0.72-mol sample of is put into a 1.00-L vessel and heated. At equilibrium, the vessel contains 0.40 mol of and 0.40 mol of . Calculate the value of the equilibrium constant for the decomposition of to and at this temperature.

A 0.72-mol sample of PCl₅ is put into a 1.00-L vessel and heated. At equilibrium, the vessel contains 0.40 mol of PCl₃(g) and 0.40 mol of Cl₂(g). Calculate the value of the equilibrium constant for the decomposition of PCl₅ to PCl₃ and Cl₂ at this temperature.

Step 1: Calculate the molar concentrations

[PCl₅]i = 0.72 mol/1.00 L = 0.72 M

[PCl₃]eq = 0.40 mol/1.00 L = 0.40 M

[Cl₂]eq = 0.40 mol/1.00 L = 0.40 M

Step 2: Make an ICE chart

PCl₅(g) ⇄ PCl₃(g) + Cl₂(g)

I 0.72 0 0

C -x +x +x

E 0.72-x x x

Step 3: Determine the value of x

Since [PCl₃]eq = [Cl₂]eq = 0.40 M, x = 0.40 M

Step 4: Determine the concentration of PCl₅ at equilibrium

[PCl₅]eq = 0.72-x = 0.72-0.40 = 0.32 M

Step 5: Calculate the equilibrium constant

Kc = [PCl₃] × [Cl₂] / [PCl₅]

Kc = 0.40 × 0.40 / 0.32 = 0.50