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  4. The cell potential for the given cell at 298 K Pt mid H 2( g , 1 bar )| H +( aq ) | Cu 2+( aq )| Cu ( s ) is 0.31 V. The pH of the acidic solution is found to be 3 , whereas the concentration of Cu 2+ is 10-x M. The value of x is (Given: E Cu 2+ / Cu Θ=0.34 V and (2.303 RT / F )=0.06 V )

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Q. The cell potential for the given cell at $298 K$ $Pt \mid H _{2}( g , 1$ bar $)\left| H ^{+}( aq ) \| Cu ^{2+}( aq )\right| Cu ( s )$ is $0.31 V$. The $pH$ of the acidic solution is found to be 3 , whereas the concentration of $Cu ^{2+}$ is $10^{-x} M$. The value of $x$ is___
(Given: $E _{ Cu ^{2+} / Cu }^{\Theta}=0.34 V$ and $\frac{2.303 RT }{ F }=0.06 \,V$ )

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Solution:

$H _{2}( g )+ Cu ^{2+}($ aq. $) \rightarrow 2 H ^{+}($aq. $)+ Cu ( s )$
$0.31=0.34-\frac{0.06}{2} \log \frac{\left[ H ^{+}\right]^{2}}{\left[ Cu ^{2+}\right]}$
${\left[ Cu ^{2+}\right]=10^{-7} M }$
$x =7$