Question

Phosphorus pentachloride decomposes according to the chemical equation PCI5 (g) <---> PCI3 (g) + Cl2(g) Kc= 1.80 at 250°C

A 0.244 mol sample of PCl5(g) is injected into an empty 2.65 L reaction vessel held at 250 °C. Calculate the concentrations of PCl5(g) and PCl3(g) at equilibrium.

Answer 1

Given that

[PCl5 (g)] = moles / volume in Litres = 0.244 mol / 2.65 L = 0.092 M       

Kc= 1.80  

           PCI5 (g) <---> PCI3 (g) + Cl2(g)   

Initial                   0.092 M                0                 0

At equilibrium           0.092 -x                 x                  x

                         Kc = [PCl3] [Cl2] / [PCl5]

                         1.8 = x.x / 0.092 -x

                         0.1656 - 1.8 x = x²

                         x² + 1.8 x - 0.1656 = 0

                       On solving,

                             x = 0.0877 M

   Therefore, equilibrium concentrations are

   [PCl5 (g)] = 0.092 -x = 0.092 - 0.0877 = 0.0043 M

      [PCl3 (g)] = x = 0.0877 M

      [Cl2 (g)] = x = 0.0877 M