Experiment 5: Determination Of The Conductance Of Strong And Weak

Electrolytes

Objective

1. To measure the conductance of potassium chloride, hydrochloric acid, sodium

chloride and sodium acetate.

2. To determine the dissociation constant of acetic acid.

Introduction

Pure water does not conduct electricity, but any solvated ionic species would

contribute to conduction of electricity. An ionically conducting solution is called an

electrolyte solution and the compound, which produces the ions as it dissolves, is

called an electrolyte. A strong electrolyte is a compound that will completely

dissociate into ions in water. Correspondingly, a weak electrolyte dissolves only

partially. The conductivity of an electrolyte solution depends on concentration of the

ionic species and behaves differently for strong and weak electrolytes.

The conductance (L) is generally used for dealing with electrolytes and it is defined as

the reciprocal of the resistance of the solution

Equation 1:

Once R is known, the conductivity or specific conductance (X) may be obtained from

Equation 2:

where A and d are the area and separation between the electrodes of the cell.

The cell constant k of the conductivity cell is defined as

Equation 3:

and therefore

L (Ω-1) =1 R

X (Ω-1 cm-1) =_d AR

k = d A

Equation 4: X = k L

Thus, the molar conductivity Λ of an electrolyte solution is defined as

Equation 5:

where C is the molar concentration.

For weak electrolytes, the increase of molar conductivity with increasing dilution is

ascribed to increased dissociation of the electrolyte molecules to free ions. The degree

of dissociation (α) at a given concentration C is given by

Equation 6:

where Λ0 is the molar conductivity in the limit of zero concentration.

For strong electrolytes, the molar conductivity is higher than those of weak

electrolytes at high concentrations. As the electrolytes become dilute, the molar

conductivities also increase but is less steep than for weak electrolytes. For strong

electrolytes in dilute solution, the variation of molar conductivity with dilution can be

expressed as

Equation 7: Λ = Λ0 – (A + B Λ0) C1/2

where A and B are constants.

For weak electrolytes, the values of Λ0 can be deduced from the limiting molar

conductivities of strong electrolytes using Kohlrausch’s law. Alternatively, Λ0 and the

dissociation constant of a weak electrolyte may be obtained from the Ostwald dilution

law

Equation 8:

Apparatus

Λ (Ω-1 cm2 mol-1) = X

=k L

C C

α =Λ Λ0

1 =

_1 +

C Λ Λ Λ0 kaΛ0

2

Conductivity meter, dilution flasks (100mL), pipette, burette and measuring cylinder.

Materials

0.2000 M potassium chloride solution, 0.1000 M acetic acid, 0.1000 M hydrochloric

acid, 0.1000 M sodium chloride solution and 0.1000 M sodium acetate solution.

Experimental Procedures

1. Determination of cell constant

The conductance (L) of 0.2000 M potassium chloride solution was measured.

The specific conductance (X) of this solution is 2.768 x 10-3 Ω-1 cm-1.

The cell constant (k) was determined by using equation 6.

2. Measurement of conductance

From the solution of acetic acid provided, successive dilution with

conductivity water solution of 0.0500, 0.0250, 0.0125, 0.00625, 0.00312,

0.00156 and 0.00078 M were prepared.

The conductance of these solutions was measured.

The procedure was repeated with hydrochloric acid, sodium chloride and

sodium acetate.

The conductance of water used was measured.

Results and Calculation

Calculation of cell constant (k)

Conductance of 0.2000 M KCl = 1 / 49.59 = 0.0202 Ω-1

By using equation 6,Cell constant, k = X / L

= (2.768 x 10-3 Ω-1 cm-1) / 0.0202 Ω-1

= 0.1373 cm-1

Table 1: Resistance (Ω) of four electrolytes

Resistance, R (Ω)C (mol dm-3) CH3COOH HCl NaCl CH3COONa

0.1000 2883 31.91 96.04 1660.0500 3669 63.79 193.3 297.90.0250 6440 122.70 366.0 600.50.0125 8605 243 717.1 11780.00625 12395 472.44 1438 25770.00312 18280 940.88 2825 44850.00156 25100 1823.4 5451 89750.00078 44970 3569.8 10400 17210

