Question

One litre of solution contains ${10}^{-5}$ moles of $H^{+}$ ions at ${25}^{\circ }C$ percentage ionisation of water in solution is:

• A. $1.8\times {10}^{-7}$ %
• B. $1.8\times {10}^{-9}$ %
• C. $3.6\times {10}^{-9}$ %
• D. $1.8\times {10}^{-11}$%

Answer 1

The correct option is B $1.8\times {10}^{-9}$ %

In the presence of $\left[H^{+}\right]={10}^{-5}$, the dissociation of water is suppressed to a large extent.
Dissociation of water takes place as :
$H_{2}O\rightleftharpoons H^{+}+O{H}^{-}\left[H^{+}\right].\left[O{H}^{-}\right]={10}^{-14}{k}_w=({10}^{-5}+x)\left(x\right)$

$x$ can be neglected in comparison to ${10}^{-5}$
$\left[O{H}^{-}\right]={10}^{-9}as\left[H^{+}\right]={10}^{-5}\text{We know that for water d}=1gm{L}^{-1}$
1 L water = 1000 g water
moles of water $=\frac{1000}{18}=55.55$
$\alpha =\frac{{10}^{-9}}{55.5}=1.8\times {10}^{-11}$
% ionisation $=100\times 1.8\times {10}^{-11}=1.8\times {10}^{-9}$