CEM
834
ACID–BASE
EQUILIBRIA
FALL
2005
I.
Monoprotic Acid–Base Systems
For the general monoprotic weak acid (HA) and its conjugate base
(
29
A

, the following
equilibrium reaction occurs in water
HA
H O
H O
A
2
3
+
⇔
+
+

This reaction may be expressed as the independent contributions from dissociation of the
weak acid
HA
H
A
K
a
a
a
a
d
H
A
HA
⇔
+
=
+

+

(1)
and dissociation of water
H O
H
OH
K
a
a
2
w
H
OH
⇔
+
=
+

+

(2)
For certain applications, it is necessary to determine the exact concentration of these
species.
In this case, rigorous solution of the stoichiometric equations describing the acid–
base system, perhaps with subsequent activity corrections, must be performed.
For other
applications, however, approximate knowledge of the concentrations or pH is sufficient.
In
this case, a rapid solution by graphical methods is appropriate.
Both the simultaneous
equation and graphical approaches will be described below.
A.
Simultaneous Equation Approach
1.
Write down all equilibria and dissociation constants for the acid–base system, as
shown in equations (1) and (2).
2.
Write a mass balance equation that relates the analytical concentrations of weak
acid and conjugate base
(
29
C
and C
respectively
HA
A

,
to the equilibrium
concentrations
[
]
[
]
(
29
HA and A
respectively

,
[
]
[
]
C
C
HA
A
HA
A
+
=
+


(3)
3.
Write a charge balance equation that relates the equilibrium concentrations of all
cations and anions
[
]
[
]
[
]
[
]
H
M
OH
A
+
+


+
=
+
(4)
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View Full DocumentNote that
M
+
, the cation associated with the conjugate base, must have a
concentration equal to the analytical concentration of the conjugate base
C
A

.
By
substitution and rearrangement of the charge balance equation (4)
[
]
[
]
[
]
(
29
A
C
H
OH
A

+

=
+


(5)
and by rearrangement of the mass balance equation (3)
[
]
[
]
HA
C
C
A
HA
A
=
+



(6)
By substitution of equation (5) into equation (6)
[
]
[
]
[
]
(
29
HA
C
H
OH
HA
=


+

(7)
From the equilibrium constant for the weak acid in equation (1)
[
]
[
]
γ
γ
=
=


+

A
HA
d
a
A
HA
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 Fall '05
 MCGUFFIN
 pH, H Ka

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