122
ACIDS AND BASES
4.2 Acidity and pK a values
For the ionization of the acid HA in water
H 2 O
HA
+
A
H 3 O
+
K
the equilibrium constant K is given by the formula
K =
[A
− ][H 3 O
+ ]
[HA][H 2 O]
where [HA] signifies the concentration of HA, etc.
However, because the concentration of water is
essentially constant in aqueous solution, a new
equilibrium constant K a is defined as
K a =
[A
− ][H 3 O
+ ]
[HA]
K a is termed the acidity constant, and its magnitude
allows us to classify acids as strong acids (a
large value for K a and, consequently, a high H 3 O
+
concentration) or weak acids (a small value for K a
and, thus, a low H 3 O
+ concentration). For example,
the strong acid HCl has K a = 10
7 . However, for
weak acids, the amount of ionization is much less
and, consequently, the value of K a is rather small.
Thus, acetic acid CH 3 CO 2 H has K a = 1.76 × 10
−5 .
To avoid using such small numbers as these, K a is
usually expressed in the logarithmic form pK a where
pK a = − log 10 K a
Accordingly, the pK a for acetic acid is 4.75:
pK a = − log(1.76 × 10
−5 ) = −(−4.75) = 4.75
The pK a for hydrochloric acid can similarly be
calculated to be −7:
pK a = − log(10
7 ) = −7
This means there is an inverse relationship between
the strength of an acid and pK a :
• a strong acid has a large K a and, thus, a small pK a ,
i.e. A
− is favoured over HA;
• a weak acid has a small K a and, thus, a large pK a ,
i.e. HA is favoured over A
− .
Or, put another way:
• the smaller the value of pK a , the stronger is the
acid;
• the larger the value of pK a , the weaker is the
acid.
We find that pK a values range from about −12 to
52, but it must be appreciated right from the start that
a difference of one pK a unit actually represents a 10fold difference in K a and, thus, a 10-fold difference in
H 3 O
+ concentration. A twofold difference in acidity
would be indicated by a pK a difference of just 0.3
units (log 2 = 0.3). Accordingly, a difference of n
pK a units indicates a 10
n -fold difference in acidity,
so that the range −12 to 52 actually represents a
huge factor of 10
64 . A compound with pK a < 5
is regarded as a reasonably strong acid, and those
with pK a < 0 are very strong acids. At first glance,
negative pK a values seem rather strange, but this
only means that the equilibrium lies heavily towards
ionization; K a is large and, therefore, pK a = − log K a
becomes negative.
H 2 O
HA
+
A
H 3 O
+
K a = 10
K a = 1
K a = 0.1
pK a = −log 10 K a
K a = 0.01
K a = 100
increasing acid strength
pK a = 2 pK a = 1 pK a = 0 pK a = −1 pK a = −2
As we use pK a values, we shall find that, in most
cases, relative, rather than specific, values are all
we need to consider to help us predict chemical
behaviour and reactivity. Thus, from pK a values, we
can see that acetic acid (pK a 4.75) is a weaker acid
than hydrochloric acid (pK a − 7).
pK a values for a wide variety of different compounds are given in Tables 4.1–4.6. Compounds are
listed in order of increasing acidity. Although pK a
values included extend from about 52 to −10, values
in the middle of the range are known most accurately.
This is because they can be measured readily in aqueous solution. Outside of the range from about 2 to 12,
pK a values have to be determined in other solvents,
ACIDS AND BASES
4.2 Acidity and pK a values
For the ionization of the acid HA in water
H 2 O
HA
+
A
H 3 O
+
K
the equilibrium constant K is given by the formula
K =
[A
− ][H 3 O
+ ]
[HA][H 2 O]
where [HA] signifies the concentration of HA, etc.
However, because the concentration of water is
essentially constant in aqueous solution, a new
equilibrium constant K a is defined as
K a =
[A
− ][H 3 O
+ ]
[HA]
K a is termed the acidity constant, and its magnitude
allows us to classify acids as strong acids (a
large value for K a and, consequently, a high H 3 O
+
concentration) or weak acids (a small value for K a
and, thus, a low H 3 O
+ concentration). For example,
the strong acid HCl has K a = 10
7 . However, for
weak acids, the amount of ionization is much less
and, consequently, the value of K a is rather small.
Thus, acetic acid CH 3 CO 2 H has K a = 1.76 × 10
−5 .
To avoid using such small numbers as these, K a is
usually expressed in the logarithmic form pK a where
pK a = − log 10 K a
Accordingly, the pK a for acetic acid is 4.75:
pK a = − log(1.76 × 10
−5 ) = −(−4.75) = 4.75
The pK a for hydrochloric acid can similarly be
calculated to be −7:
pK a = − log(10
7 ) = −7
This means there is an inverse relationship between
the strength of an acid and pK a :
• a strong acid has a large K a and, thus, a small pK a ,
i.e. A
− is favoured over HA;
• a weak acid has a small K a and, thus, a large pK a ,
i.e. HA is favoured over A
− .
Or, put another way:
• the smaller the value of pK a , the stronger is the
acid;
• the larger the value of pK a , the weaker is the
acid.
We find that pK a values range from about −12 to
52, but it must be appreciated right from the start that
a difference of one pK a unit actually represents a 10fold difference in K a and, thus, a 10-fold difference in
H 3 O
+ concentration. A twofold difference in acidity
would be indicated by a pK a difference of just 0.3
units (log 2 = 0.3). Accordingly, a difference of n
pK a units indicates a 10
n -fold difference in acidity,
so that the range −12 to 52 actually represents a
huge factor of 10
64 . A compound with pK a < 5
is regarded as a reasonably strong acid, and those
with pK a < 0 are very strong acids. At first glance,
negative pK a values seem rather strange, but this
only means that the equilibrium lies heavily towards
ionization; K a is large and, therefore, pK a = − log K a
becomes negative.
H 2 O
HA
+
A
H 3 O
+
K a = 10
K a = 1
K a = 0.1
pK a = −log 10 K a
K a = 0.01
K a = 100
increasing acid strength
pK a = 2 pK a = 1 pK a = 0 pK a = −1 pK a = −2
As we use pK a values, we shall find that, in most
cases, relative, rather than specific, values are all
we need to consider to help us predict chemical
behaviour and reactivity. Thus, from pK a values, we
can see that acetic acid (pK a 4.75) is a weaker acid
than hydrochloric acid (pK a − 7).
pK a values for a wide variety of different compounds are given in Tables 4.1–4.6. Compounds are
listed in order of increasing acidity. Although pK a
values included extend from about 52 to −10, values
in the middle of the range are known most accurately.
This is because they can be measured readily in aqueous solution. Outside of the range from about 2 to 12,
pK a values have to be determined in other solvents,