Relative Concentrations of Conjugate Acids & Bases
Every weak acid has a conjugate weak base (and, of course, every weak base has a conjugate weak acid). For
example, acetic acid,
CH3COOH
for example, is in equilibrium with the acetate ion,
CH3COO–
, as shown by
the following reaction
CH3COOH(aq) + H2O(l)H3O+(aq) + CH3COO–(aq)
According to Le Châtelier’s principle, adding a strong acid, a source of H3O+, shifts this equilibrium to the
left, increasing the concentration of
CH3COOH
, and adding a strong base, a source of
OH–
, consumes
H3O+
and shifts the equilibrium to the right, increasing the concentration of
CH3COO–
. Clearly there are pH levels
that favor acetic acid and pH levels that favor the acetate ion, although the exact pH levels are not clear
from this simple treatment.
The acid dissociation constant for a weak acid is a good starting point for considering how pH affects the
relative amount of a weak acid and its conjugate weak base. For acetic acid the Kaexpression is
Ka=[H3O+][CH3COO–]
[CH3COOH]
Taking the log of both sides, multiplying through by –1, and substituting in pH for –log[
H3O+
] and p
Ka
for
–logKagives
pKa=pH −log [CH3COO–]
[CH3COOH]
Solving for the ratio of weak base-to-weak acid, we obtain
[CH3COO–]
[CH3COOH]= 10pH−pKa
This equation shows us that the relative amounts of
CH3COOH
and of
CH3COO–
are determined by how
close the solution’s pH is to acetic acid’s
pKa
value, which is 4.74. Some actual values are shown in the
following table:
pH pH −pKa[CH3COO–]
[CH3COOH]
1.74 –3.00 0.0010
2.74 –2.00 0.010
3.74 –1.00 0.10
4.74 0 1.0
5.74 +1.00 10
6.74 +2.00 100
7.74 +3.00 1000
We can use these results to make some general statements about the relative importance of acetic acid’s
conjugate weak acid and conjugate weak base forms as a function of pH. At a pH of 3.74, for example, there
is one acetate ion for every 10 molecules of acetic acid; thus, for all practical purposes, at any pH < 3.74,
CH3COOH
accounts for more than 90% of a mass balance on acetic acid and it is the only important form of
acetic acid in solution. At a pH of 5.74, there are 10 acetate ions for every one molecule of acetic acid; thus,
at any pH > 5.74,
CH3COO–
accounts for more than 90% of a mass balance on acetic acid and it is the only
