Question

Consider the single electrode process $4H^{+}+4e^{-}\rightleftharpoons 2H_2$ catalysed by platinum black electrode in $HCl$ electrolyte. The potential of the electrode is $-0.059$V vs. $SHE$.

What is the concentration of the acid in the hydrogen half cell if the $H_2$ pressure is $1$ bar?

• A. $1M$
• B. $10M$
• C. $0.1M$
• D. $0.01M$

Answer 1

The correct option is C $0.1M$

The electrode reaction is $4H^{+}+4e^{-}\rightleftharpoons 2H_2$

The potential of the electrode is $-0.059V$ vs. SHE.

The $H_2$ pressure is $1$ bar.

$E=E^o-\frac{0.059}{n}log\frac{P_{H_2}^2}{[H^{+}{]}^4}$

$-0.059=0-\frac{0.059}{4}log\frac{1^2}{[H^{+}{]}^4}$

$4=log\frac{1}{[H^{+}{]}^4}$

$\frac{1}{[H^{+}{]}^4}={10}^4$

$[H^{+}{]}^4={10}^{-4}$

$\therefore \left[H^{+}\right]={10}^{-1}=0.1$ M $=\left[HCl\right]$.

The concentration of the acid in the hydrogen half cell is $0.1M$.