GATE 2021 MT – Question 53

Metallurgical Thermodynamics · Reaction equilibria and Ellingham diagrams · 2 marks · Numerical answer

For $2Cu(s)+SO_2(g)\rightleftharpoons Cu_2S(s)+O_2(g)$ at 973 K, $\ln(p_{O_2}/p_{SO_2})=$ ______ (two decimal places). Given $\Delta G^\circ=-100$ kJ for $2Cu(s)+0.5S_2(g)\to Cu_2S(s)$ and $\Delta G^\circ=292$ kJ for $SO_2(g)\to0.5S_2(g)+O_2(g)$, both at 973 K. $R=8.314$ J mol$^{-1}$ K$^{-1}$. Cu and $Cu_2S$ are pure solids.

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Correct answer: -24.00 to -23.50

Explanation

Adding the two supplied reactions yields 2Cu+SO2→Cu2S+O2 with ΔG°=−100+292=192 kJ/mol. Pure-solid activities are one, so ln(pO2/pSO2)=−ΔG°/(RT)=−192000/(8.314×973)=**−23.73**.