In this and following chapter’s, more difficult problems are indicated by an asterisk.The...

In this and following chapter’s, more difficult problems are indicated by an asterisk.

The efficiency of a buffer in resisting changes in pH upon addition of base or acid is referred to as the buffer capacity. One way to define this quantity, which we shall call B, is B = dx/dpH,where x is the number of moles of base added to a weak acid. Note that the Henderson-Hasselbalch equation may be written as

where A0is the total concentration of acid.

(a) Obtain an expression for B, in terms of A0 and the fraction of acid titrated f,

where f = x/A0. [Hint: It is easiest to determine dpH/dx and take the reciprocal]

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(b) At what value of f is buffer capacity maximal? (The easiest way to determine this is to make a graph of B versus f.)

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 (c) What is the maximal value of B?

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 (d) What is the effect of A0 on B?