GATE 2020 CH – Question 41
For ideal gases, N₂O₄ ⇌ 2NO₂ proceeds at 298 K and total pressure 1 bar. Standard reaction Gibbs energy is 5253 J/mol with pure ideal-gas standard states at 1 bar. Initially one mole of pure N₂O₄ is present. Given R = 8.314 J/(mol K), find its equilibrium dissociation fraction.
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Correct answer: (B) 0.17
Explanation
The equilibrium constant is $K_p=e^{-\Delta G^\circ/(RT)}=e^{-5253/(8.314\times298)}\simeq0.120$. If fraction α dissociates, mole fractions are $(1-\alpha)/(1+\alpha)$ and $2\alpha/(1+\alpha)$. At total pressure equal to standard pressure, $K_p=4\alpha^2/(1-\alpha^2)$. Hence $\alpha=\sqrt{K_p/(4+K_p)}\simeq0.17$, B.