the
average of three values of weight is used in data processing. Obtained weights are compiled in
Table 1.
49
Fig. 1. Scheme of Traube stalagmometer.
Table 1. m0 = .................., t = .................., γ0 = ..................
No.
1
⋅⋅⋅
c/mol m–3
1000
m/g
γ/N m–1
Γ/mol m–2
Processing of the measured data
Temperature dependence of water surface tension can be expressed as follows
γH2O = γ0 = (75.872 – 0.154t – 0.00022t2)×10–3 N m–1
where t is temperature in °C. From eq. 3, we calculate surface tensions of the measured
solutions and construct γ = f(c) plot.
According Szyszkowski equation, we determine the values of parameters a and b by means
of non-linear least squares method. From eq. 6, we calculate Gibbs adsorption, Γ, values and
summarize them in Table 1. We construct also Γ = f(c) plot. Using eq. 7, we find values of
Γmax and s.
50
23 Adsorption on solid phase Aim
On the basis of determined amount of adsorbate on solid adsorbent to find parameters of
Freundlich and Langmuir isotherm.
Theoretical part
Adsorption means an increase in molecules concentration in the phase boundary. It can be
observed in solid phase – gas phase or solid phase – liquid phase boundaries.
Molecules or atoms can attach to surface in two ways. In physical adsorption, weak van
der Waals interactions (for example, dispersion or dipolar interactions) between adsorbate and
adsorbent (substrate) occur. In chemical adsorption, the molecules or atoms are attached to the
adsorbent surface by forming a chemical bond. The enthalpy of chemical adsorption is
significantly larger than that of physical adsorption.
In the case of adsorption from a solution, the number of moles of bound adsorbate at the
unit mass of adsorbent depends on adsorbent (especially on its specific surface) and adsorbate
properties, equilibrium concentration of adsorbate and temperature. Number of moles of
adsorbate, a, adsorbed on the unit mass (1 kg) of adsorbent vs equilibrium concentration of
adsorbate in solution dependence is expressed by means of adsorption isotherm
a = f(c)
(dT = 0)
(1)
Relatively simple and often used adsorption isotherms are empiric Freundlich isotherm and
Langmuir isotherm based on monolayer surface coverage assumption.
Freundlich adsorption isotherm (Fig. 1) is
a = k⋅c1/n
(dT = 0)
(2)
where k and n are constants which are independent on concentration, c.
Langmuir adsorption isotherm (Fig. 1) is defined as follows
a = a max
Kc
1 + Kc
(3)
where K is a constant and amax is maximum amount of adsorbate that can be bound on 1 kg of
adsorbent (Fig. 1) when monolayer coverage of the adsorbent surface occurs.
Equipment and chemicals
50 ml burette (2 pieces); funnel (6 pieces); 100 ml Erlenmayer flask (6 pieces); filter paper;
25 ml pipette; 250 ml titration flask (2 pieces); activated carbon; CH3COOH (c = 1 mol L–1);
NaOH (c = 0,2 mol L–1); phenolphthalein.
51
Fig. 1. Freundlich and Langmuir adsorption isotherm.
Experimental part
In each of six Erlenmayer flasks, we add 5 g (weighted with 0.01 g precision) of activated
carbon. Using two burettes we add to the flasks water and acetic acid – amounts are given in
Table 1.
Table 1
Flask No.
1
2
3
4
5
6
V(H2O)/ml
0
15
25
35
40
45
V(CH3COOH)/ml
50
35
25
15
10
5
We close the flasks with stoppers, stir the mixtures and keep them stay 20 minutes. During
this period, we stir the mixtures several times. Then, we filter the mixtures through dry filter
paper. The first amounts of filtrates (ca 5 ml), we pour out in order to eliminate the adsorption
of acetic acid on dry filter paper.
From obtained filtrates, we add to titration flasks volumes, Vi, according Table 2.
Table 2
Flask No.
1, 2
3, 4
5, 6
Vi/ml
10
20
40
52
Then, we add phenolphthalein and titrate the solutions with NaOH (c = 0.2 mol L–1 and
determine the consumption of titrant, xi. In the second experiment – without the active carbon,
we determine acetic acid concentrations, c0, before adsorption. Consumptions of titrant in this
case we denote x0i. Consumptions xi aj x0i we summarize in Table 3.
Table 3
Flask No.
1
⋅⋅⋅
6
xi/ml
x0i/ml
Processing of the measured data
Acetic acid concentration in titrated solution we calculate from expression
ci = (xict)/Vi, c0i = (x0ict)/Vi
(5)
where ct is the concentration of titrant (NaOH) and Vi is volume of titrated solution. All values
we compile in Table 4.
The quantity a, required for the construction of adsorption isotherm, we calculate as
follows
a=
(c0 − c)V
m
(6)
where c0 is the concentration of acetic acid before adsorption, c is the concentration after
adsorption, V is solution volume (50 ml), and m is the adsorbent mass.
Table 4
Flask No.
1
⋅⋅⋅
6
c0/mol L–1
c/mol L–1
a/mol kg–1
Values of Freundlich adsorption isotherm, k and n, we find from the equation
ln a = ln k + (1/n)⋅ln c
derived from eq. 2. Using least squares fit, from ln a = f(ln c) dependence, we obtain
intercept, ln k, and line slope, 1/n, values.
