Question

The standard oxidation potential of $Ni/N{i}^{2+}$ electrode is 0.236 V. If this is combined with a hydrogen electrode in acid solution, at what pH of the solution will the measured emf be zero at ${25}^{0}C$? assume $\left[N{i}^{2+}\right]=1M$ and $P_{H2}=1atm$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is D 4

The Nernst equation for the emf of the cell is $E_{cell}=E_{cell}^0-\frac{0.0592}{n}log\frac{{\lfloor {Ni}^{2+}\rfloor \times P}_{H2}}{{\lfloor H^{+}\rfloor }^2}$
The standard emf of the cell is $E_{cell}^0=E_{H2}^0-E_{Ni2+|Ni}^0=0-(-0.236)=0.236V$
The emf of cell will be zero when
$E_{cell}=E_{cell}^0-\frac{0.0592}{n}log\frac{{\lfloor {Ni}^{2+}\rfloor \times P}_{H2}}{{\lfloor H^{+}\rfloor }^2}0.0V=0.236V-\frac{0.0592}{2}log\frac{\lfloor 1\rfloor \times 1}{{\lfloor H^{+}\rfloor }^2}$
Hence, $log\frac{1}{{\lfloor H^{+}\rfloor }^2}=7.9729\lfloor H^{+}\rfloor =1.03\times {10}^{-4}$
$=>$ pH $=-lo{g}_{10}\left[H^{+}\right]=-lo{g}_{10}1.03\times {10}^{-4}=$ 4.