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Question

The e.m.f. of a cell corresponding to the reaction Zn+2H+(aq)Zn2+(0.1M)+H2(g)(1atm) is 0.26 volt at 25C. The pH of the solution at the hydrogen electrode is: (EZn2+/Zn=0.76 V and EH+/H2=0)

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Solution

Ecell=0.26
Ecell=EH+/H2EZn2+/Zn
Ecell=0(0.76)=0.76 V
Applying Nernst equation:
Ecell=Ecell0.05912log[Zn+2][PH2][H+]2
0.26=0.760.05912log[0.1][1][H+]2
log0.1[H+]2=2×0.500.0591
or log0.1 log[H+]2 = 17
or 2pH = 17 log0.1=18
pH =182=9

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