Values of Langmuir adsorption isotherm, K and amax, we find from linear form of eq. 3
1
1
1 1
=
+
a amax Kamax c
1/a = f(1/c) dependence is linear with 1/amax intercept and 1/(Kamax) line slope.
53
We construct the plots of the two dependences, ln a = f(ln c) and 1/a = f(1/c). Adsorption
isotherm, i.e. the scatter plot of a = f(c) dependence, we construct on the basis of
experimentally determined a and c quantities. In the same plot, we draw a = f(c) dependences
corresponding to Freundlich (eq. 2) and Langmuir adsorption isotherms (eq. 3). Finally, we
decide, which adsorption isotherm describes experimental data.
54
24 Determination of molar absorption coefficient Aim
Photocolorimetric determination of molar absorption coefficient of CuSO4 and NiSO4 at
635 nm wavelength (or red filter).
Theoretical part
Incident light can pass through the sample (transmission), can be reflected (reflection) or
absorbed (absorption). Absorbed portion of monochromatic radiation with given wavelength,
λ, depends on the following factors:
• sample material properties,
• thickness of the sample, l, i.e. the optical path of the ray.
The ratio of the transmitted intensity, I, to the incident intensity I0 of the light with a given
wavelength is called the transmittance, τ, of the sample at that wavelength
τλ =
Iλ
I 0λ
(1)
It is also useful to introduce another quantity, absorbance, A, of the sample at a given
wavelength
Aλ = − logτ λ = − log
Iλ
I
= log 0λ
I 0λ
Iλ
(2)
In eqs. 1 and 2, index λ indicates that the values of quantities depend on wavelength of
incident radiation.
Fig. 1. Absorption of the incident light in a material with a thickness l.
The majority of light-absorbing solutions obeys Lambert-Beer law
Aλ = ελcl
(3)
The quantity ελ is called molar absorption coefficient. It depends on the wavelength
(frequency) of the incident radiation and is greatest where the most intensive absorption
occurs. Its dimension is 1/(concentration×length) and it is convenient to express ελ in
55
L mol–1 cm–1. At high concentrations of a light-absorbing substance, deviations from
Lambert-Beer law may occur and A = f(c) dependence losses its linearity.
Colorimetry represents an analytical method for determinations of the concentrations of
visible light absorbing substances or substances that show color change during a reaction.
Photocolorimeter measures the intensity of light transmitted through the solution of a sample
at selected wavelength. Light from the source passes through a cuvette that contains the
solution. A light-sensitive photocell (detector) at the other end of the optical path detects
intensity of transmitted light (see eqs. 1 and 2).
Equipment and chemicals
Colorimeter with color filters or laboratory system CoachLab with colorimeter 03581;
cuvette; volumetric flasks 100 ml (2 pieces) and 25 ml (5 pieces); pipette 25 ml; beakers 100
ml (2 pieces); CuSO4⋅5H2O; NiSO4⋅7H2O.
Experimental part
In volumetric flask, we prepare CuSO4 and NiSO4 solutions with given concentrations. First,
we need to select appropriate wavelength (635 nm) or color filter (red). Before measurements,
colorimeter requires the calibration using the cuvette with the solvent (water). Usually, the
most accurate results are obtained in 0.05–1.0 range of absorbance.
After each measurement, the cuvette is rinsed with next solution to prevent the measured
solution from a concentration change stemming from a residue of the previously measured
solution. Outer surface of the cuvette has to be thoroughly cleaned before its placement into
the colorimeter.
Solutions with given concentrations are prepared (diluted) from the stock solution.
Measured absorbance values for CuSO4 and NiSO4 solutions are compiled in tables (see
Table 1).
Table 1. Substance: ..................
No.
1
⋅⋅⋅
c/mol L–1
A
Processing of the measured data
For the two solutions, plots of Aλ = f(c) dependences are constructed. On the basis of eq. 3,
using linear regression molar absorption coefficients at given wavelength for CuSO4 and
NiSO4 are determined.
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Supplementary material – CD The supplementary CD contains:
1.
PDF files about CoachLab measuring system and descriptions of sensors employed in
practices.
2.
Microsoft Excel 2007 workbook with measured data processing and statistical analysis of
obtained results for selected practices performed at Department of Physical Chemistry.
3.
Word 2007 document with short overview of topics of the lectures from Physical
Chemistry I and II at the Faculty of Chemical and Food Technology of Slovak University
of Technology in Bratislava.
4.
Photographs of individual practices arrangements.
57
References 1.
Klein E. a kol.: Fyzikálna chémia – Praktikum, Nakladateľstvo STU, 2009, Bratislava,
ISBN 978-80-227-3187-4. Figures and Schemes used in this report were taken from this
publication with the permission of the author.
2.
Šimon P. a kol.: Laboratórne cvičenia z fyzikálnej chémie. Slovenská technická
univerzita v Bratislave, Bratislava 1998.
3.
Centre for Microcomputer Applications: Guide to Coach 6, AMSTEL Institute/CMA
Foundation, 2007, Amsterdam; http://www.cma.science.uva.nl/english/
4.
Atkins P. W.: Physical Chemistry, 6th Ed. Oxford University Press, Oxford 1998.
58