7.22 Bromine monochloride, BrCl decomposes into bromine and chlorine and reaches the equilibrium:

2BrCl (g) Br2 (g) + Cl2 (g)

for which Kc= 32 at 500 K. If initially pure BrCl is present at a concentration of
3.3 × 10
–3 mol L–1, what is its molar concentration in the mixture at equilibrium?

Let the amount of bromine and chlorine formed at equilibrium be x. The given reaction is:

                              2BrClg         Br2g     +      Cl2gInitial conc.         3.3×10-3                    0                    0At equilibrium     3.3×10-3 -2x       x                  x

Now, we can write,

Br2Cl2BrCl2=Kcx×x3.3×10-3-2x2=32x=18.678×10-3-11.32x12.32x=18.678×10-3x=1.5×10-3

Therefore, at equilibrium,

BrCl=3.3×10-3-2×1.5×10-3           =3.3×10-3-3.0×10-3           =0.3×10-3            =3.0×10-4 molL-1