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

• A
  $561$
• B
  $500$
• C
  $600$
• D
  $450$