Question

The standard oxidation potential of $Ni/N{i}^{+2}$ electrode is $0.236\text{V}$. If this is combined with a hydrogen in acid solution, at what $pH$ of the solution will the measured emf be zero at ${25}^{\circ }\text{C}$ ?
Given $\left[N{i}^{+2}\right]=1\text{M},\frac{RT}{F}=0.059\text{V}$

Answer 1

According to the question
$Ni\to N{i}^{+2}+2e^{-};E_{OP}^{\circ }=0.236V$
$2H^{+}+2e^{-}\to H_2;E_{RP}^{\circ }=0.0V$
So, the standard cell potential of combination of the two half cells is
$E_{\text{cell}}^0=E_{OP}^{\circ }+E_{RP}^{\circ }=0.236\text{V}$
We know that
$E_{\text{cell}}=E_{\text{cell}}^0+\frac{0.059}{2}\log \frac{[H^{+}{]}^2}{\left[N{i}^{+2}\right]}$
$\Rightarrow 0=0.236+\frac{0.059}{2}\log [H^{+}{]}^2$
$\Rightarrow -\log H^{+}=4$
$\therefore pH=4$