$A + B \rightleftharpoons C + D$. If the final equilibrium concentrations of $A$ and $B$ are equal,and the equilibrium concentration of $D$ is twice that of $A$,what is the equilibrium constant $(K_c)$ of the reaction?

In the reaction $PCl_5 \rightleftharpoons PCl_3 + Cl_2$,if at equilibrium there are $2 \ mol$ each of $PCl_5$,$PCl_3$,and $Cl_2$,and the total pressure is $3 \ atm$,then the value of the equilibrium constant $K_p$ is ....... $atm$.

For the reaction $2NOCl_{(g)} \rightleftharpoons 2NO_{(g)} + Cl_{2_{(g)}}$ at $1060 \ K$,the equilibrium constant $K_p$ is $0.033 \ atm$. Find the value of $K_c$. (Given $R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1}$)

For the following gaseous equilibria at $300 \ K$,find the increasing order of the ratio $\frac{K_p}{K_c}$ for $X, Y,$ and $Z$:
$X: 2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$
$Y: PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$
$Z: 2HI_{(g)} \rightleftharpoons H_{2(g)} + I_{2(g)}$

The value of equilibrium constant of the reaction $HI_{(g)} \rightleftharpoons \frac{1}{2} H_{2_{(g)}} + \frac{1}{2} I_{2_{(g)}}$ is $8.0$. The equilibrium constant of the reaction $H_{2_{(g)}} + I_{2_{(g)}} \rightleftharpoons 2HI_{(g)}$ will be

For a gaseous reversible reaction,the enthalpy of reaction at constant pressure is $1.8 \ Kcal/mol$ greater than that at constant volume at $300 \ K$. The value of $\left( \frac{K_P}{K_C} \right)$ for the reaction at $T = \left( \frac{1}{0.00821} \right) \ K$ is: