Question

Hydrogen ion concentration of an aqueous solution is $1\times {10}^{-4}M$. The solution is diluted with equal volume of water. Hydroxyl ion concentration of the resultant solution in terms of mol $d{m}^{-3}$ is __________.

• A. $1\times {10}^{-8}$
• B. $1\times {10}^{-6}$
• C. $2\times {10}^{-10}$
• D. $0.5\times {10}^{-10}$

Answer 1

The correct option is C $2\times {10}^{-10}$

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

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

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

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

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

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

$\Rightarrow pH=4.3$

$\Rightarrow pOH=14-pH=9.69$

$\Rightarrow -log\left[O{H}^{-}\right]=9.69$

$\Rightarrow \left[O{H}^{-}\right]={10}^{-9.69}=2\times {10}^{-10}$

$\text{Thus the concentration of}\left[O{H}^{-}\right]is2\times {10}^{-10}M.$