Physical Chemistry Third Edition

322 7 Chemical Equilibrium

It is customary to specify the acidity of a solution in terms of the pH, which has

been variously defined. We would like to use the definition

pH−log 10

[

a

(

H+

)]

−log 10

(

γ

(

H+

)

m

(

H+

)

m◦

)

(desired

definition) (7.3-10)

where log 10 denotes the logarithm to the base 10 (thecommon logarithm). The activity

coefficientγ(H+) cannot be measured, but if it can be approximated in some way we

can use Eq. (7.3-10) as a working equation.

Exercise 7.8

Find the pH of the solution in Example 7.11.

EXAMPLE7.12

a.Find the value of the equilibrium constant at 298.15 K for the ionization of acetic acid.

b.Find the percentage of acetic acid molecules that ionize and the pH in a solution prepared

from 0.100 mol of acetic acid and 1.000 kg of water and maintained at 298.15 K. Use the

Davies equation to estimate activity coefficients. Neglect any H+ions contributed by the

ionization of water.

Solution

a.Write the ionization equation in the form

HA
H++A−

∆G◦ 0 +(− 369 .31 kJ mol−^1 )−(− 396 .46 kJ mol−^1 )

 27 .15 kJ mol−^1

Kexp

(

−27,150 J mol−^1

(8.3145 J K−^1 mol−^1 )(298.15 K)

)

 1. 752 × 10 −^5

b.Letxm(H+)/m◦m(A−)/m◦. First assume that all activity coefficients equal 1.

1. 752 × 10 −^5 

x^2

(0. 100 −x)

x^2 +(1. 752 × 10 −^5 )x− 1. 752 × 10 −^6  0

x

− 1. 752 × 10 −^5 ±

√

(1. 752 × 10 −5)2+4(1. 752 × 10 −^6 )

2

 1. 315 × 10 −^3

This corresponds to an ionic strength of 1.315× 10 −^3 mol kg−^1. From the Davies

equation

log 10 (γ±)− 0. 510

( √

0. 001315

1 +

√

0. 001315

−(0.30)(0.001315)

)

− 0. 01523