The partial pressures of $CH_3OH$,$CO$ and $H_2$ in the equilibrium mixture for the reaction $CO(g) + 2H_2(g) \rightleftharpoons CH_3OH(g)$ at $427 \ ^oC$ are $2.0 \ atm$,$1.0 \ atm$ and $0.1 \ atm$ respectively. The value of $K_P$ for the decomposition of $CH_3OH$ to $CO$ and $H_2$ is:

The gas phase reaction $2A_{(g)} \rightleftharpoons A_{2(g)}$ at $400 \ K$ has $\Delta G^{\circ} = +25.2 \ kJ \ mol^{-1}$. The equilibrium constant $K_{C}$ for this reaction is $...... \times 10^{-2}$. (Round off to the nearest integer) $[$Use: $R = 8.3 \ J \ mol^{-1} \ K^{-1}$,$\ln 10 = 2.3$,$\log_{10} 2 = 0.30$,$1 \ atm = 1 \ bar]$ $[$antilog $(-3.3) = 5.01 \times 10^{-4}]$

$(1) \ N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)} \ ; \ K_1$
$(2) \ N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)} \ ; \ K_2$
$(3) \ H_{2(g)} + \frac{1}{2}O_{2(g)} \rightleftharpoons H_2O_{(g)} \ ; \ K_3$
The equation for the equilibrium constant of the reaction
$2NH_{3(g)} + \frac{5}{2}O_{2(g)} \rightleftharpoons 2NO_{(g)} + 3H_2O_{(g)}$
$(K_4)$ in terms of $K_1$,$K_2$,and $K_3$ is

The values of $K_p/K_c$ for the following reactions at $300 \ K$ are respectively (At $300 \ K, RT = 24.62 \ dm^3 \ atm \ mol^{-1}$):
$(i) \ N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$
$(ii) \ N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$
$(iii) \ N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$

$9.2 \ g$ of $N_2O_{4(g)}$ is taken in a closed $1 \ L$ vessel and heated until the following equilibrium is reached: $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$. At equilibrium,$50\%$ of $N_2O_{4(g)}$ is dissociated. What is the equilibrium constant $K_c$ (in $mol \ L^{-1}$)? (Molecular weight of $N_2O_4 = 92$)

If $K_C$ for the equilibrium reaction $2 ABC_{(g)} \rightleftharpoons 2 AB_{(g)} + C_{2(g)}$ is $X$ at $T \ K$,its $K_P$ at the same temperature is: