Question

How many times 1M $C{H}_{3}COOH$ solution should be diluted so that pH of the solution is doubled? $(K_{a}ofC{H}_{3}COOH=1.8\times {10}^{-5})$

• A. $20times$
• B. $200times$
• C. $5.55\times {10}^{2}times$
• D. $5.55\times {10}^{4}times$

Answer 1

The correct option is D $5.55\times {10}^{4}times$

pH of a weak acid $=\frac{1}{2}\left[pK{a}_{l}ogC\right]$
$\therefore x=\frac{1}{2}[p{K}_a-log1]=\frac{1}{2}p{K}_a$
and $2x=\frac{1}{2}[p{K}_a-logC]$
or, $p{K}_a=\frac{1}{2}p{K}_a=\frac{1}{2}logC,(\because 2x=p{K}_a)$
or, $\frac{1}{2}logC=-\frac{1}{2}p{K}_a$
or, $logC=-p{K}_a=log{K}_a$
or, $C=K_a=1.8\times {10}^{-5}$
$\therefore$ Dilution $=\frac{1}{1.8\times {10}^{-5}}=5.55\times {10}^{4}times$