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Aim
To determine the dissociation constant, K_{a,}
of a weak acid (acetic acid, CH_{3}COOH) by measuring the electrical
conductance of a series of concentrations of the electrolyte solutions (acetic
acid and sodium chloride).
Results and calculation
Conductance of Conductance Water = 0.880
S cm^{1}
[CH_{3}COOH] /M

Recorded Conductance / µS cm^{1}

0.00156

66.50

0.00312

91.80

0.00625

133.3

0.01250

191.4

0.02500

273.0

0.05000

376.0

Table 1: Conductance
Reading of CH_{3}COOH
When the concentration of acetic acid is
0.00156 M,
actual specific conductance =recorded
conductance – conductance of water
= 66.5 0.880
= 65.62 μScm^{1}
equivalent conductance , Ʌ = specific
conductance of the solution / [CH_{3}COOH]
= 65.62 μS cm^{1}/0.00156 mol dm^{3}
= 65.62 x 10^{6} S cm^{1}/ 0.00156 x 10^{3} mol
cm^{3}
≈ 42.06 S cm^{2} mol
= 42060 mScm^{2}equiv^{1}
The specific conductance and equivalent
conductance of the remaining concentrations are calculated using the same
method shown above and tabulated in table 2.
[CH_{3}COOH]/
M

√[CH_{3}COOH]/
M^{½}

Recorded Conductance / µS cm^{1}

Specific Conductance /
µS cm^{1}

Equivalent Conductance,
/ mS cm^{2}equiv^{1}

0.00156

0.03950

66.50

65.62

42060

0.00312

0.05586

91.80

90.92

29140

0.00625

0.07906

133.3

132.4

21190

0.01250

0.1118

191.4

190.5

15240

0.02500

0.1581

273.0

272.1

10880

0.05000

0.2236

376.0

375.1

7502

Table
2: The specific conductance and equivalent conductance for acetic acid
solution.
Graph 1: Graph of
equivalent conductance,
/mS cm^{2} equiv^{1} against √[CH_{3}COOH]// M^{1/2}
Similarly, the specific and equivalent
conductance of NaCl at different concentrations can be found.
[NaCl]/
M

√[NaCl]/M^{½}

Recorded Conductance /
µS cm^{1}

Specific conductance /
μS cm^{1}

Equivalent Conductance,
/
mS cm^{2}equiv^{1}

0.00125

0.03536

169.8

168.9

135100

0.00250

0.05000

334.0

333.1

133200

0.00500

0.07071

656.0

655.1

131000

0.01000

0.10000

1264

1263

126300

0.02000

0.14142

2510

2509

125500

0.04000

0.20000

4950

4949

123700

0.06000

0.24495

7100

7099

118300

0.08000

0.28284

9510

9510

118900

Table 3: The specific conductance and equivalent conductance of NaCl
Graph 2: Equivalent Conductance / mS cm^{2}
equiv^{1} against √[NaCl]/M^{½}
For dilute solutions, Λ = Λ_{o} – D
,
By plotting Λ against
, the equivalent conductance at
infinite dilution Λ_{o} for strong electrolyte NaCl can be obtained from the graph.
From graph 2,
since the yintercept = 135660, Λ_{o}_{ NaCl }=135660 mScm^{2}equiv^{1}
Λ_{0HR}
= Λ_{0HCl} +Λ_{0NaR} Λ_{0NaCl}
In
this experiment, the value of equivalent conductance at infinite dilution, Λ_{o
}of HCl and Na(CH_{3}COO) are not determined. Hence, the
literature values at 25^{0}C will be used.
CH_{3}COONa =
91.00 S cm^{2 }equiv^{1}
HCl =
426.16 S cm^{2 }equiv^{1}
Using the equation, Λ_{o}_{ CH3COOH} = Λ_{o}_{ HCl} + Λ_{o} _{CH3COONa+}  Λ_{o}_{ NaCl}
= 426.16 + 91.00 – 135.66
= 383.50 S cm^{2 }equiv^{1}
=
383500 mS cm^{2} equiv^{1}
When [CH_{3}COOH] = 0.00156M,
Λ _{CH3COOH }= 42060
mScm^{2}equiv^{1}
Degree of dissociation, α = Λ /Λ_{o} = = 0.1097
Degree of dissociation, α = Λ /Λ_{o} = = 0.1097
Apparent dissociation constant, K = α^{2}C / (1 – α) = (0.1096^{2}
x 0.00156) / (1 – 0.1096) ≈ 2.108 x 10^{5} M
Similar calculations were repeated
for various CH_{3}COOH concentrations and the results were tabulated in
Table 4 below.
[CH_{3}COOH]/M

