What pressure (bar) of \(\mathrm{H}_2\) would be required to make emf of hydrogen electrode zero in pure…

What pressure (bar) of \(\mathrm{H}_2\) would be required to make emf of hydrogen electrode zero in pure water at \(25^{\circ} \mathrm{C}\) ?
  1. \(10^{-7}\)
  2. 0.5
  3. 1
  4. \(10^{-14}\)

Solution

$\begin{aligned} & 2 \mathrm{e}^{-}+2 \mathrm{H}^{+}(\mathrm{aq}) \rightarrow \mathrm{H}_2(\mathrm{~g}) \\ & \mathrm{E}=\mathrm{E}^{\circ}-\frac{0.059}{\mathrm{n}} \log \frac{\mathrm{P}_{\mathrm{H}_2}}{\left[\mathrm{H}^{+}\right]^2} \\ & 0=0-\frac{0.059}{2} \log \frac{\mathrm{P}_{\mathrm{H}_2}}{\left(10^{-7}\right)^2} \\ & \log \frac{\mathrm{P}_{\mathrm{H}_2}}{\left(10^{-7}\right)^2}=0 \\ & \frac{\mathrm{P}_{\mathrm{H}_2}}{10^{-14}}=1 \\ & \mathrm{P}_{\mathrm{H}_2}=10^{-14} \text { bar }\end{aligned}$

Asked in: JEE Main 2024 (04 Apr Shift 1)

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