Addition of a catalyst in a system at equilibrium:

The equilibrium constant in a reversible reaction at a given temperature:

Given the reactions at $500 \ K$:
$(i) \ H_{2(g)} + 1/2 O_{2(g)} \rightleftharpoons H_2O_{(g)}$,$K_c = 2.4 \times 10^{47}$
$(ii) \ H_2O_{(g)} \rightleftharpoons H_{2(g)} + 1/2 O_{2(g)}$,$K_c = 4.1 \times 10^{-48}$
What does the magnitude of $K_c$ indicate about the formation of the product in reaction $(i)$?

For the reaction $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$,the equilibrium constant changes with:

Identify which of the following reactions represent homogeneous and heterogeneous equilibria:
$(a)$ $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$
$(b)$ $Ca(OH)_{2(s)} \rightleftharpoons Ca^{2+}_{(aq)} + 2OH^{-}_{(aq)}$
$(c)$ $CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$
$(d)$ $Ag_{2}O_{(s)} + 2H^{+}_{(aq)} \rightleftharpoons H_{2}O_{(l)} + 2Ag^{+}_{(aq)}$
$(e)$ $NH_{3(g)} + H_{2}O_{(l)} \rightleftharpoons N{H_{4}}^{+}_{(aq)} + OH^{-}_{(aq)}$
$(f)$ $CH_{3}COOC_{2}H_{5(l)} + H_{2}O_{(l)} \rightleftharpoons CH_{3}COOH_{(l)} + C_{2}H_{5}OH_{(l)}$

For the reaction $N_2 + 3H_2 \rightleftharpoons 2NH_3$,the value of $K_c$ does not depend on: $(a)$ Initial concentration of reactants $(b)$ Pressure $(c)$ Temperature $(d)$ Catalyst