150
ACIDS AND BASES
to non-ionized forms by a factor of 10. Every further
shift of pH by one unit changes the ratio by a further
factor of 10.
Thus, for example, if the pK a of a base is 10, at pH
7 the ratio of free base to protonated base is 1:10
3 .
An acid with pK a 2 at pH 7 would produce a ratio
of acid to anion of 10
5 :1.
Box 4.6
Calculation of percentage ionization
Using the Henderson–Hasselbalch equation, we can
easily calculate the amount of ionized form of an acid
or base present at a given pH, provided we know the
pK a .
For example, consider aqueous solutions of acetic
acid (pK a 4.75) first at pH 4.0 and then at pH 6.0.
Since
pH = pK a + log
[A
− ]
[HA]
at pH 4.0
log
[A
− ]
[HA]
= pH − pK a = 4.0 − 4.75 = −0.75
Thus
[A
− ]
[HA]
= 10
−0.75 = 0.18
If we consider [A
− ] = I , the fraction ionized, then
[HA] is the fraction non-ionized, i.e. 1 − I , and
I/(1 − I ) = 0.18, from which I may be calculated
to be about 0.15 or 15%.
At pH 6.0, pH – pK a = 1.25, and the calculation
yields I/(1 − I ) = 10 1.25 = 17.8, so that I = 0.95,
i.e. 95% ionized.
With a base such as ammonia (pK a 9.24), the
percentages ionized at pH 8.0 and 10.0 are calculated
as follows:
pH = pK a + log
[B]
[BH
+ ]
At pH 8.0
log
[B]
[BH
+ ]
= pH − pK a = 8.0 − 9.24 = −1.24
Thus
[B]
[BH
+ ]
= 10
−1.24 = 0.057
Now with bases, [B] is the non-ionized fraction
1 − I and [BH
+ ] is the ionized fraction I , so
(1 − I )/I = 0.057, and therefore I = 0.95, i.e. 95%
ionized.
At pH 10.0, the calculation yields (1 − I )/I =
10
0.76
= 5.75, so that I = 0.15, i.e. 15% ionized.
Box 4.7
The ionization of amino acids at pH 7
Peptides and proteins are composed of α-amino acids linked by amide bonds (see Section 13.1). Their properties,
for example the ability of enzymes to catalyse biochemical reactions, are dependent upon the degree of ionization
of various acidic and basic side-chains at the relevant pH. This aspect will be discussed in more detail in
Section 13.4, but, here, let us consider a simple amino acid dissolved in water at pH 7.0. An α-amino acid has
an acidic carboxylic acid group and a basic amine group. Both of these entities need to be treated separately.
NH 2
R
CO 2 H
α-amino acid
The carboxylic acid groups of amino acids have pK a values in a range from about 1.8 to 2.6 (see Section 13.1).
Let us consider a typical carboxylic acid group with pK a 2.0. Using the Henderson–Hasselbalch equation
pH = pK a + log
[RCO 2
− ]
[RCO 2 H]
ACIDS AND BASES
to non-ionized forms by a factor of 10. Every further
shift of pH by one unit changes the ratio by a further
factor of 10.
Thus, for example, if the pK a of a base is 10, at pH
7 the ratio of free base to protonated base is 1:10
3 .
An acid with pK a 2 at pH 7 would produce a ratio
of acid to anion of 10
5 :1.
Box 4.6
Calculation of percentage ionization
Using the Henderson–Hasselbalch equation, we can
easily calculate the amount of ionized form of an acid
or base present at a given pH, provided we know the
pK a .
For example, consider aqueous solutions of acetic
acid (pK a 4.75) first at pH 4.0 and then at pH 6.0.
Since
pH = pK a + log
[A
− ]
[HA]
at pH 4.0
log
[A
− ]
[HA]
= pH − pK a = 4.0 − 4.75 = −0.75
Thus
[A
− ]
[HA]
= 10
−0.75 = 0.18
If we consider [A
− ] = I , the fraction ionized, then
[HA] is the fraction non-ionized, i.e. 1 − I , and
I/(1 − I ) = 0.18, from which I may be calculated
to be about 0.15 or 15%.
At pH 6.0, pH – pK a = 1.25, and the calculation
yields I/(1 − I ) = 10 1.25 = 17.8, so that I = 0.95,
i.e. 95% ionized.
With a base such as ammonia (pK a 9.24), the
percentages ionized at pH 8.0 and 10.0 are calculated
as follows:
pH = pK a + log
[B]
[BH
+ ]
At pH 8.0
log
[B]
[BH
+ ]
= pH − pK a = 8.0 − 9.24 = −1.24
Thus
[B]
[BH
+ ]
= 10
−1.24 = 0.057
Now with bases, [B] is the non-ionized fraction
1 − I and [BH
+ ] is the ionized fraction I , so
(1 − I )/I = 0.057, and therefore I = 0.95, i.e. 95%
ionized.
At pH 10.0, the calculation yields (1 − I )/I =
10
0.76
= 5.75, so that I = 0.15, i.e. 15% ionized.
Box 4.7
The ionization of amino acids at pH 7
Peptides and proteins are composed of α-amino acids linked by amide bonds (see Section 13.1). Their properties,
for example the ability of enzymes to catalyse biochemical reactions, are dependent upon the degree of ionization
of various acidic and basic side-chains at the relevant pH. This aspect will be discussed in more detail in
Section 13.4, but, here, let us consider a simple amino acid dissolved in water at pH 7.0. An α-amino acid has
an acidic carboxylic acid group and a basic amine group. Both of these entities need to be treated separately.
NH 2
R
CO 2 H
α-amino acid
The carboxylic acid groups of amino acids have pK a values in a range from about 1.8 to 2.6 (see Section 13.1).
Let us consider a typical carboxylic acid group with pK a 2.0. Using the Henderson–Hasselbalch equation
pH = pK a + log
[RCO 2
− ]
[RCO 2 H]