Download Buffer Capacity

Buffer Capacity (aka buffer index)
About the only time a buffer solution is used in its pure state, without any threat to its composition and,
therefore pH value, is in standardizing a pH meter. The immersion of a glass electrode does not contaminate
the buffer in the slightest, so the pH is completely unaffected.
Most of the time buffer solutions are used as supporting media in which various chemical and biological
processes are studied. For example, a spectrophotometric study of a pH-sensitive dye, such as an acid-base
indicator, involves dissolving a small concentration of the dye in a series of buffers. The kinetics of chemical
reactions are often studied by following the progress of the reaction at a (nearly) constant pH in a buffer.
Bacterial growth studies may use an agar medium containing a buffer of certain pH.
Frequently, the processes taking place in the buffer release small amounts of acidic or basic species. These,
in turn, react with one member of the buffer conjugate pair, causing small changes in the pair ratio and,
therefore, the solution pH. While some change may be inevitable, the researcher often wants to keep the pH
as nearly constant as possible. This requires design of a buffer with a satisfactory buffer capacity.
Buffer capacity may be thought of as “how much abuse the buffer can take without having its pH vary beyond
acceptable limits.” A kineticist may begin an experiment with the buffer system at pH 7.00 and be satisfied if
the studied reaction does not cause the pH to drop below, say, 6.5. Other experiments may require pH
constancy to within 0.001 unit.
Suppose you put 100 mL of a buffer in a beaker, attached a pH meter, and proceeded to add increments of
NaOH solution from a buret. The first tiny addition might not change the pH more than, say, 0.01 unit. As
the titration proceeds the buffer conjugate acid is converted to the conjugate base and, eventually, the buffer is
destroyed.
Differential Definition
The mathematical definition of buffer capacity is not based on destruction, but relates to the effect on pH of a
tiny addition of NaOH. Using calculus,
buffer capacity =  = [NaOH] / pH
that is, the derivative of the concentration of added NaOH with respect to pH. For practical purposes one
could add a millimole of NaOH to a liter of buffer and see how much the pH changes. Suppose pH was 0.02
units. Then,  = 0.001/0.02 = 0.05.
Deriving an expression for 
Consider a typical buffer comprising a mixture of a weak acid HA and its conjugate base salt NaA. The only
ions in the solution are H+, Na+, OH-, and A-. There must be as many cations as anions: the “Electroneutrality
Rule.” Therefore, no matter what variation of the mixture is used, it is always true that
h + na
=
oh + a
(simple symbols for concentrations, [H+], etc.
Using the water autoprotolysis constant Kw and the weak acid ionization constant Ka, you can derive this:
na = -h +Kw/h + C Ka/(h + Ka)
where C is the total concentration of HA and NaA.
We want to determine how the pH varies with tiny additions of NaOH. First, differentiate na with respect to h:
na / h
= -1 -Kw/h2 -C Ka/(h + Ka)2
Then, using the definition of pH = -ln(h)/2.3, show that h = -2.3 h pH. When this expression for h is
substituted, the result is an expression for buffer capacity:
 = na / pH = 2.3(h + oh + C Ka h /(h + Ka)2
If you enjoy using calculus, differentiate  with respect to h, and set the derivative to zero to find the conditions
for a maximum in the buffer capacity, assuming a constant value for C (it’s when h = K a).
Note that this expression also holds when C = 0. It can be used for a solution of 0.1 M HCl (h = 0.1), which
has a buffer capacity of 0.23. Similiarly, a solution of 1 M NaOH has a buffer capacity of 2.3. Pure water has
a buffer capacity of 4.6.10-7, essentially zero.
Buffer Capacity and Titrations
Look at a typical titration curve and you will see that it is relatively flat near the half-way point, and changing
sharply in the vicinity of the equivalence point. Think about this in terms of changing buffer capacity. Where
does it go through a maximum, and through a minimum? Indeed, the best way to detect the precise endpoint
of a potentiometric (glass electrode) titration is to plot experimental values of buffer capacity, calculated
point-by-point as V/ pH, versus volume V of added titrant.
Alternative Definition
The above differential definition of buffer capacity goes back to I. M. Kolthoff (1937) and even earlier to D. D.
Van Slyke (1922). According to IUPAC (1977) the definition is “The capacity of a solution to resist changes in
pH on the addition of strong acid or strong base which may be expressed numerically as the number of moles
required to change the pH by one unit when added to one liter of the specified buffer solution.”
The numerical values of buffer capacity based on this definition are different from those using the differential
definition. For a thorough discussion see Veronica Chiriac and Gabriel Balea, Journal of Chemical Education,
74, 937-9, (1997).