Consider the following two half-cell… - JEE Main 2026 Chemistry PYQ

JEE Main 2026 — Chemistry Physical Chemistry

2026integerhard

Consider the following two half-cell reactions along with the standard reduction potential given:

$CO_2 + 6H^+ + 6e^- \rightarrow CH_3 OH + H_2 O \quad E°_{red} = 0.02$ V

$\dfrac{1}{2} O_2 + 2H^+ + 2e^- \rightarrow H_2 O \quad E°_{red} = 1.23$ 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 $CH_3 OH$ 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 $^{-1}$

Official previous-year question

Held on 2 Apr 2026 · Verified 6 Jul 2026.

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Solution

The half-cell reactions for the fuel cell are:

Anode (Oxidation): $CH_3OH + H_2O \rightarrow CO_2 + 6H^+ + 6e^- \quad E^{\circ}_{ox} = -0.02$ V

Cathode (Reduction): $\dfrac{3}{2}O_2 + 6H^+ + 6e^- \rightarrow 3H_2O \quad E^{\circ}_{red} = 1.23$ V

The overall cell reaction is:

$CH_3OH + \dfrac{3}{2}O_2 \rightarrow CO_2 + 2H_2O$

The standard cell potential is:

$E^{\circ}_{cell} = E^{\circ}_{cathode} - E^{\circ}_{anode} = 1.23 - 0.02 = 1.21$ V

The number of electrons transferred per mole of $CH_3OH$ is $n = 6$ .

The maximum electrical work that can be obtained from the cell is given by the decrease in Gibbs free energy:

$W_{max} = nFE^{\circ}_{cell} = 6 \times 96500 \times 1.21 = 700590$ J

Since the fuel cell operates at $80\%$ efficiency, the actual work derived is:

$W_{actual} = 0.80 \times 700590 = 560472$ J

This work is used to compress an ideal gas isothermally against a constant external pressure of $1$ kPa ( $1000$ Pa). The work done on the gas during compression is positive:

$W = -P_{ext} \Delta V$

Substituting the values:

$560472 = -1000 \times \Delta V$

$\Delta V = -560.472$ m $^3$

Rounding to the nearest integer, the change in volume is $-560$ m $^3$ .

Answer: $-560$

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