Physical Chemistry Third Edition

372 8 The Thermodynamics of Electrochemical Systems

Solution

From Eq. (8.4-2)

ln(γ±m/m◦)

(96,485 C mol−^1 )(0.2223 V− 0 .3524 V)

2(9.3145 J K−^1 mol−^1 )(298.15 K)

− 2. 532

γ±

e−^2.^532

0. 1000

 0. 795

For comparison, the Davies equation givesγ± 0 .781.

Determination of the Activity of Hydrogen Ions. pH

Since the activity of a single ion cannot be measured, we cannot correctly use the defi-

nition of the pH in terms of the activity of the hydrogen ion that is given in Eq. (7.3-10).

We modify the definition by replacing the true activity of hydrogen ions by the closest

approximation that we can obtain, denoted bya′(H+):

pH−log 10

[

a′(H+)

]

(8.4-3)

For a solution of HCl, we can write

a(H+)a(Cl−)a(HCl) (8.4-4)

If no other ions are present, the molalities of H+and Cl−are equal. If we can assume

thatγ(H+) is equal toγ(Cl−) we have a value ofγ(H+)m(H+)/m◦, and thus of the

pH for this solution.

Exercise 8.10

Find the pH of the solution in the cell of Example 8.7, assuming thatγ(H+)γ(Cl−).

In order to measure the pH of a solution other than an HCl solution the silver–silver

chloride electrode in the cell of Figure 8.2 is replaced by a calomel electrode confined

in a container that is fitted with a porous plug, as depicted in Figure 8.10. The solution in

the container of the calomel electrode is a KCl solution that is saturated with calomel

(Hg 2 Cl 2 ). If the concentration of the KCl is 1.0000 mol L−^1 , the electrode is called

thenormal calomel electrode. If the solution is saturated with KCl as well as with

calomel, the electrode is called thesaturated calomel electrode. The half-cell potential

of the normal calomel electrode is equal to 0.2802 V and that of the saturated calomel

electrode is equal to 0.2415 V. We place a hydrogen electrode and a saturated calomel

electrode, including its container, into the solution whose pH we wish to measure, as

shown in the figure. A liquid junction is formed inside the porous plug. The solution

does not have to be a solution of HCl, since the chloride ions needed to react at the

calomel electrode are inside the container of the calomel electrode.

The Nernst equation for the cell of Figure 8.10 is

E 0 .2415 V+ELJ−

RT

F

ln

(

a(H+)a(Cl−)

(P(H 2 )/P◦)^1 /^2

)

(8.4-5)

wherea(H+) is measured in one solution anda(Cl−) is measured in the solution that

is inside the container of the calomel electrode. Since the KCl solution on the calomel