For the reaction $SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)},$ if $K_P = K_C (RT)^x$ where the symbols have usual meaning,then the value of $x$ is (assuming ideality):

At $1000 \ K$,if the equilibrium constant $K_p$ for the reaction $2 \ NOCl_{(g)} \rightleftharpoons 2 \ NO_{(g)} + Cl_{2(g)}$ is $4.157 \times 10^{-4} \ bar$,the $K_c$ (in $mol \ L^{-1}$) is $(R = 0.083 \ L \ bar \ K^{-1} \ mol^{-1})$

For the reaction,$2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$ at $300 \ K$,the value of $\Delta G^{\circ}$ is $-690.9 R$. The equilibrium constant value for the reaction at that temperature is ($R$ is gas constant).

The equilibrium concentrations of $N_2, H_2$ and $NH_3$ in the formation of $NH_3$ at $500 \ K$ are $1.25 \times 10^{-2} \ M, 4.0 \times 10^{-2} \ M$ and $1.6 \times 10^{-2} \ M$ respectively. The equilibrium constant $K_{p}$ at the same temperature is

For the reaction: $SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$,$K_P = 2 \times 10^{12}$ at $27^{\circ} C$ and $1 \ atm$ pressure. The $K_C$ for the same reaction is $......... \times 10^{13}$. (Nearest integer)
(Given $R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1}$)

For the elementary reaction $A_{2(g)} + B_{2(g)} \rightleftharpoons 2AB_{(g)}$,the rate of the forward reaction is given by $r_f = 1.7 \times 10^{-18} [A_2][B_2]$. If the rate of decomposition of gaseous $AB$ into $A_2$ and $B_2$ is given by $r_r = 2.4 \times 10^{-21} [AB]^2$,then the equilibrium constant for the formation of $AB$ from $A_2$ and $B_2$ will be ...