Chapter 14.6, Problem 14.9E

Phosphorus pentachloride gives an equilibrium mixture of PCl₅ PCl₃, and Cl₂ when heated.

${\text{PCl}}_5(g)\stackrel{}{\rightleftharpoons }{\text{PCl}}_3(g)+{\text{Cl}}_2(g)$

A 1.00-L vessel contains an unknown amount of PCl₅ and 0.020 mol each of PCl₃ and Cl₂ at equilibrium at 250°C. How many moles of PCl₅ are in the vessel if K_c for this reaction is 0.0415 at 250°C?