JEE Advanced 2020 — Paper 1 — Question 26

Consider a $70 \%$ efficient hydrogen-oxygen fuel cell working under standard conditions at 1 bar and 298 K . Its cell

reaction is

$\mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\ell)$

The work derived from the cell on the consumption of $10 \times 10^{-3} \mathrm{~mol}$ of $\mathrm{H}_{2}(\mathrm{~g})$ is used to compress 1.00

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.

$\mathrm{O}_{2}(\mathrm{~g})+4 \mathrm{H}^{+}(\mathrm{aq})+4 \mathrm{e}^{-} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\ell), \mathrm{E}^{0}=1.23 \mathrm{~V}$,

$2 \mathrm{H}^{+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}(\mathrm{~g}), \mathrm{E}^{0}=0.00 \mathrm{~V}$.

Use $F=96500 \mathrm{C} \mathrm{mol}^{-1}, \mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$.