PHYSICAL CHEMISTRY IN BRIEF

CHAP. 11: ELECTROCHEMISTRY [CONTENTS] 391

We obtain the pH of a buffer solution formed by a weak acid HA of the concentrationcand
its salt NaA of the concentrationcsby solving equation (11.53)

pH =−log

(γ

±

2 cst

[

−(K′+cs) +

√

(K′+cs)^2 + 4K′c

])

, (11.100)

whereK′=K cst

γHA

γ±^2

, andKis the dissociation constant of the acid. If the degree of dissoci-

ation of the acid is very low, the relation simplifies to

pH =−log

K′c γ±

cstcs

. (11.101)

We obtain the pH of a buffer solution formed by a weak base BOH of the concentrationc
and its salt BCl of the concentrationcsby solving equation (11.57)

pH =−log



^2 Kwcst

γ±

[

−(K′+cs) +

√

(K′+cs)^2 + 4K′c

]



, (11.102)

whereK′=K cst

γHA

γ±^2

, andKis the dissociation constant of the base. For a low degree of the

base dissociation this relation rearranges to

pH =−log

Kwcscst

K′c γ±

. (11.103)

In relations (11.100) through (11.103) the influence of water dissociation is not considered.
If their application leads to a pH close to the pH of pure water, it is a warning signal indicating
that their application was not necessarily justified.

Note:The reason for the low sensitivity of the pH of a buffer solution to the addition of

an acid or a base relates to Le Chatelier’s principle, see8.5. In the case of a weak acid

and its salt, the following reaction proceeds in the system

HA = H++ A−, NaA−→Na++ A−.

The addition of an acid to this system, i.e. H+ions, will suppress the dissociation of the

acid because H+ions are actually the products of the reaction, see8.5.1The addition of

a base, i.e. OH−ions, will increase the dissociation of the acid. The hydroxylic ions react

with the hydrogen ions and thus withdraw the products of the dissociation.