PHYSICAL CHEMISTRY IN BRIEF

CHAP. 11: ELECTROCHEMISTRY [CONTENTS] 390

11.6.11pH of the salt of a strong acid and a weak base

In consequence of hydrolysis, see section11.5.9, solutions of the salts of strong acids and weak
bases exhibit acidic reactions. When calculating the pH it is usually necessary to consider not
only the hydrolytic equilibrium but also the dissociation of water. We solve the set of equations
(11.75) and (11.49), which does not have an analytical solution. When the degree of hydrolysis
is low, however, we obtain an analytical relation for the pH

pH =−

1

2

log

Kwc

K cst

, (11.98)

whereKwis the ionic product of water,Kis the dissociation constant of the base, andcis the
initial concentration of the salt.

11.6.12pH of the salt of a weak acid and a weak base

When calculating the pH, we have to solve the set of three equations (11.81), (11.82) and
(11.49), of which the first two describe a hydrolytic equilibrium and the third describes the
dissociation of water. This set does not have an analytical solution and thus has to be solved
numerically. If, however, the degrees of hydrolysisα 1 andα 2 are low, we obtain a simplified
relation for the pH

pH =−

1

2

log

KaKw

Kb

, (11.99)

whereKais the dissociation constant of the acid,Kbis the dissociation constant of the base,
andKwis the ionic product of water.

Note:From relation (11.99) it follows that atKa> Kbthe solution of the salt solution is

acidic while in the opposite case it is alkaline.

11.6.13Buffer solutions

Abuffer solution(buffer) is a system whose pH changes only a little with the addition of an
acid or a base. It is usually an aqueous solution of a weak acid and its salt with a strong base
(e.g. CH 3 COOH + CH 3 COONa), or a solution of a weak base and its salt with a strong acid
(e.g. NH 4 OH + NH 4 Cl).