Table 2: Conductance, L (Ω -1 ) of four electrolytes

Conductance, L (Ω-1)C (mol dm-3) CH3COOH HCl NaCl CH3COONa

0.1000 3.469 x 10-4 0.0313 0.0104 6.024 x 10-3

0.0500 2.726 x 10-4 0.0157 5.173 x 10-3 3.357 x 10-3

0.0250 1.553 x 10-4 8.150 x 10-3 2.732 x 10-3 1.665 x 10-3

0.0125 1.162 x 10-4 4.115 x 10-3 1.395 x 10-3 8.489 x 10-4

0.00625 8.068 x 10-5 2.117 x 10-3 6.954 x 10-4 4.207 x 10-4

0.00312 5.470 x 10-5 1.063 x 10-3 3.540 x 10-4 2.230 x 10-4

0.00156 3.984 x 10-5 5.484 x 10-4 1.835 x 10-4 1.114 x 10-4

0.00078 2.224 x 10-5 2.801 x 10-4 9.615 x 10-5 5.811 x 10-5

Table 3: Specific conductance, X (Ω -1 cm -1 ) of four electrolytes

Specific Conductance, X (Ω-1 cm-1)C (mol dm-3) CH3COOH HCl NaCl CH3COONa

0.1000 4.762 x 10-5 4.302 x 10-3 1.430 x 10-3 8.271 x 10-4

0.0500 3.742 x 10-5 2.152 x 10-3 7.103 x 10-4 4.609 x 10-4

0.0250 2.132 x 10-5 1.119 x 10-3 3.751 x 10-4 2.286 x 10-4

0.0125 1.596 x 10-5 5.650 x 10-4 1.915 x 10-4 1.166 x 10-4

0.00625 1.108 x 10-5 2.906 x 10-4 9.548 x 10-5 5.776 x 10-5

0.00312 7.511 x 10-6 1.459 x 10-4 4.860 x 10-5 3.061 x 10-5

0.00156 5.470 x 10-6 7.530 x 10-5 2.519 x 10-5 1.530 x 10-5

0.00078 3.053 x 10-6 3.846 x 10-5 1.320 x 10-5 8.020 x 10-6

Table 4: Molar conductivity, Λ (Ω -1 cm 2 mol -1 ) of four electrolytes

C (mol cm-3)C1/2

(mol cm-3)1/2

Molar conductivity, Λ (Ω-1 cm2 mol-1)CH3COOH HCl NaCl CH3COONa

1.0 x 10-4 0.01 0.4762 43.0210 14.3000 8.27115.0 x 10-5 7.071 x 10-3 0.7484 43.0475 14.2059 9.21792.5 x 10-5 5.000 x 10-3 0.8528 44.7596 15.0055 9.14571.25 x 10-5 3.536 x 10-3 1.2768 45.2039 15.3173 9.32436.25 x 10-6 2.500 x 10-3 1.7728 46.4990 15.2768 9.24193.12 x 10-6 1.766 x 10-3 2.4074 46.7717 15.5775 9.81191.56 x 10-6 1.249 x 10-3 3.5064 48.2680 16.1462 9.80640.78 x 10-6 8.832 x 10-4 3.9141 49.3098 16.9255 10.2819

Table 5: 1 / Λ and C Λ values for acetic acid

1 / Λ (Ω cm-2 mol) C Λ (mol cm-3) (Ω-1 cm2 mol-1)2.100 4.762 x 10-5

1.336 3.742 x 10-5

1.173 2.132 x 10-5

0.783 1.596 x 10-5

0.564 1.108 x 10-5

0.415 0.751 x 10-5

0.285 0.547 x 10-5

0.255 0.305 x 10-5

Calculation of Λ0 for CH3COOH using Kohlrausch’s law

From Figure 1,

Λ0 (HCl) = 53.0 Ω-1 cm2 mol-1

Λ0 (NaCl) = 24.5 Ω-1 cm2 mol-1

Λ0 (CH3COONa) = 11.5 Ω-1 cm2 mol-1

By using Kohlrausch’s law,

Λ0 (CH3COOH) = Λ0 (CH3COONa) +Λ0 (HCl) – Λ0 (NaCl)= (11.5 + 53.0 – 11.5) Ω-1 cm2 mol-1

= 40.0 Ω-1 cm2 mol-1

Calculation of degree of dissociation (α) of CH3COOH at the concentrations of 0.0500, 0.0125 and 0.00156 M

At 0.05000 M, Λ = 0.7484, α = Λ / Λ0

= 0.7484 / 40.0= 0.0187

At 0.01250 M, Λ = 1.2768, α = Λ / Λ0

= 1.2768 / 40.0= 0.0319

At 0.00156 M, Λ = 3.5064, α = Λ / Λ0

= 3.5064 / 40.0= 0.0877

Calculation of dissociation constant ka of CH3COOH

ka =α 2 C 1 - α

=(0.0187) 2 (0.05 mol dm -3 )

