Let be the fraction of PCl 5 molecules that has decomposed to PCl 3 and Cl

Let α be the fraction of PCl₅ molecules that has decomposed to PCl₃ and Cl₂ in the reaction PCl₅(g) ⇌ PCl₃(g) + Cl₂(g) in a constant-volume container; then the amount of PCl₅ at equilibrium is n(1 – α), where n is the amount present initially. Derive an equation for K in terms of a and the total pressure P, and solve it for a in terms of P. Calculate the fraction decomposed at 556 K, at which temperature K = 4.96, and the total pressure is

(a) 0.50 bar;

(b) 1.00 bar.