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Special Topic I
113
Copyright © 2017 Pearson Education, Inc.
Acetic acid
1
CH
3
COOH
2
is an example of a weak acid. It has an acid dissociation constant of
1.74
*
10
-
5
1
p
K
a
=
4.76
2
.
The pH of a 1.00 M solution of acetic acid can be calculated as follows:
CH COOH
H CH COO
H CH COO
CH COOH
a
3
3
3
3
+
−
+
−
+
=
K
[ ][
]
[
]
Each molecule of acetic acid that dissociates forms one proton and one acetate ion. Therefore, the concentration of
protons in solution equals the concentration of acetate ions. Each has a concentration that can be represented by
x
.
The concentration of acetic acid, therefore, is the concentration we started with minus
x
.
1 74 10
1 00
5
.
( ) ( )
.
×
=
−
−
x x
x
The denominator
1
1.00
-
x
2
can be simplified to 1.00 because 1.00 is much greater than
x
. (When we actually
calculate the value of
x
, we see that it is 0.004. And
1.00
-
0.004
=
1.00.
)
1.74 10
1.00
4.17 10
pH log 4.17 10
pH 2.38
5
2
3
3
×
=
= ×
= −
×
=
−
−
−
x
x
Formic acid (HCOOH) has a
p
K
a
value of 3.75. The pH of a 1.50 M solution of formic acid can be calculated as follows:
HCOOH
H HCOO
H HCOO
HCOOH
a
+
−
+
−
+
=
K
[ ] [
]
[
]
A compound with a
p
K
a
=
3.75
has an acid dissociation constant of
1.78
*
10
-
4
.
1.78 10
( ) ( )
1.50
1.50
= 1.50 (1.78 10 )
2.67 10
4
2
2
4
2
×
=
−
=
×
= ×
−
−
x x
x
x
x
x
−
4
2
2
1.63 10
pH log 1.63 10
pH 1.79
x
= ×
= −
×
=
−
−
(
)
Weak Bases
When a weak base is dissolved in water, it accepts a proton from water, creating hydroxide ion.
Determining the concentration of hydroxide allows the pOH to be determined, and this, in turn, allows the pH to be
determined.