Download Ka and Kb from pH and Conductivity Measurements

LABORATORY EXPERIMENT
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Ka and Kb from pH and Conductivity Measurements:
A General Chemistry Laboratory Exercise
Frazier Nyasulu,* Michael Moehring, Phyllis Arthasery, and Rebecca Barlag
Department of Chemistry and Biochemistry, Ohio University, Athens, Ohio 45701, United States
bS Supporting Information
ABSTRACT: The acid ionization constant, Ka, of acetic acid and the base ionization constant, Kb, of ammonia are determined easily
and rapidly using a datalogger, a pH sensor, and a conductivity sensor. To decrease sample preparation time and to minimize waste,
sequential aliquots of a concentrated standard are added to a known volume of water and measurements are made after each
addition. In this laboratory exercise, students show that Ka and Kb are constants, compare and contrast pH and conductivity
approaches, and evaluate how solution components (weak acid alone and weak acid plus conjugate base) affect the results.
KEYWORDS: First year/Undergraduate/General, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Acids-Bases, Conductivity, Equilibrium, pH
A
majority of general chemistry textbooks have examples or
problems in which the acid ionization constant of a weak
acid, Ka, is calculated from a given formal concentration and the
pH of the solution. This approach is rarely used in the associated
laboratory course. Instead, Ka is typically determined from an
acid-base titration curve.1-3 If an acid or base is uncharged, pH
and conductivity measurements can be used to determine Ka or
Kb. Until recently, a pH meter and a conductivity meter were
required and the cost was such that conductivity-based Ka and Kb
determinations were only performed in the physical chemistry
laboratory.4-6 Today, a single datalogger connected to a pH
sensor and a conductivity sensor can make these two measurements simultaneously and at a significantly reduced cost. As dataloggers are now available in general chemistry labs, it is now
possible to include the determination of Ka and Kb from conductivity measurements.7
In these experiments, acetic acid (HC2H3O2) and ammonia
(NH3) were chosen because both are uncharged compounds and
Ka or Kb can be determined using pH and conductivity measurements. Ammonia and acetic acid are highly favored examples in
general chemistry textbooks and are present in most homes
(acetic acid in vinegar and ammonia in some household cleaning
solutions). In addition to determining the Ka or Kb value, it is
pedagogically useful for students to make a number of measurements with varying concentrations and demonstrate that Ka or
Kb is a constant. Instead of making several solutions of different
concentrations and measuring the pH and conductivity of each
solution, it is faster and easier to add successive aliquots of a concentrated standard to a known volume of water and make
measurements without moving the sensors or solution.
For HC2H3O2(aq), the acid ionization constant is determined
in three ways. Method 1 is based on conductivity measurements
in solutions consisting of varying concentrations of HC2H3O2(aq). Method 2 is based on pH measurements in solutions
consisting of varying concentrations of HC2H3O2(aq). Data for
methods 1 and 2 are collected at the same time. Method 3 is
Copyright r XXXX American Chemical Society and
Division of Chemical Education, Inc.
based on pH measurements in solutions consisting of varying
concentrations of HC2H3O2(aq) and NaC2H3O2(aq). The
determination of Kb of NH3(aq) is also performed in three ways,
the first and second methods are similar to that described for
HC2H3O2(aq). In the third method, instead of adding NH4þ
(aq), the NH4þ(aq) is generated in situ by the reaction between
NH3(aq) and HCl(aq).
Determination of Ka or Kb values from pH measurements is
well-known, hence will not be described here. However, determination of Ka from conductivity measurements is less well-known
and therefore a description is provided. The molar conductivity of a
weak acid (ΛM) is given by the expression
ΛM ¼
Λ
c
ð1Þ
where Λ is the conductivity of the weak acid and c is its molarity.
The fraction (R) dissociated is
R¼
ΛM
Λo
ð2Þ
where Λo is the molar conductivity at infinite dilution. For strong
electrolytes, Λo can be determined by plotting ΛM versus square
root of the concentration; Λo is the y intercept of this linear plot.
For weak electrolytes, a plot of ΛM versus square root of the
concentration curves and so Λo is obtained indirectly. For example,
for acetic acid, Λo(HC2H3O2) is
Λo ðHC2 H3 O2 Þ ¼ Λo ðNaC2 H3 O2 Þ þ Λo ðHClÞ - Λo ðNaClÞ
ð3Þ
In this lab, Λo(HC2H3O2) is provided.
