GATE 2026 MT – Question 64
$\mathrm{Al_2O_3}$ can be electrolyzed with an inert or a carbon anode. The overall reactions are:
I, inert anode: $\frac23\mathrm{Al_2O_3(s)}\to\frac43\mathrm{Al(l)}+\mathrm{O_2(g)}$, with $\Delta G_I^\circ=1124800-218T$ J.
II, carbon anode: $\frac23\mathrm{Al_2O_3(s)}+\mathrm{C(s)}\to\frac43\mathrm{Al(l)}+\mathrm{CO_2(g)}$, with $\Delta G_{II}^\circ=730700-218T$ J.
$T$ is in kelvin and the Faraday constant is $96500\ \mathrm{C/mol}$. If the inert anode is replaced by carbon at 1300 K, the decrease in the magnitude of decomposition potential is ________ V. (Rounded off to two decimal places.)
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Correct answer: 1.00 to 1.05
Explanation
The free-energy difference is $\Delta G_I^\circ-\Delta G_{II}^\circ=1124800-730700=394100\ \mathrm J$; the equal temperature terms cancel.
Each reaction produces $4/3$ mol of aluminium, requiring $3(4/3)=4$ mol electrons. Therefore the decrease in potential is $\Delta E=394100/(4\times96500)=1.02098\ \mathrm V$, or **1.02 V**.