Question

To what volume one litre of 0.1M acetic acid solution diluted so that the pH of the solution becomes double of the initial ? ( $K_a=1.8\times {10}^{-5}$)

• A. $5.5\times {10}^{5}L$
• B. $8\times {10}^{4}L$
• C. $2.4\times {10}^{3}L$
• D. $3.6\times {10}^{8}L$

Answer 1

The correct option is A

$5.5\times {10}^{5}L$

Acetic acid is a weak acid.
pH = $\frac{1}{2}p{K}_a–\frac{1}{2}$ log[conc] = $\frac{1}{2}\times 4.7447–\frac{1}{2}$ log(0.1) = 2.3723 + 0.5 = 2.8723

pH of the diluted solution = 2 $\times$ 2.8723 = 5.7446

or, 5.7446 = $\frac{1}{2}p{K}_a–\frac{1}{2}$ log[conc]

or, log[conc] = $p{K}_a$ – 11.4892
= 4.7446 – 11.4892 = - 6.7445 = $\overline{7}.3555$

conc. = $1.8\times {10}^{-7}$

$V_1{M}_1=V_2{M}_2$
$1\times 0.1=V_2\times 1.8\times {10}^{-7}$

$V_2$ = $5.5\times {10}^{5}L$