A
dx.doi.org/10.1021/ed100132m | J. Chem. Educ. XXXX, XXX, 000–000
Journal of Chemical Education
LABORATORY EXPERIMENT
Table 1. Method 1 Conductivity Data and Results at ∼20 °C
[Hþ] =
Molar
V (1.0 M HC2H3O2)/
mL
[HC2H3O2]0/
(mol/L)
Conductivity/
(μS/cm)
Conductivty/
(μS/cm M)
Fraction
Ionized (R)
[C2H3O2-]/
(mol/L)
[HC2H3O2]/
(mol/L)
Ka
1
0.0163
188
11506
2.91 10-2
4.75 10-4
1.59 10-2
1.42 10-5
2.03 10
-2
-4
-2
1.35 10-5
1.73 10
-2
-2
1.44 10-5
1.56 10
-2
-2
1.55 10-5
1.39 10
-2
-2
1.51 10-5
-2
8.95 10
1.03 10-1
1.46 10-5
1.48 10-5
Average
1.46 10-5
STD
6 10-7
2
3
4
5
6
7
0.0322
0.0475
0.0623
0.0767
0.0906
0.1042
258
8024
324
6826
385
6179
422
5503
452
488
-2
1.26 10
1.18 10-2
4987
4685
6.52 10
3.15 10
-4
8.19 10
4.66 10
-4
9.73 10
6.13 10
-3
1.07 10
7.56 10
-3
1.14 10
1.23 10-3
Table 2. Method 2 pH Data and Results at ∼20 °C
V (1.0 M HC2H3O2)/ mL
1.00
2.00
3.00
[HC2H3O2]0/ (mol/L)
1.63 10
-2
3.22 10
-2
4.75 10
-2
pH
3.32
3.16
3.11
Ka
-2
1.44 10-5
-2
1.52 10-5
-2
1.29 10-5
-2
1.59 10
3.15 10
4.67 10
4.00
5.00
6.23 10
7.67 10-2
3.02
2.95
6.14 10
7.56 10-2
1.49 10-5
1.67 10-5
6.00
9.06 10-2
2.91
8.94 10-2
1.69 10-5
-1
1.03 10
1.61 10-5
Average
1.5 10-5
STD
1 10-6
7.00
-2
[HC2H3O2]/(mol/L)
1.04 10
-1
2.89
The acid ionization constant, Ka, for acetic acid is
Ammonia
½Hþ ðaqÞ½C2 H3 O2 - ðaqÞ
ðRcÞ2
R2 c
ð4Þ
¼
¼
Ka ¼
½HC2 H3 O2 ðaqÞ
1-R
ð1 - RÞc
Aliquots (1.00 mL) of 1.00 M NH3(aq) are added to 60.0 mL
of water and the pH and conductivity of the solution are
measured after each addition. To avoid premature recording of
the pH (pH stabilizes slowly), the datalogger is run displaying pH
versus time. Additions are terminated when the pH changes by
e0.05. Aliquots (1.00 mL) of 1.00 M HCl(aq) are added and the
pH measured. The total number of HCl(aq) aliquots is one less
than the number of NH3(aq) aliquots in order to ensure the
presence of unreacted NH3(aq).
For NH3 (aq), equations similar to those of HC2H3O2(aq) apply
and Kb is
Kb ¼
½NH4 þ ðaqÞ½OH- ðaqÞ
ðRcÞ2
R2 c
¼
¼
½NH3 ðaqÞ
1-R
ð1 - RÞc
ð5Þ
The value of Λo(NH3) is also provided.
This lab gives students an opportunity to compare and
contrast pH and conductivity procedures and to evaluate how
the solution components (weak acid alone and weak acid plus
conjugate base) affect the efficacy of each method.
’ HAZARDS
Hydrochloric acid is corrosive. Contact can cause severe burns
to skin and eyes.
’ RESULTS AND DISCUSSION
This is our second general chemistry laboratory exercise in
which the conductivity sensor is used. In the first exercise,8 the
factors that affect conductivity were explored. As part of this lab,
Λo(HCl) was determined.
Typical conductivity data and results obtained for HC2H3O2(aq) based on method 1 are shown in Table 1. The calculations
were performed using an Excel spreadsheet template. The acid
ionization constant was calculated to be (1.46 ( 0.06) 10-5 at
∼20 °C using a Λo value of 3.955 105 μS/(cm mol L-1). On
the basis of pH (method 2), Ka for solutions consisting of acetic
acid alone was (1.5 ( 0.1) 10-5 (Table 2), and based on pH
and solutions consisting of acetic acid and sodium acetate
’ EXPERIMENT
Materials and equipment
Datalogger, conductivity sensor, pH sensor, 1.00 mL autopipettor, 1.0 M NH3(aq), 1.0 M HC2H3O2(aq), 1.00 M HCl(aq).
Acetic Acid
Aliquots (1.00 mL) of 1.00 M HC2H3O2(aq) are added to
60.0 mL of water and the pH and conductivity of the solution are
measured after each addition. To avoid premature recording of
the pH (pH stabilizes slowly), the datalogger is run displaying pH
versus time. Additions are terminated when the pH changes by
e0.05. After deactivating the conductivity sensor, aliquots of
NaC2H3O2 are added and the pH measured.