Equivalent Conductance,
/ mS cm^{2}equiv^{1}

Degree
of dissociation, α

Apparent
dissociation constant, K/ 10^{5} M

0.00156

42060

0.1097

1.962

0.00312

29140

0.07598

1.908

0.00625

21190

0.05525

1.880

0.01250

15240

0.03974

1.854

0.02500

10880

0.02837

1.781

0.05000

7502

0.01956

1.850

Table 4: apparent dissociation
constant of acetic acid at various concentrations
Experimental value of K_{a}
= Mean value of K at various concentration of CH_{3}COOH
=
≈ 1.873 × 10^{5} M
Literature value of K_{a} of CH_{3}COOH
= 1.752 x 10^{5} M
Percentage
discrepancy =
≈ 6.91 %
Discussion
Conductance
The movement of ions through its solution to
electrodes is known as conductance^{[1]}. When electrodes are placed in
a solution, the cations are attracted to the negativelycharged cathode while
the anions move towards the positivelycharged anode. This conductance may be
affected by changes in ionic concentration and differs between compounds.
For a strong electrolyte, there is
complete dissociation into mobile ions. At infinite dilution, the distance
between neighboring ions is significant; therefore, only the effect of the
applied electric field is experienced by individual ions. However, in a concentrated solution, each ion is surrounded by other
ions. The ions are close enough to be influenced by both the electric field
applied by the electrodes as well as that by their surrounding ions.
In this experiment, the conductance of NaCl and CH_{3}COOH
is measured. NaCl, being an ionic salt, dissociates completely in water to
produce Na^{+} and Cl^{} ions. Due to a high concentration of
mobile ions, it has significant conductance. On the other hand, CH_{3}COOH
is a weak acid which only partially ionises in water; hence, its conductance is
weaker than that of NaCl.
Kohlrausch’s law
For dilute solutions of strong electrolytes, the equivalent conductance is a linear function of the square root of
the concentration. This is in accordance to
Kohlrausch’s Square Root Law^{[2]}, Ʌ=Ʌ_{0}  D
where Ʌ is the conductance of the salt, C, its concentration and D, a function
of the valence of the salt.
At infinite dilution, the equivalent conductance of
strong electrolyte, NaCl approaches a definite value (graph 2). The
extrapolation of graph 2 allows the conductance at
infinite dilution, Ʌ_{0}, to be calculated.
However, this may not be done for a weak
electrolyte. In the case of CH_{3}COOH, the equivalent conductance at infinite
dilution cannot be extrapolated to a definite value. From graph 1, it can
be observed that the gradient of the curve varying even at very low concentrations.
Thus, for the weak CH_{3}COOH acid, the value of Ʌ may be
obtained from a knowledge of the values for Ʌ_{0} for HCl, NaCl and Na^{+}CH_{3}COO^{},
according to the equation, Λ_{o}_{ CH3COOH} = Λ_{o}_{ HCl} + Λ_{o} _{CH3COONa+}  Λ_{o}_{ NaCl}.
After calculating the conductance
of the acid, its dissociation constant may be determined. Weak electrolytes
such as acetic acid, do not dissociate completely in solution. Instead, there
is an equilibrium between ions and associated electrolyte^{[2]}.
CH_{3}COOH
+ H_{2}O ↔ CH_{3}COO^{} + H_{3}O^{+}
Equilibrium concentration c(1a) ca
ca
K_{a} =
=
=
Hence, according to
the above equation, the acid dissociation constant may be determined.
Sources of discrepancy and handling
of experiment

