3O₂(g) ⇌ 2O₃(g)
For the above reaction at 298 K, Kc is found to be 3.0 × 10⁻⁵⁹. If the concentration of O₂ at equilibrium is 0.040M the then concentration of O₃ in M is:

A(g) ->B(g) + $\frac{1}{2}$ (g)

Initial moles             n                         0             0

Eqb. moles               n(1 – a)   $\frac{n\alpha }{2}$           n_a            

total moles =   $n\left(1+\frac{\alpha }{2}\right)$

Eqb. pressure   $\frac{\left(1-\alpha \right)p}{1+\frac{\alpha }{2}}$ $\frac{\alpha p}{1+\frac{\alpha }{2}}$ $\frac{\left(\frac{\alpha }{2}\right)p}{1+\frac{\alpha }{2}}$

$\frac{K_p=\frac{\alpha p}{\left(1+\frac{\alpha }{2}\right)}\times {\left[\frac{\alpha p}{\left(2+\alpha \right)}\right]}^{\frac{1}{2}}}{\frac{\left(1+\alpha \right)p}{1+\frac{\alpha }{2}}}$

$K_p=\frac{{\alpha }^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{p}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{{\left(2+\alpha \right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\left(1-\alpha \right)}$