Question

The cell potential for the following cell
$Pt \left| H _{2}( g )\right| H ^{+}( aq ) \| Cu ^{2+}(0.01 M ) \mid Cu ( s )$
is $0.576 \,V$ at $298 \,K$. The $pH$ of the solution is ___ (Nearest integer)

Answer 1

$E _{\text {cell }}= E _{\text {cell }}^{0}-\frac{0.06}{2} \log \frac{\left[ H ^{+}\right]^{2}}{\left[ Cu ^{2+}\right]}$
$0.576=0.34-\frac{0.06}{2} \log \left\{\frac{\left[ H ^{+}\right]^{2}}{(0.01)}\right\}$
$+3.93-\log \left( H ^{+}\right)+\log 0.1 $
$\Rightarrow pH =4.93 \simeq 5$