experimental

literature

Percentage
discrepancy

Λ_{o}_{ NaCl
}

135.66 S cm^{2}equiv^{1}

126.45 S cm^{2} equiv^{1}

7.28
%

Λ_{o}_{ CH3COOH}

383.50 S cm^{2} equiv^{1}

390.71 S cm^{2} equiv^{1}

7.21
%

K_{a}
of CH_{3}COOH

1.873 × 10^{5} M

1.752 x 10^{5} M

6.91
%

As seen from the table above, the
experimental values of Λ_{o} for NaCl and CH_{3}COOH differ
very slightly from their respective literature values. Likewise, the
discrepancy between experimental and theoretical dissociation constants of
acetic acid is not significant.
Reasons
for these deviations may be attributed to the different temperatures at which the
literature and experimental values are recorded; the literature
values are recorded at the temperature of 25^{o}C while the experimental
values were taken around 28^{o}C. Variation in temperature affects the
position of the equilibrium; this causes K_{a} to be a
temperaturedependent constant. To reduce discrepancy between the observed and experimental values, a water
bath at 25^{o}C could be used.
Also, the solutions should be insulated
during the preparation and measurement of the conductance. This minimizes the
fluctuations in temperature, hence allowing a more accurate K_{a} value
to be determined.
Conductance water
Ordinary distilled water is not suitable
for use in this experiment as it has a high conductance, usually because of
dissolved CO_{2} gas from the air. Likewise, tap water, with dissolved
ions, is unsuitable for use in this experiment.
The conductance water is therefore
deionised by passing the water through an ionexchange resin. It should have
conductance of less than 5 × 10^{6} siemens. If the conductance of the
water is significant, it may mask the conductance of the solutions and reduces
the accuracy of their measured conductance. Prior to the experiment, the
conductance of water was measured to be 0.88 x 10^{6} siemens, which
is an acceptable reading.
Experimental techniques
To prepare the various concentrations of
solutions, successive dilutions were carried out carefully. This must be done with utmost precision:
should the concentration of a preceding solution be wrongly prepared, this will
result in a propagation of errors in the concentrations of successive
solutions, thereby further leading to inaccurately measured conductance for all
these successive solutions.
After the preparation of the solutions,
conductivity measurements are carried out with a dip cell. When not in use, the
dip cell is placed in a beaker filled with deionized water to ensure it is
reasonably stowed.
Prior to each measurement, the electrodes
on the dip cell are rinsed a few times with a dropper containing the solution
to be tested. This displaces any residual ions that may be on it. For the same
reason, the beaker is also rinsed several times with the solution for which
conductance is to be measured.
Time is allowed for the solution to
equilibrate before its conductance is measured. Also, a magnetic stirrer should
be place in the beaker containing the solution to be measured; this ensures
even mixing such that a more representative conductance may be recorded.
Conclusion
The equivalent
conductance of strong electrolyte sodium chloride at infinite dilution is 136 S cm^{2 }equiv^{1}
and that of acetic acid is 384 S cm^{2} equiv^{1}. The experimentally
determined value of dissociation constant, K of acetic acid is 1.87 × 10^{5}
M.
References
[1] Appelo and
Postma. Specific Conductance: how to calculate, to use and the pitfalls. Geochemistry,
groundwater and pollution, 2^{nd} ed.
[2]
Quid United, Protein Crystallography. Kohlrausch’s law. Article retrieved on 20 Feb 2012:
[3] Anonymous.
Acid dissociation constant. Article retrieved on 22 Feb 2012: <http://www.avogadro.co.uk/definitions/acidka.htm>
thanks
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