7.19 A sample of pure PCl5 was introduced into an evacuated vessel at 473 K. After equilibrium was attained, concentration of PCl5 was found to be
0.5 × 10
–1 mol L–1. If value of Kc is 8.3 × 10–3, what are the concentrations of PCl3 and Cl2 at equilibrium?

PCl5 (g) PCl3 (g) + Cl2(g)

Let the concentrations of both PCl3 and Cl2 at equilibrium be x molL-1. The given reaction is:

                             PCl5g                    PCl3g           +      Cl2gAt equilibrium    0.5×10-1 mol L-1      x mol L-1            x mol L-1

It is given that of the value of the equilibrium constant, Kc is 8.3×10-3.

Now we can write the expression for equilibrium as:

PCl2Cl2PCl5=Kcx×x0.5×10-1=8.3×10-3x2=4.15×10-4x=2.04×10-2       =0.0204      =0.02 approx.

Therefore, at equilibrium,

  PCl3=Cl2=0.02 mol L-1.