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

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Solution

Q.
What pressure (bar) of $H_{2}$ would be required to make emf of hydrogen electrode zero in pure water at $25^{°} C$ [2024]

1 $10^{- 7}$

2 $10^{- 14}$

3 $0.5$

4 $1$

Ans.
(2)

   $2 H^{+} (aq) + 2 e^{-} \to H_{2} (g)$

By Nernst equation at 298K

   $E_{H^{+} / H_{2}} = E_{H^{+} / H_{2}}^{\circ} - \frac{0.059}{n} \log_{10} \frac{P_{H_{2}}}{[H^{+}]^{2}}$

For pure water $[H^{+}] = 10^{- 7} M and E_{H^{+} / H_{2}}^{\circ} = 0$

$0 = 0 - \frac{0.059}{2} \log_{10} \frac{P_{H_{2}}}{{[10^{- 7}]}^{2}}$

   $\log_{10} \frac{P_{H_{2}}}{{[10^{- 7}]}^{2}} = 0$

   $\frac{P_{H_{2}}}{{[10^{- 7}]}^{2}} = 1$

   $P_{H_{2}} = 10^{- 14} bar$

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