$PCl_5$,$PCl_3$,and $Cl_2$ are at equilibrium at $500 \ K$ with concentrations $[PCl_3] = 1.59 \ M$,$[Cl_2] = 1.59 \ M$,and $[PCl_5] = 1.41 \ M$. Calculate $K_c$ for the reaction:
$PCl_5 \rightleftharpoons PCl_3 + Cl_2$

If $K_1, K_2, K_3$ are equilibrium constants for the formation of $AD, AD_2, AD_3$ respectively as follows: $A + D \rightleftharpoons AD$,$AD + D \rightleftharpoons AD_2$,$AD_2 + D \rightleftharpoons AD_3$. Then the equilibrium constant '$K$' for $A + 3D \rightleftharpoons AD_3$ is related as:

At $T \ (K)$,$K_{p}$ value for the reaction,$2 \ AO_{2(g)} + O_{2(g)} \rightleftharpoons 2 \ AO_{3(g)}$ is $4 \times 10^{10}$. What is the $K_{p}^{\prime}$ value for $3 \ AO_{2(g)} + \frac{3}{2} \ O_{2(g)} \rightleftharpoons 3 \ AO_{3(g)}$ at $T \ (K)$?

For the reaction $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$,the correct expression of equilibrium constant $K$ is

$A$ sample of pure $PCl_{5}$ was introduced into an evacuated vessel at $473 \, K$. After equilibrium was attained,the concentration of $PCl_{5}$ was found to be $0.5 \times 10^{-1} \, mol \, L^{-1}$. If the value of $K_{c}$ is $8.3 \times 10^{-3}$,what are the concentrations of $PCl_{3}$ and $Cl_{2}$ at equilibrium?
$PCl_{5(g)} \longleftrightarrow PCl_{3(g)} + Cl_{2(g)}$

For the gaseous reaction,equilibrium constant is given:
$XeF_6 + H_2O \rightleftharpoons XeOF_4 + 2HF, K_1$
$XeO_4 + XeF_6 \rightleftharpoons XeOF_4 + XeO_3F_2, K_2$
The equilibrium constant for the reaction:
$XeO_4 + 2HF \rightleftharpoons XeO_3F_2 + H_2O$ will be