Question

The concentration of $\left[H^{+}\right]$ and concentration of $\left[O{H}^{-}\right]$ of a 0.1M aqueous solution of 2% ionised weak acid is:
[Ionic product of water $=$ $1\times {10}^{-14}$ ]

• A. $2\times {10}^{-3}M$ and $5\times {10}^{-12}M$
• B. $1\times {10}^{3}M$ and $3\times {10}^{-11}M$
• C. $0.02\times {10}^{-3}M$ and $5\times {10}^{-11}M$
• D. $3\times {10}^{-2}M$ and $4\times {10}^{-13}M$

Answer 1

The correct option is A $2\times {10}^{-3}M$ and $5\times {10}^{-12}M$

The weak acid is 2% ionized.

Hence, the degree of ionization $\alpha =\frac{2}{100}=0.02$.

The concentration of the solution is $C=0.1$ M.

The hydrogen ion concentration is $\left[H^{+}\right]=\alpha \times C=0.02\times 0.1=2\times {10}^{-3}M$.

But $\left[H^{+}\right]\left[O{H}^{-}\right]=K_w={10}^{-14}$.

Hence, $\left[O{H}^{-}\right]=\frac{{10}^{-14}}{2\times {10}^{-3}}=5\times {10}^{-12}$M.

Option A is correct.