104
PART I
THERMODYNAMICS AND KINETICS
log x
n
= n log x
At the stoichiometric point, this relationship leads to a much sharper dependence on the added base than was determined at lower concentrations
(Figure 5.4), due to the conversion of the weak acid into its conjugate
base. If the strong base is added beyond the stoichiometric point, then
the pH behavior will predominately reflect the properties of the strong
base alone:
pH = pK W + log[excess base]
(5.27)
As an example of this pH behavior, consider a mixture of acetic acid,
CH 3 COOH, as the weak acid that is titrated with the strong base sodium
hydroxide, NaOH. Acetic acid has a pK A value of 4.75. For a solution with
0.1 M acetic acid, the pH is given by eqn 5.22:
(5.28)
Adding sodium hydroxide at a concentration of 0.05 M, which is half
of the concentration of the acetic acid, will convert half of the acetic acid
to its conjugate base, yielding from eqn 5.23 a pH of:
(5.29)
log 1 = 0 since e
0
= 1
Notice that the pH equals the pK A when the amount of the acid and its
conjugate base are equal.
Adding more sodium hydroxide to a concentration of 0.1 M converts
the acetic acid to its conjugated base and the pH is determined by eqn 5.26:
(5.30)
Finally, increasing the sodium hydroxide concentration to 0.2 M results
in a pH, as determined by eqn 5.27, of:
pH = pK W + log[excess base] = 14.0 − log(0.2) = 12.7
(5.31)
pH
.
log( . )
.
.
=
+
+
=
+
4 75
2
14
2
1
2
0 1 2 37 7 00
.
.
−
=
0 5 8 87
pH
p
p
A
log[ ]
=
+
+
−
1
2
1
2
1
2
K
K
A
W
pH p
A
HA
log
[ ]
[ ]
.
log
.
.
=
+
=
+
−
K A
4 75
0 05
0 05
.
= 4 75
pH
p
HA
log[ ]
.
log( . )
=
+
=
+
=
1
2
4 75
2
0 1 2
K A
. .88
9781405124362_4_005.qxd 4/29/08 9:08 Page 104
PART I
THERMODYNAMICS AND KINETICS
log x
n
= n log x
At the stoichiometric point, this relationship leads to a much sharper dependence on the added base than was determined at lower concentrations
(Figure 5.4), due to the conversion of the weak acid into its conjugate
base. If the strong base is added beyond the stoichiometric point, then
the pH behavior will predominately reflect the properties of the strong
base alone:
pH = pK W + log[excess base]
(5.27)
As an example of this pH behavior, consider a mixture of acetic acid,
CH 3 COOH, as the weak acid that is titrated with the strong base sodium
hydroxide, NaOH. Acetic acid has a pK A value of 4.75. For a solution with
0.1 M acetic acid, the pH is given by eqn 5.22:
(5.28)
Adding sodium hydroxide at a concentration of 0.05 M, which is half
of the concentration of the acetic acid, will convert half of the acetic acid
to its conjugate base, yielding from eqn 5.23 a pH of:
(5.29)
log 1 = 0 since e
0
= 1
Notice that the pH equals the pK A when the amount of the acid and its
conjugate base are equal.
Adding more sodium hydroxide to a concentration of 0.1 M converts
the acetic acid to its conjugated base and the pH is determined by eqn 5.26:
(5.30)
Finally, increasing the sodium hydroxide concentration to 0.2 M results
in a pH, as determined by eqn 5.27, of:
pH = pK W + log[excess base] = 14.0 − log(0.2) = 12.7
(5.31)
pH
.
log( . )
.
.
=
+
+
=
+
4 75
2
14
2
1
2
0 1 2 37 7 00
.
.
−
=
0 5 8 87
pH
p
p
A
log[ ]
=
+
+
−
1
2
1
2
1
2
K
K
A
W
pH p
A
HA
log
[ ]
[ ]
.
log
.
.
=
+
=
+
−
K A
4 75
0 05
0 05
.
= 4 75
pH
p
HA
log[ ]
.
log( . )
=
+
=
+
=
1
2
4 75
2
0 1 2
K A
. .88
9781405124362_4_005.qxd 4/29/08 9:08 Page 104