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For the equilibrium dissociation of phosphorus pentachloride, PCl₅ ⇌ PCl₃ + Cl₂, if the degree of dissociation is α and the total pressure is P, which expression gives the equilibrium constant Kₚ?

1. Kₚ = α²P/(1 - α²)
2. Kₚ = αP/(1 - α)
3. Kₚ = α²P/(1 + α²)
4. Kₚ = αP/(1 + α)

Correct answer: Kₚ = α²P/(1 - α²)

Solution

For PCl5 -> PCl3 + Cl2 starting with 1 mol, equilibrium moles are (1-a), a, a with total (1+a). Mole fractions times P give partial pressures, so Kp = [aP/(1+a)][aP/(1+a)] / [(1-a)P/(1+a)] = a^2 P/(1-a^2).

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