Question

A chemist wishes to prepare a buffer solution of $pH=2.90$ that efficiently resists a change in $pH$ yet contains only small concentration of buffering agents. Which one of the following weak acid along with its salt would be best to use?

• A. m-chlorobenzoic acid $(p{K}_a=3.98)$
• B. Acetoacetic acid $(K_a=3.58)$
• C. $2.5$-dihydroxy benzoic acid $(p{K}_a=2.97)$
• D. p-chlorocinnamic acid $(p{K}_a=4.41)$

Answer 1

The correct option is C $2.5$-dihydroxy benzoic acid $(p{K}_a=2.97)$

The buffer solution to be made should effectively resist a change in pH, i.e., should have a higher buffer capacity.

Buffer capacity$\left(\varphi \right)$ $=\frac{No.ofmolesofacidorbaseaddedto1L}{ChangeinpH}$

By one of any two ways, we can obtain it,
(i) The higher the concentration of the components of a buffer mixture, the greater will be the buffer capacity. But, the condition is to maintain small concentrations of buffering components.

(ii) Buffer capacity of a buffer is maximum when the concentration of the weak acid and its salt are equal, i.e., $\left[salt\right]=\left[acid\right]$

$\therefore pH=p{K}_a+log\frac{\left[salt\right]}{\left[acid\right]}$

$=p{K}_a+log1$ (as $\left[salt\right]=\left[acid\right]$)

or $pH=p{k}_a=2.9$

As $2,5$-dihydroxy benzoic acid has $p{K}_a$ value $=2.97$, hence it is the best choice for a chemist to prepare buffer solution.