Question

Consider a $70 \%$ efficient hydrogen-oxygen fuel cell working under standard conditions at $1$ bar and $298 \,K$ Its cell reaction is
$H _{2}( g )+\frac{1}{2} O _{2}( g ) \rightarrow H _{2} O ( l )$
The work derived from the cell on the consumption of $1.0 \times 10^{-3} mol$ of $H _{2}( g )$ is used to compress $100\, mol$ of a monoatomic ideal gas in a thermally insulated container. What is the change in the temperature (in $K$ ) of the ideal gas?
The standard reduction potentials for the two half-cells are given below
$O _{2}(g)+4 H ^{+}(a q)+4 e^{-} \rightarrow 2 H _{2} O ( I ), E^{\circ}=1.23 \,V$
$2 H ^{+}(a q)+2 e^{-} \rightarrow H _{2}(g), E^{\circ}=0.00 \,V$
Use $F =96500 \,C\,mol ^{-1}, R=8.314\, J\,mol ^{-1} K ^{-1}$

Answer 1

Change in temperature (in K ) of the ideal gas is 13.32