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Question

The EMF of a cell corresponding to the reaction:
Zn(s)+2H(aq)Zn2+(0.1M)+H2(g,1atm) is 0.82V at 25C.
The pH of the solution at the hydrogen electrode is:
EZn2+|Zn=0.76V
EH|H2=0
If the value is 63×10x, then what is the value of x?

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Solution

Half cell reactions are :
[Zn(s)Zn2+(aq)+2e] at anode
[H+e12H2] at cathode
For zinc electrode:
EZn|Zn2+=EZn|Zn2+0.0591nlog[Zn2+Zn(s)]
=0.760.05912log0.11
=0.760.05912×(1)
= +0.76 + 0.03 = 0.79 V
Similarly, for hydrogen electrode
EH|H2=00.05912log1[H]2
or EH|H2=00.05912×2(log[H]
EH|H2=0.0591pH
Now, Ecell=EZn|Zn2+EH/H2
0.28=+0.790.0591pH
or 0.0591 pH = +0.79 - 0.28
or 0.0591 pH = 0.51
pH=0.510.0591 = 0.63

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