At $500 \ K$,for the reaction $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$,the $K_p$ is $0.036 \ atm^{-2}$. What is its $K_C$ in $L^2 \ mol^{-2}$? $(R = 0.082 \ L \ atm \ mol^{-1} \ K^{-1})$.

$(i)$ $\frac{1}{2}N_{2(g)} + \frac{3}{2}H_{2(g)} \rightleftharpoons NH_{3(g)}$ at $298 \ K$ has $\Delta G^{\Theta} = -16.5 \ kJ \ mol^{-1}$. Find $K_p$.
$(ii)$ At $298 \ K$,for $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$,calculate $K_p$ and $\Delta G^{\Theta}$.

For the reaction $C_{(s)} + CO_{2_{(g)}} \rightleftharpoons 2CO_{(g)}$,the partial pressures of $CO$ and $CO_2$ at equilibrium are $2.0 \ atm$ and $4.0 \ atm$ respectively. The value of $K_p$ for the reaction is:

At equilibrium,the concentrations are $[N_2] = 3.0 \times 10^{-3} \ M$,$[O_2] = 4.2 \times 10^{-3} \ M$,and $[NO] = 2.8 \times 10^{-3} \ M$ in a sealed vessel at $800 \ K$ and $1 \ atm$ pressure. What will be $K_p$ for the given reaction?
$N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$

Partial pressures of $A$,$B$,$C$,and $D$ for the gaseous system $A + 2B \rightleftharpoons C + 3D$ are $A = 0.20 \ atm$,$B = 0.10 \ atm$,$C = 0.30 \ atm$,and $D = 0.50 \ atm$. The numerical value of the equilibrium constant $(K_p)$ is:

For the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,$1 mol$ of $PCl_5$ is taken at $5 atm$ pressure. If $50\%$ of $PCl_5$ dissociates at equilibrium,calculate $K_p$.