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Question

The emf of a cell corresponding to the reaction,
Zn+2H+(aq.)Zn2+(0.1 M)+H2(g)1 atm
is 0.28 volt at 25C. Write the half-cell reactions and calculate the pH of the solution at the hydrogen electrode.
EZn2+/Zn=0.76 volt and EH+/H2=0.

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Solution

Ecell=0.76 volt
Ecell=Ecell0.05912log[Zn2+][H2][H+]2
0.28=0.760.05912log(0.1)×1[H+]2
log0.1[H+]2=2×0.480.0591
log0.1log[H+]2=16.2436 [Since, log[H+]=pH]
2 pH=16.2436log0.1
pH=17.24362=8.6218.

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