1 – 0.0187 = 1.782 x 10-5 M

Calculation of ka and Λ0 from Figure 2

Gradient of graph, __1

=_(2.14 – 0.30) Ω cm -2 mol _

kaΛ20 (4.75 – 0.60) x 10-5 Ω-1 cm-1

==

44337.35 mol cm-3

4.4337 x 107 mol dm-3

kaΛ20 =

=1 / (4.4337 x 107 mol dm-3)2.2554 x 10-8 mol-1 dm3

The intercept at CΛ = 0, 1

= 0.04Ω cm-2 molΛ0

Λ0 ====

1 / (0.04 Ω cm-2 mol)25.0 Ω-1 cm2 mol-1

25.0 Ω-1 (0.1dm)2 mol-1

0.25 Ω-1 dm2 mol-1

Equilibrium constant,ka = kaΛ2

0 /Λ2

0

= 2.2554 x 10-8 mol-1 dm3 / (0.25 Ω-1 dm2 mol-1)2

= 3.609 x 10-7 Ω2 mol dm-1

According to Atkins’ Physical Chemistry (8th edition) page 1007 Table 7.4, the

theoretical value of dissociation constant of acetic acid (ka) is 1.4 x 10-5 M.

From calculation, the experimental value of ka is 1.782 x 10-5 M.

Percentage error of ka = 1.782 x 10 -5 M – 1 .4 x 10 -5 M

x 100%1.4 x 10-5 M

= 27.29 %

According to lab manual Component A page 19, the theoretical value of molar

conductivity in the limit of zero concentration of acetic acid,

Λ0 = Λ+ + Λ-

= 34.96 + 4.09

= 39.05 mS m2 mol-1

From calculation, the experimental value of Λ0 is 40.0 Ω-1 cm2 mol-1(from

Kohlrausch’s law).

Percentage error ofΛ0 = (40.0 – 39.05) Ω -1 cm 2 mol -1

x 100%39.05 Ω-1 cm2 mol-1

= 2.43 %

Discussion

The molar conductivity is found to vary according to the

concentration. One reason for this variation is that the number of

ions in the solution might not be proportional to the concentration of

the electrolyte. For instance, the concentration of ions in a solution

of a weak acid depends on the concentration of the acid in a

complicated way, and doubling the concentration of the acid added

does not double the number of ions. Secondly, because ions interact

strongly with one another, the conductivity of a solution is not

exactly proportional to the number of ions present.

The concentration dependence of molar conductivities indicates that

there are two classes of electrolyte. The characteristic of a strong

electrolyte is that its molar conductivity depends only slightly on the

molar concentration. The characteristic of a weak electrolyte is that

its molar conductivity is normal at concentrations close to zero, but

falls sharply to low values as the concentration increases.

The solution conducts electricity through motion of the ions under the effect of an

electric field. At high concentrations, each ion is surrounded by other ions, both

positive and negative. The field affecting any particular ion changes slightly because

of these surrounding ions. At infinite dilution, the distance between nearest neighbor

ions is large, and only the effect of the applied electric field is felt by individual ions.

This is the reason for extrapolating the data to infinite dilution.

The conductivity of any particular ion will also be affected by the ease with which the

ion can more through the water. Hence different ions should contribute differently to

the total measured conductivity. The ease with which any ion moves through the

solution depends on considerations such as the total charge and the size of the ion;

large ions offer greater resistance to motion through the water than small ions.

Conclusion

The conductance (L) of potassium chloride, hydrochloric acid, sodium chloride and

sodium acetate range from 9.615 x 10-5 Ω-1 to 0.0104 Ω-1.

The experimental value of dissociation constant of acetic acid (ka) is 1.782 x 10-5 M.

The experimental value of molar conductivity of acetic acid (Λ0) is 40.0 Ω-1 cm2 mol-1

Precaution

1. Always rinse the electrode with deionized water before use.

2. Blot the inside of the electrode cell dry before the next measurement to avoid

water droplets diluting or contaminating the sample to be tested.

3. Before taking readings, always shake the electrode briefly to release possible air

bubbles trapped in the electrode.

4. Ensure that the electrode surfaces in the elongated cell are completely submerged

in the liquid.

5. Always stir to ensure that the solution is homogenous during the measurement.

References

1. http://www.csun.edu/~jeloranta/CHEM355L/experiment4.pdf

2. http://www-ec.njit.edu/~grow/conductivity.htm

3. http://wwwchem.uwimona.edu.jm:1104/lab_manuals/c10expt19.html

4. Atkins’ Physical Chemistry , Peter Atkins and Julio de Paula, (8 th edition), Oxford

New York