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

The Correct Option is C

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 \( 10^{-14} \, \text{bar} \).