**Experiment 19 Conductivities of electrolyte
solutions**

**Objectives**

1. To measure the conductivity of solutions of KCl and to
establish the dependence of molar conductivity on
concentration.

2. To measure the conductivity of acetic acid solutions and
calculate the dissociation constant of the acid from the
data.

**Introduction**

1. *Molar Conductivity and Concentration*

The experimentally measured conductance, G, of a solution is
that of a certain volume of the solution contained between the
electrodes of the conductivity cell. (These electrodes are the
thin metal plates that can be seen on the inside of the cell, and
must be completely covered during measurements). The meter
actually measures the resistance, R, of the solution between the
electrodes and converts it to conductance.

G = 1 / R

In order to use this quantity to compare different solutions we
introduce another quantity called specific conductivity, k
and

k = G x cell constant

where the cell constant is a quantity describing the geometry of
the cell and

cell constant = *l*/A

where *l* is the distance between the electrodes and A is
the common electrode area (or the area of one electrode if both
have the same area). The cell constant is not found by measuring
distances but is determined by measuring the conductance of an
electrolyte whose specific conductivity is already known. The
molar conductivity,

Λ_{m} = κ / c

w here c is the molar concentration.

Kohlrausch found an empirical expression for the molar
conductivity as

Λ_{m} =
Λ_{m}^{o} - k √c

where Λ_{m}^{o} is the molar conductivity
at infinite dilution and 'k' is a constant whose value
depends on the type of electrolyte used (i.e. MA, M_{2}A, MA_{2},
etc.). The refined, Debye-Onsager theory gives essentially the
same result.

2. *Dissociation Constant*

Consider the dissociation of acetic acid (a weak acid),

HOAc + H_{2}O <=> H_{3}O^{+} + OAc- (OAc- = acetate ion)
(1 - α)c αc αc

where α is the degree of dissociation and c is the initial
concentration of the acid before dissociation. The dissociation
constant, K, is given by

K = α^{2}c / (1- α)

If this equation is solved for α, and α is expressed as the ratio
Λ_{m} / Λ_{m}^{o} we get the following equation

1 / Λ_{m} = 1 / Λ_{m}^{o} + c Λ_{m}/ K(Λ_{m}^{o})^{2}

which is known as the Ostwalds dilution law, and we can see that,
from a plot of 1 / Λ_{m} against cΛ_{m}, the values of
Λ_{m}^{o} and K can be obtained from the intercept and slope respectively.

**Materials**

Conductivity meter and cell, 0.1 M solutions of KCl and acetic
acid, beakers, 2 burettes and a graduated pipette.

**Procedure**

Switch on the conductivity meter. Familiarize yourself with the
controls on the front panel. From the stock solutions *use the
burettes* to prepare 50 cm^{3} of the following dilutions for
each electrolyte: 0.0500, 0.0400, 0.0300, 0.0200 and 0.0100 M.
Use one burette for the stock solution and ones for the distilled
water. Rinse the conductivity cell thoroughly in distilled water,
drain off the excess water and dip it into the solution whose
conductance you wish to determine, taking care that the
electrodes are completely immersed in the solution. Connect the
cell leads to the terminals marked cell on the meter. Set the
range switch to the highest value and observe the reading on the
meter. If you do not observe any movement on the meter (no
movement of the needle), move to the next range, and so on. The
reading on the meter multiplied by the range is the conductance
value. Measure the conductance of all the solutions that you have
prepared, beginning with the least concentrated, *rinsing the
electrodes thoroughly with the next solution*. From the value
of the conductance for 0.1 M KCl, calculate the cell constant
using κ_{KCl} = 1.285 x 10^{-1} S dm^{-1}
(S = siemens = ohm^{-1}) at 25 °C.
Using this value for the specific conductivity you can calculate
all the other specific conductivities.

**Treatment of Data**

For each electrolyte solution calculate κ and hence Λ_{m} at each
concentration. Plot Λ_{m} vs. √c for KCl. Compare your experimental
value of Λ_{m}^{o} with that obtained from the literature.

For acetic acid plot 1/ Λ_{m} against cΛ_{m} and determine the value of
the dissociation constant (K). Use the box method to calculate
the error in the slope and hence determine the error in the value
of K. Compare your value with the literature value.

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