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,
Λm = κ / c

w here c is the molar concentration.
Kohlrausch found an empirical expression for the molar conductivity as
Λm = Λmo - k √c

where Λmo is the molar conductivity at infinite dilution and 'k' is a constant whose value depends on the type of electrolyte used (i.e. MA, M2A, MA2, etc.). The refined, Debye-Onsager theory gives essentially the same result.

2. Dissociation Constant

Consider the dissociation of acetic acid (a weak acid),
HOAc  +  H2O  <=>  H3O+    +   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 = α2c / (1- α)

If this equation is solved for α, and α is expressed as the ratio Λm / Λmo we get the following equation

1 / Λm = 1 / Λmo + c Λm/ K(Λmo)2

which is known as the Ostwalds dilution law, and we can see that, from a plot of 1 / Λm against cΛm, the values of Λmo 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 cm3 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 κKCl = 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 Λm at each concentration. Plot Λm vs. √c for KCl. Compare your experimental value of Λmo with that obtained from the literature.
For acetic acid plot 1/ Λm against cΛm 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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