Question

The ratio of $pH$ of a solution containing $1$ mole of ${CH}_{3}COONa+1$ mole of $HCl$ per litre and of other solution containing $1$ mole of ${CH}_{3}COONa+1$ mole of acetic acid per litre is:

• A. $p{H}_1:p{H}_2::2:5$
• B. $p{H}_1:p{H}_2::2:3$
• C. $p{H}_1:p{H}_2::1:2$
• D. none of these

Answer 1

Answer: (C)

$C{H}_{3}COONa+HCl⟶C{H}_{3}COOH+NaCl$

$\left[C{H}_{3}COOH\right]=\left[C{H}_{3}COONa\right]=1$ $mol/L$

$pH$ for weak acid $=-\log \sqrt{\frac{K_a}{C}}=\frac{1}{2}[p{K}_a+\log C]=\frac{1}{2}[p{K}_a+\log 1]=\frac{p{K}_a}{2}\left(1\right)$

$1$ $mole$ of $C{H}_{3}COONa+1$ $mole$ of acetic acid for a buffer solution.

$pH$ of this buffer $=p{K}_a+\log \frac{\left[C{H}_{3}COONa\right]}{\left[C{H}_{3}COOH\right]}=p{K}_a+\log 1=p{K}_a\left(2\right)$

$\therefore$ Required ratio $=\frac{pHin\left(1\right)}{pHin\left(2\right)}=\frac{p{K}_a/2}{p{K}_a}=\frac{1}{2}$