The expression for the equilibrium constant (Kc) for the given reaction is:
Kc = [NO2]^2 / [N2O4]
Where [NO2] and [N2O4] are the molar concentrations of NO2 and N2O4, respectively, at equilibrium.
Substituting the given equilibrium concentrations into the expression for Kc, we get:
Kc = (0.24 M)^2 / (0.032 M) = 1.8 M
Therefore, the numerical value of Kc for the given reaction, when the equilibrium mixture contains 0.032 M N2O4 and 0.24 M NO2, is 1.8 M.