Page 108 - Basic physical chemistry for the atmospheric sciences

94 Basic physical chemistry

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acid-base con u gate pair provided that neither the acid nor the base is
very strong [e.g. , acetic acid, HC2H30 , and the acetate ion,
2
C2H30 2 ( aq)] . If a small amount of a strong acid is added to s u ch a
solution, most of the added H30 + (aq) will combine with the weak
base of the buffer (to form the con u gate acid of that weak base), so
j
that the H3Q + ( aq) concentration and pH of the solution will not
l
change very much. Similar y , if a small amount of a strong base is
added to the solution, most of the oH - ( aq) will combine with the
weak acid of the buffer. From the equilibrium equation for the ioniza­
tion of acetic acid, the reverse reaction of (5. 2 3), we have

[C 2 H30i (aq)][H30 + (aq)]
Ka (acetic acid)
H 0
[HC 2 3 2 (aq)]
Therefore, to achieve a specific pH, or [H3Q + ( aq)] , the ratio of the
concentration of acetic acid to acetate ion must be
+
[HC2H30 (aq)] [H3Q (aq)]
2
[C 2 H30i (aq)] Ka(acetic acid)
We can generalize the above ideas as follows. Let us represent the
weak acid in a buffer by HA and the corresponding salt by MA. The
equilibrium reaction for the acid dissociation is

HA(aq) � H + (aq) + A - (aq)
and the acid-dissociation constant is given by
[H + (aq)][A - ( aq)]
K (5 .26)
[HA(aq)]
a
Or, since A - ( aq) is the base and HA(aq) the acid in the buffer,
[acid]
[H + (aq)] = [base] K a (5 .27)

From Eq. (5. 2 6)
[A - (aq)]
logKa - log[H (aq)] + log
+
_
[HA(aq)]
or,
[A - ( aq)]
- logK = pH - log [HA(aq)]
a