Question

An aqueous solution contains ${10}^{-4}\left[H^{+}\right]$. If it is diluted by mixing equal volume of water then the concentration of $O{H}^{-}$ in mol dm${}^{-3}$ will be:

• A. $0.5\times {10}^{-10}$
• B. $2\times {10}^{-10}$
• C. ${10}^{-6}$
• D. ${10}^{-8}$

Answer 1

Answer: (B)

$2\times {10}^{-10}$

Concentration of aqueous solution= ${10}^{-4}M$

If we add equal volume, let say $V$ of water. The final volume of solution will be $2V$. The new concentration is

$\Rightarrow M_1{V}_1=M_2{V}_2$

$\Rightarrow {10}^{-4}M\times V=M_2\times 2V$

$\Rightarrow M_2=5\times {10}^{-5}M$ $⟶$ New concentration of $\left[H^{+}\right]$ .

$pH=-\log \left[H^{+}\right]=-\log [5\times {10}^{-5}]$

$\Rightarrow pH=4.3$

$\Rightarrow pOH=14-pH=9.69$

$\Rightarrow -\log {[}^{-}OH]=9.69$

$\Rightarrow {[}^{-}OH]={10}^{-9.69}=2\times {10}^{-10}$

Thus the concentration of ${[}^{-}OH]$ is $2\times {10}^{-10}M$ .