Redox Reactions and Electrochemistry: JEE Main 2026 Chemistry question

Consider the following two half-cell reactions along with the standard reduction potential given : $\mathrm{CO_2+6H^++6e^-\rightarrow CH_3OH+H_2O}$, $E^\circ_{red}=0.02$ V; $\frac{1}{2}\mathrm{O_2+2H^++2e^-\rightarrow H_2O}$, $E^\circ_{red}=1.23$ V. A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of 1 bar pressure and 298 K temperature. The fuel cell works with 80% efficiency. If the work derived from the cell using 1 mol of $\mathrm{CH_3OH}$ is used to compress an ideal gas isothermally against a constant pressure of 1 kPa, then the change in the volume of the gas, $\Delta V$ = ______ m$^3$. (nearest integer) Given : F = 96500 C mol$^{-1}$