Question

The potential of a hydrogen electrode at $pH=10$ is:

• A. $0.59V$
• B. $0.00V$
• C. $-0.59V$
• D. $-0.059V$

Answer 1

Answer: (C)

$-0.59V$

$pH=10$

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

$\left[H^{+}\right]={10}^{-10}$ M
$2H^{+}+2e^{-}\to H_2$

$E_{cell}=E_{cell}^0-\frac{0.059}{n}\log \frac{P_{H_2}}{[H^{+}{]}^2}$

$E_{cell}=0.0V-\frac{0.059}{2}\log \frac{1atm}{[{10}^{-10}{]}^2}$

$E_{cell}=-\frac{0.059}{2}\log {10}^{20}$

$E_{cell}=-\frac{0.059\times 20}{2}$

$E_{cell}=-0.59V$

The potential of a hydrogen electrode at $pH=10$ is $-0.59V$.

Hence, the correct option is $\text{C}.$