JEE Main 2026 · 2 Apr · Shift 2, Chemistry question 73

Consider the following two half-cell reactions along with the standard reduction potential given :
$$\ce{CO2 + 6H+ + 6e- -> CH3OH + H2O}\qquad E^\circ_\text{red}=0.02\ \mathrm V$$
$$\ce{1/2O2 + 2H+ + 2e- -> H2O}\qquad E^\circ_\text{red}=1.23\ \mathrm V$$
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 $\ce{CH3OH}$ is used to compress an ideal gas isothermally against a constant pressure of 1 kPa, then the change in the volume of the gas, $\Delta V$ = ________ m³. (nearest integer)
Given : $F=96500$ C mol$^{-1}$