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I-2
added OH
-
. Again, no dramatic change in the pH is observed. This is the chemical principle that
makes buffer solutions effective.
If the initial concentrations of HA and A
–
used to prepare the solution are 0.010 M or greater, their
equilibrium concentrations, will not change appreciably. Also, the concentrations of HA and A
–
are
large when compared to [H3O
+
]. In fact, [H3O
+
] and the pH are determined by the ratio of the
concentrations of HA and A
–
, through the acid dissociation constant:
K
a
=
[H3O
+
][A
-
]
[HA]
(4)
Rearrangement gives:
[H3O
+
] =
K
a
[HA]
[A
-
]
(5)
and taking the negative logarithm of both sides gives:
pH = pK
a
- log
[HA]
[A
-
]
or
pH = pK
a
+ log
[A
-
]
[HA]
(6)
The Henderson-Hasselbalch equation (6) is the general form of this relationship that can be applied
to many weak acid - conjugate base pairs.
The Henderson-Hasselbalch equation is commonly used to estimate the pH of buffer solutions. All that
is required is the K
a
of the weak acid (or the K
b
of it’s conjugate base) and the concentrations of both
the weak acid and its conjugate base. By selecting the appropriate weak acid and its conjugate base and
manipulating the concentrations, the pH of a solution can be buffered to almost any desired value. It is
important to realize that a buffer cannot maintain the pH of a solution when relatively large amounts of
acid or base are added, which means, each buffer solution has a certain capacity for absorbing acids or
bases.
The effectiveness of a buffer or a buffer’s capacity refers to the amount of strong acid or strong base
that a buffer can neutralize before its pH changes appreciably. It should be noted that the term
“appreciable” depends strongly upon the situation. In biological systems, a pH change of 0.2 units is
appreciable, while in some industrial processes pH changes of 3 units may be considered appreciable.
In general, when calculating the capacity of a buffer, a pH change of 1 unit (ten fold increase or
decrease in the [H3O
+
]) is considered appreciable. The acid capacity of a buffer (amount of acid that a
buffer can absorb before its pH changes by one unit) is not necessarily equal to the buffer’s base
capacity (amount of base that a buffer can absorb before its pH changes by one unit). The maximum
