Question

If $10$ litres aqueous solution of $\left(A\right)$ is electrolysed when $1$ faraday of electricity is passed, then $pH$ of the solution is:

• A. $1$
• B. $13$
• C. $2$
• D. $12$

Answer 1

The correct option is B $13$

If 10 litres aqueous solution of (A) is electrolysed when 1 faraday of electricity is passed, then pH of the solution is 13.

At cathode, 2 mol of $O{H}^{-}$ is obtained by 2 faraday. (Or 1 faraday produces 1 equivalent of $O{H}^{-}$ ions).
1 faraday $\Rightarrow$ 1 mol of $O{H}^{-}$ ions

Concentration of $O{H}^{-}$ ions $\frac{Mole}{Volume\left(inlitres\right)}=\frac{1}{10}$
$=0.1M={10}^{-1}M$

$pOH=-log\left[O{H}^{-}\right]=-log\left[{10}^{-1}\right]=1$
$pH=14-pOH=14-1=13$

So the answer is the option (B).