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# The reduction potential of hydrogen half-cell will be negative if

$\begin{array}{1 1}p(H_2)=1bar\;and\;[H^+]=1M\\p(H_2)=1bar\;and\;[H^+]=2M\\p(H_2)=2bar\;and\;[H^+]=1M\\p(H_2)=2bar\;and\;[H^+]=2M\end{array}$

Answer : $p(H_2)=2bar\;and\;[H^+]=1M$
For the reaction $H^+(aq)+e^-\rightarrow H_2(g)$,the standard potential is given by
$E=-\large\frac{RT}{nF}$$\ln \large\frac{(p_{H_2}/bar)^{1/2}}{([H^+]/mol\;dm^{-3})}$
E will be negative if $p^{1/2}_{H_2}/[H^+] > 1$.