Physical Chemistry Third Edition

8.4 The Determination of Activities and Activity Coefficients of Electrolytes 371

8.4 The Determination of Activities and

Activity Coefficients of Electrolytes

These activity coefficients can be determined in several ways.

Determination by Vapor Pressure

In the case of a volatile electrolyte such as HCl or HNO 3 , the mean ionic activity

coefficient can be determined from the partial vapor pressure, using Eq. (7.4-12).

EXAMPLE 8.6

Using information in Example 7.15, find the value ofγ±for HCl at 10.00 mol kg−^1 and

298.15 K, in which case the partial vapor pressure of HCl is equal to 4.20 torr.a

Solution

γ^2 ±

P(HCl)

k±(m)m^2



(4.20 torr)

(

1 atm

760 torr

)

(4. 92 × 10 −^7 atm kg^2 mol−^2 )(10.00 mol kg−^1 )^2

 112

γ± 10. 6

aS. J. Bates and H. D. Kirschman,J. Am. Chem. Soc., 41 , 1991 (1919).

Activity Coefficients of Nonvolatile Electrolytes

The activities and activity coefficients of nonvolatile electrolytes can be determined

by the isopiestic method, as described in Chapter 6. They can also be determined

by electrochemical measurements. As an example consider the cell of Figure 8.2, for

which the Nernst equation is

EE◦−

RT

2 F

ln

(

a(HCl)^2

P(H 2 )/P◦

)

(8.4-1)

If the value ofE◦is known, the activity coefficient of HCl can then be determined

from the Nernst equation. Let us maintainP(H 2 ) equal toP◦and measure the

voltage at a molality of HCl equal tom. The Nernst equation can be written in

the form

lna(HCl)2ln

(

γ±m/m◦

)



F(E◦−E)

RT

(8.4-2)

EXAMPLE 8.7

In a cell such as that of Figure 8.2, a voltage of 0.3524 V was measured with a solution having

a molality of HCl equal to 0.1000 mol kg−^1 and a hydrogen pressure equal to 1.000 bar. Find

the value of the activity and of the mean ionic activity coefficient of HCl, assuming hydrogen

to be an ideal gas.