Page 187 - Modern Analytical Chemistry

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170 Modern Analytical Chemistry

Substituting the new concentrations into the Henderson–Hasselbalch equation
gives a pH of
0 021
.
.
pH = 924 +log =910
.
.
0 029
Multiprotic weak acids can be used to prepare buffers at as many different pH’s
as there are acidic protons. For example, a diprotic weak acid can be used to prepare
buffers at two pH’s and a triprotic weak acid can be used to prepare three different
buffers. The Henderson–Hasselbalch equation applies in each case. Thus, buffers of
malonic acid (pK a1 = 2.85 and pK a2 = 5.70) can be prepared for which
C HM –
pH = 285 +log
.
C HM
2
C M 2–
.
pH = 570 +log
C HM –
2–
–
where H 2 M, HM , and M are the different forms of malonic acid.
The capacity of a buffer to resist a change in pH is a function of the absolute
concentration of the weak acid and the weak base, as well as their relative propor-
tions. The importance of the weak acid’s concentration and the weak base’s con-
centration is obvious. The more moles of weak acid and weak base that a buffer
has, the more strong base or strong acid it can neutralize without significantly
changing the buffer’s pH. The relative proportions of weak acid and weak base af-
fect the magnitude of the change in pH when adding a strong acid or strong base.
Buffers that are equimolar in weak acid and weak base require a greater amount of
2
strong acid or strong base to effect a change in pH of one unit. Consequently,
buffers are most effective to the addition of either acid or base at pH values near
the pK a of the weak acid.
Buffer solutions are often prepared using standard “recipes” found in the
3
chemical literature. In addition, computer programs have been developed to aid in
4
the preparation of other buffers. Perhaps the simplest means of preparing a buffer,
however, is to prepare a solution containing an appropriate conjugate weak acid
and weak base and measure its pH. The pH is easily adjusted to the desired pH by
adding small portions of either a strong acid or a strong base.
Although this treatment of buffers was based on acid–base chemistry, the idea
of a buffer is general and can be extended to equilibria involving complexation or
redox reactions. For example, the Nernst equation for a solution containing Fe 2+
3+
and Fe is similar in form to the Henderson–Hasselbalch equation.
+
2
[ Fe ]
E = E ° 3 + / Fe 2 + -0 05916 log 3 +
.
Fe
[ Fe ]
Consequently, solutions of Fe 2+ and Fe 3+ are buffered to a potential near the
3+
standard-state reduction potential for Fe .
6H.2 Representing Buffer Solutions with Ladder Diagrams
Ladder diagrams provide a simple graphical description of a solution’s predominate
species as a function of solution conditions. They also provide a convenient way to
show the range of solution conditions over which a buffer is most effective. For ex-