B
dx.doi.org/10.1021/ed100132m |J. Chem. Educ. XXXX, XXX, 000–000
Journal of Chemical Education
LABORATORY EXPERIMENT
Table 3. Method 3 pH Data and Results at ∼20 °C
V (1.0 M HC2H3O2)/mL
[acetic]/(mol/L)
[acetate]/(mol/L)
pH
1.00
1.03 10-1
1.38 10-2
3.93
4.80
1.58 10-5
1.01 10
-1
2.73 10
-2
4.23
4.80
1.59 10-5
9.97 10
-2
4.03 10
-2
4.44
4.83
1.47 10-5
9.83 10
-2
5.30 10
-2
4.53
4.80
1.59 10-5
9.70 10
-2
6.53 10
-2
4.67
4.84
1.44 10-5
9.56 10
-2
7.73 10
-2
4.58
4.67
2.13 10-5
9.43 10
-2
8.90 10
-2
4.82
4.85
1.43 10-5
Average
1.6 10-5
STD
2 10-6
2.00
3.00
4.00
5.00
6.00
7.00
(method 3, Table 3), Ka was (1.6 ( 0.2) 10-5. The Ka values
differ from the textbook value that students are familiar with
(1.75 10-5) because (i) the temperature is ∼20 °C and
not 25 °C, (ii) the temperature and pH sensors were not
temperature calibrated, and (iii) the starting pH of the deionized
water was acidic (pH 6.6-6.7). Acid ionization constants
between 1.4 10-5 and 2.8 10-5 were considered reasonable
and ∼90% of the students performed satisfactorily using method
1 and method 3. Methods 1 and 3 results were equivalent
(typically within 20% of each other). However, only 30% of
the students perform satisfactorily well using method 2. It is not
unusual for method 2 values to show an acceptable standard
deviation (<4% RSD) and yet be 20% of the values obtained
using methods 1 and 3. This can be partly attributed to students
reading the pH values before stable values were attained. The pH
readings tend to stabilize faster in solutions consisting of weak
acid and conjugate base.
On the basis of method 1, Kb for NH3(aq) was (2.2 ( 0.3) 10-5. On the basis of method 2, Kb was (1.6 ( 0.2) 10-5 and
based on method 3, Kb was (2.2 ( 0.3) 10-5. A student was
considered to have performed satisfactory work if their Kb was
between 1.2 10-5 and 2.6 10-5. According to this criterion,
84% of the students performed satisfactorily using methods 1 and
3. Methods 1 and 3 results were equivalent (within 20% of each
other). Unlike methods 1 and 3, only 15% of the students
performed satisfactorily using method 2. It was not unusual for
values to be 20% of expected values.
Group results were analyzed in the next lab session. From this
analysis, students concluded that methods 1 and 3 produce
satisfactory results whereas method 2 does not.
pKa
Ka
is present with its conjugate base. Comparative study of the three
methods exposes students to the realization that all the methods
are not equally effective.
’ ASSOCIATED CONTENT
bS
Supporting Information
Instructor notes; Excel spreadsheet template. This material is
available via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected].
’ REFERENCES
(1) Beran, J. A. Laboratory Manual for Principles of General Chemistry,
5th ed.; Wiley: New York, 1994; pp 333-344.
(2) Stanton, S.; Zhu, L.; Atwood, C. H. Experiments in General
Chemistry Featuring MeasureNet; Thompson Brooks/Cole: Belmont,
CA, 2006; pp 343-358.
(3) Nelson, J. H.; Kemp, K. C., Laboratory Experiments, Chemistry
The Central Science, 8th ed.; Prentice Hall: Upper Saddle River, NJ, 2000;
pp 237-252.
(4) Kemp, M. K., Physical Chemistry, A Step-by-Step Approach;
Marcel Dekker: New York, 1979; pp 274-304.
(5) Barrow, G. M. Physical Chemistry, 5th ed.; McGraw Hill: New
York, 1988, pp 303-313.
(6) Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments in
Physical Chemistry, 6th ed.; McGraw Hill: New York, 1996; pp 228-237.
(7) One of the reviewers suggested that this lab is more appropriate
at the honors level of general chemistry or the quantitative analysis
laboratory.
(8) Nyasulu, F.; Stevanov, K.; Barlag, R. J. Chem. Educ. 2010,
87, 1364–1366.
’ CONCLUSION
The addition of small volume increments of concentrated weak
acid (or base) to a known volume of water is a fast and easy way to
prepare solutions with different concentrations. Another advantage
of this approach is that the pH and conductivity sensor measurements can be made without moving the sensors or the solutions.
This method also conserves materials and minimizes waste.
In addition to determining Ka and Kb from pH and conductivity measurements, this lab deliberately covers a number of
weak acid and weak base solution variations. In one case, the
solution consists of weak acid or weak base, and in the other, the
solution consists of weak acid and its conjugate base. Although
conductivity measurements work well, Ka and Kb determination
is only possible for uncharged weak acids and weak bases. For pH
measurements, the best results are obtained when the weak acid
C
dx.doi.org/10.1021/ed100132m |J. Chem. Educ. XXXX, XXX, 000–000