Question

What pressure (bar) of $\text{H}_2$ would be required to make the emf of a hydrogen electrode zero in pure water at $25^\circ \text{C}$?

• A. $10^{-14}$
• B. $10^{-7}$
• C. 1
• D. 0.5

Answer 1

Answer: (C)

1

Answer 2

Understanding the Hydrogen Electrode Reaction:

The reaction at the hydrogen electrode is:

$2e^- + 2H^+(aq) \rightarrow H_2(g)$

Nernst Equation for the Electrode Potential:

The Nernst equation for this half-cell reaction is:

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

where:

• $E$ is the electrode potential,
• $E^\circ = 0$ (standard electrode potential for the hydrogen electrode),
• $P_{H_2}$ is the partial pressure of hydrogen gas,
• $[H^+]$ is the concentration of hydrogen ions.

Setting $E = 0$:

To make the emf zero, set $E = 0$:

$0 = 0 - \frac{0.059}{2} \log \frac{P_{H_2}}{(10^{-7})^2}$

Solve for $P_{H_2}$:

$\frac{0.059}{2} \log \frac{P_{H_2}}{10^{-14}} = 0$

$\log \frac{P_{H_2}}{10^{-14}} = 0$

$\frac{P_{H_2}}{10^{-14}} = 1$

$P_{H_2} = 10^{-14} \, \text{bar}$

Conclusion:

The required pressure of $H_2$ is $10^{-14} \, \text{bar}$.