GATE 2025 MT – Question 53
Consider the reactions and standard Gibbs free energies (J):
$\mathrm{Fe}(s)+\tfrac12\mathrm O_2(g)\rightleftharpoons\mathrm{FeO}(s)$, $\Delta G^\circ=-264900+65T$.
$2\mathrm H_2(g)+\mathrm O_2(g)\rightleftharpoons2\mathrm H_2O(g)$, $\Delta G^\circ=-492900+109T$.
Assume pure Fe and FeO and no solubility of gases in the solids. The value of $p_{H_2O}/p_{H_2}$ required to reduce solid FeO to Fe at 1000 K is ______ (rounded to two decimal places). Given: $R=8.314\ \mathrm{J\,mol^{-1}K^{-1}}$.
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Correct answer: 0.37 to 0.39
Explanation
Take half the water-formation reaction and subtract the Fe oxidation reaction. This gives $\mathrm{FeO}+\mathrm H_2\rightleftharpoons\mathrm{Fe}+\mathrm H_2O$.
Its standard free energy is $\Delta G^\circ=(-492900+109T)/2-(-264900+65T)=18450-10.5T$. At 1000 K this is 7950 J.
Pure-solid activities are unity, so $K=p_{H_2O}/p_{H_2}=\exp[-7950/(8.314\times1000)]=0.3843\ldots$. The equilibrium threshold is **0.38**; a smaller actual ratio favors reduction.