SECTION
1.2
Buffers
5
Titration profile of acetic acid (CH
3
COOH) with sodium hydroxide
(NaOH). Maximum buffering capacity is at pH = pK', at which point
minimal change in pH occurs upon addition of acid or base.
When OH
is added, almost all of the hydroxyl radicals
react with acetic acid molecules to produce more acetate
ions and water (OH- + CH
3
COOH
CH
3
COO- + H
2
0).
The additional OH- is thus consumed with little increase
in pH.
Adding H+ or OH- to a buffer causes only
slight
pH
changes provided there is excess salt (CH
3
COO ) or acid
(CH
3
COOH). If all of the acid is converted to the salt form
by the addition of a large amount of OH- , the solution can
no longer behave as a buffer. Adding more OH- will cause
the pH to rise rapidly, as if the solution contained no buffer
or only salt. The maximum buffering capacity exists when
the molarities of the salt and acid are equal, i.e., when pH =
pK' (or —
log K'). The pK' is at an inflection point on the
titration curve and hence is the point of minimum slope or
minimum change in pH for a given addition of acid or base
(Figure 1-4). In a generalized weak acid buffer reaction,
h
2
o + h a ^ h
3
o + + a -
a hydronium ion, H
3
0 +, is formed by the association of a
hydrogen ion with a water molecule. In dilute solutions,
the concentration of water changes very little when HA is
added; therefore, by convention, the dissociation reaction
equation is usually written as
H A ^ H + + A"
(1.3)
A weak acid, HA, does not readily dissociate, owing
to the high affinity of the conjugate base, A- , for the
hydrogen ion. Similarly in the hydrolysis reaction of a
weak base (B) and water, the ions OH
and HB+ (the
conjugate acid) are produced.
B + H20
HB++OH
The
concentration
of the
conjugate
base
(or acid)
generated from a weak acid (or base) is small, since,
by definition, weak acids and bases are only slightly
dissociated in aqueous solution. Examples of weak acids
are organic acids (e.g., acetic) and of strong acids are
mineral acids (e.g., hydrochloric and sulfuric).
Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation was developed
independently
by
the
American
biological
chemist
L. J. Henderson and the Swedish physiologist K. A.
Hasselbalch, for relating the pH to the bicarbonate buffer
system of the blood (see below). In its general form, the
Henderson-Hasselbalch equation is a useful expression
for buffer calculations. It can be derived from the equilib-
rium constant expression for a dissociation reaction of the
general weak acid (HA) in Equation (1.3):
[H+3CA- ]
[HA]
(1-4)
where
K
is the equilibrium constant at a given temper-
ature. For a defined set of experimental conditions, this
equilibrium constant is designated as
K ' (K
prime) and re-
ferred to as an apparent dissociation constant. The higher
the value of
K ',
the greater the number of H+ ions liber-
ated per mole of acid in solution and hence the stronger
the acid.
K'
is thus a measure of the strength of an acid.
Rearrangement of Equation (1.4) yields
7f'[HA]
=
[A- ]
(1.5)
Taking logarithms of both sides of Equation (1.5) and mul-
tiplying throughout by —
1
gives
- log[H+] = - log
K'
- log [HA] + log [A- ]
(1.6)
Substituting pH for —
log[H+] and pK' for —
log
K'
yields
or
pH = pK' + log
[A- ]
[HA]
pH = pK' + log
[conjugate base]
[acid]
(1.7)
(
1
.
8
)
This relationship is represented by the Henderson-
Hasselbalch equation.
Since a buffer is intended to give only a small change
in pH with added H+ or OH- , the best buffer for a given
pH is the one that gives the smallest change. As may be
