PCl 5 vapour decomposes on heating according to the reaction: PCl 5 g ⇌ PCl 3 g + Cl 2 g The density of a sample of a partially dissociated PCl 5 at 1 .0 atm and 500 K was found 4 .8 g/L . Calculate the degree of dissociation and Δ G ∘ for

Question

PCl 5 vapour decomposes on heating according to the reaction: PCl 5 g ⇌ PCl 3 g + Cl 2 g The density of a sample of a partially dissociated PCl 5 at 1 .0 atm and 500 K was found 4 .8 g/L . Calculate the degree of dissociation and Δ G ∘ for the reaction at 500 K . (Given: R = 0.082 LatmK − 1 mol − 1 , R = 8.314 JK − 1 mol − 1 , ln x = 2.303 log 10 x )

Quantrex Academy · Accepted Answer

Correct answer: 23.40

M avg = ρ RT P = 4 . 8 × 0 . 0 8 2 × 5 0 0 1 = 1 9 6 . 8 PCl 5 g ⇌ PCl 3 g + Cl 2 g 1 - α α α Total moles = 1 + α M avg = M PCl 5 1 + α = 1 9 6 . 8 = 2 0 8 . 5 1 + α ∴ α = 0 . 0 6 K P = α 2 1 − α 2 P = 0.06 2 1 − 0.06 2 = 3.6 × 10 − 3 Δ G ∘ = - RT ln K = - 8 . 3 1 4 × 5 0 0 × 2 . 303 log 3 . 6 × 1 0 - 3 = 23.4 kJ

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