The EMF of a cell corresponding to the reaction: Zn(s)+2H⨁(aq)→Zn2+(0.1M)+H2(g,1atm) is 0.82V at 25∘C. The pH of the solution at the hydrogen electrode is: E⊝Zn2+|Zn=−0.76V E⊝H⊝|H2=0
If the value is 63×10−x, then what is the value of x?
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Solution
Half cell reactions are : [Zn(s)→Zn2+(aq)+2e−] at anode [H⨁+e−→12H2] at cathode For zinc electrode: EZn|Zn2+=E⊝Zn|Zn2+−0.0591nlog[Zn2+Zn(s)] =0.76−0.05912log0.11 =0.76−0.05912×(−1) = +0.76 + 0.03 = 0.79 V Similarly, for hydrogen electrode EH⨁|H2=0−0.05912log1[H⨁]2 or EH⨁|H2=0−0.05912×2(−log[H⨁] ∴EH⨁|H2=−0.0591pH Now, Ecell=EZn|Zn2+−EH⨁/H2 ∴0.28=+0.79−0.0591pH or 0.0591 pH = +0.79 - 0.28 or 0.0591 pH = 0.51 ∴pH=0.510.0591 = 0.63