123 / 912
Special Topic I
115
Copyright © 2017 Pearson Education, Inc.
The pH of an acetic acid/sodium acetate buffer solution
1
p
K
a
of acetic acid
=
4.76
2
that is 1.00 M in acetic acid
and 0.50 M in sodium acetate is calculated as follows:
p
pH log
HA
A
4.76 pH log
1.00
0.50
4.76 pH log 2
4.76 pH 0
a
K
= +
[ ]
= +
= +
= +
−
[ ]
.30
pH 4.46
=
Remember from Section 2.10 that compounds exist primarily in their acidic forms in solutions that are more acidic
than their
p
K
a
values and primarily in their basic forms in solutions that are more basic than their
p
K
a
values.
Therefore, it could have been predicted that the above solution will have a pH less than the
p
K
a
of acetic acid,
because there is more conjugate acid than conjugate base in the solution.
There are three ways a buffer solution can be prepared:
1. Weak Acid and Weak Base
A buffer solution can be prepared by mixing a solution of a weak acid with a solution of its conjugate base.
The pH of a formic acid/sodium formate buffer
1
p
K
a
of formic acid
=
3.75
2
solution prepared by mixing 25 mL
of 0.10 M formic acid and 15 mL of 0.20 M sodium formate is calculated as follows:
The equation below shows that the number of millimoles (mmol) of each of the buffer components can be
determined by multiplying the number of milliliters (mL) by the molarity (M).
M molarity
moles
liters
millimoles
milliliters
=
=
=
Therefore:
25
0 10
2 5
15
0 20
3 0
mL
M mmol formic acid
mL
M mmol sodium fo
×
=
×
=
.
.
.
.
rmate
p
pH
HA
A
pH log
pH
a
K
= +
= +
= +
−
log
[ ]
[ ]
.
.
.
.
log .
.
3 75
2 5
3 0
3 75
0 83
3 75
0 08
3 83
= −
=
pH
pH
.
.
Notice that in the following equation, we use mmol for both
3
HA
4
and
3
A
-
4
rather than molarity (mmol/mL)
because both the acid and the conjugate base are in the same solution, so they have the same volume. Therefore,
volumes cancel in the equation.
25
0 10
2 5
15
0 20
3 0
mL
M mm l formic acid
mL
M mmol sodium fo
×
=
×
=
.
.
.
.
rmate
p
pH
HA
A
pH log
pH
a
K
= +
= +
= +
−
log
[ ]
[ ]
.
.
.
.
log .
.
3 75
2 5
3 0
3 75
0 83
3 75
0 08
3 83
= −
=
pH
pH
.
.
It could have been predicted that the above solution would have a pH greater than the
p
K
a
of formic acid, because
there is more conjugate base than conjugate acid in the solution.