Question

Phosphorus pentachloride decomposes according to the chemical equation

PCl₅(g) <=> PCl₃ (g) + Cl₂ (g) K_c = 1.80 at 250 C

A 0.3391 mol sample of PCl₅ (g) is injected into an empty 3.60 L reaction vessel held at 250 ∘ C.

Calculate the concentrations of PCl₅ ( g ) and PCl₃ ( g ) at equilibrium.

[PCl₅] = __________M. [PCl₃]=___________M.

Answer 1

first construct the ICE table and then substitute the values in the K equation and then calculate the equilibrium values as follows
initial concentration = 0.3391 mol / 3.60 L =>0.094194 M

       PCl5----------------------------> PCl3 + Cl2

I       0.094194                                0          0

C       -x                                         +x +x

E   (0.094194 -x)                            x          x

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

=>1.80 = x² / (0.094194 -x)

=> 1.80 * (0.094194 -x) = x²

=> x = 0.089722

at equilibrium the concentrations are

[PCl5] = (0.094194 - 0.089722) => 0.004472 M

[PCl3] = 0.089722 M

[Cl2] = 0.089722 M