Question

The percentage degree of dissociation of water at ${25}^{o}C$ is $1.9\times {10}^{-7}$ and density is 1.0 g $c{m}^{-3}$ The ionic constant for water is:

• A. $1.0\times {10}^{-10}$
• B. $1.0\times {10}^{-14}$
• C. $1.0\times {10}^{-16}$
• D. $1.0\times {10}^{-8}$

Answer 1

The correct option is B $1.0\times {10}^{-14}$

$\underset{(1-\alpha )c}{H_{2}O}\rightleftharpoons \underset{\alpha C}{H^{+}}+\underset{\alpha c}{O{H}^{-}}$
$\alpha =\frac{1.9\times {10}^{-7}}{100}=1.9\times {10}^{-9}$
$\text{Density of water}=\frac{1.0g}{c{m}^3}$
$\therefore c=\frac{1}{18}\times 1000=55.56\text{moles}\therefore \left[H^{+}\right]=55.56\times 1.9\times {10}^{-9}=1.055\times {10}^{-7}\therefore K_w=\left[H^{+}\right]\left[O{H}^{-}\right]=(1.055\times {10}^{-7}{)}^2=1.0\times {10}^{-14}$