Write the equilibrium constant (equilibrium law) for the following reactions:
$(i)$ $4NH_{3(g)} + 5O_{2(g)} \rightleftharpoons 4NO_{(g)} + 6H_{2}O_{(g)}$
$(ii)$ $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$
$(iii)$ $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$

(N/A) The equilibrium constant $(K_c)$ is defined as the ratio of the product of the molar concentrations of the products to the product of the molar concentrations of the reactants,each raised to the power of their stoichiometric coefficients.
$(i)$ For $4NH_{3(g)} + 5O_{2(g)} \rightleftharpoons 4NO_{(g)} + 6H_{2}O_{(g)}$,the expression is: $K_c = \frac{[NO]^4 [H_2O]^6}{[NH_3]^4 [O_2]^5}$
$(ii)$ For $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$,the expression is: $K_c = \frac{[HI]^2}{[H_2] [I_2]}$
$(iii)$ For $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$,the expression is: $K_c = \frac{[NH_3]^2}{[N_2] [H_2]^3}$