In the system $$X + 2Y \rightleftharpoons Z,$$   the equilibrium concentrations are, $$\left[ X \right] = 0.06\,mol\,{L^{ - 1}},$$    $$\left[ Y \right] = 0.12\,mol\,{L^{ - 1}},$$    $$\left[ Z \right] = 0.216\,mol\,{L^{ - 1}}.$$     Find the equilibrium constant of the reaction.

Solution :
$$\eqalign{ & \mathop X\limits_{0.06} + \mathop {2Y}\limits_{0.12} \rightleftharpoons \mathop Z\limits_{0.216} \cr & {K_c} = \frac{{\left[ Z \right]}}{{\left[ X \right]{{\left[ Y \right]}^2}}} \cr & \,\,\,\,\,\,\,\, = \frac{{0.216}}{{0.06 \times 0.12 \times 0.12}} \cr & \,\,\,\,\,\,\,\, = 250 \cr} $$