What pressure (bar) of H2 would be required to make emf of hydrogen electrode zero in pure water at 25°C?

Strategy: Use the Nernst Equation for a hydrogen electrode. For the potential to be zero in pure water, the concentration of $\ce{H^+}$ (calculated from the auto-ionization of water) must be balan\ced by a specific pressure of $\ce{H2}$.

Step 1: Conditions for pure water At $25^\circ \text{C}$, $[\ce{H^+}] = 10^{-7} \text{ M}$.

Step 2: Apply Nernst Equation $E = 0$ (Target). Reaction: $\ce{2H^+ + 2e^- \rightarrow H2(g)}$. $E = E^\circ - \frac{0.059}{2} \log \frac{P_{\ce{H2}}}{[\ce{H^+}]^2}$ $0 = 0 - 0.0295 \log \frac{P_{\ce{H2}}}{10^{-14}}$ $log \frac{P_{\ce{H2}}}{10^{-14}} = 0 \implies P_{\ce{H2}} = 10^{-14} \text{ bar}$

$\boxed{\text{Answer: (d) } 10^{-14}}$