Consider the following two half-cell reactions along with the standard reduction potential given: CO_2+6 H^++6 e^- → CH_3 OH + H_2 O, E^o_red =0.02…

Consider the following two half-cell reactions along with the standard reduction potential given : $$\begin{array}{ll} \mathrm{CO}_2+6 \mathrm{H}^{+}+6 \mathrm{e}^{-} \longrightarrow \mathrm{CH}_3 \mathrm{OH}+\mathrm{H}_2 \mathrm{O} & \mathrm{E}^{\mathrm{o}}{ }_{\text {red }}=0.02 \mathrm{~V} \\ \frac{1}{2} \mathrm{O}_2+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_2 \mathrm{O} & \mathrm{E}_{\text {red }}^{\mathrm{o}}=1.23 \mathrm{~V} \end{array} $$ A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of $\displaystyle 1$ bar pressure and $\displaystyle 298$ K temperature. The fuel cell works with $\displaystyle 80 \%$ efficiency. If the work derived from the cell using $\displaystyle 1$ mol of $\displaystyle \mathrm{CH}_3 \mathrm{OH}$ is used to compress an ideal gas isothermally against a constant pressure of $\displaystyle 1$ kPa, then the change in the volume of the gas, $\displaystyle \Delta \mathrm{V}=$ $\displaystyle \_\_\_\_$ $\displaystyle \mathrm{m}^3$. (nearest integer) Given : $\displaystyle \mathrm{F}=96500 \mathrm{C} \mathrm{mol}^{-1}$