Consider the following gaseous equilibrium reactions (I), (II) and (III) with equilibrium constants $K_1, K_2$ and $K_3$ respectively

(I) $\frac{1}{2} \mathrm{~N}_2+\frac{3}{2} \mathrm{H}_2 \rightleftharpoons \mathrm{NH}_3$

(II) $2 \mathrm{NO} \rightleftharpoons \mathrm{N}_2+\mathrm{O}_2$

(III) $\mathrm{H}_2+\frac{1}{2} \mathrm{O}_2 \rightleftharpoons \mathrm{H}_2 \mathrm{O}$

The correct expression for the equilibrium constant for the gaseous equilibrium reaction

$$ 2 \mathrm{NH}_3+\frac{5}{2} \mathrm{O}_2 \rightleftharpoons 2 \mathrm{NO}+3 \mathrm{H}_2 \mathrm{O} \text { is } $$

At $T(\mathrm{~K})$, the following gaseous equilibrium is established.

$$ W+X \rightleftharpoons Y+Z $$

The initial concentration of $W$ is two times to the initial concentration of $X$. The system is heated to $T(\mathrm{~K})$ to establish the equilibrium. At equilibrium the concentration of $Y$ is four times to the concentration of $X$. What is the value of $K_C$ ?

At $T(\mathrm{~K}), K_C$ value for

$\mathrm{AO}_2(\mathrm{~g})+\mathrm{BO}_2(\mathrm{~g}) \rightleftharpoons \mathrm{AO}_3(\mathrm{~g})+\mathrm{BO}(\mathrm{g})$ is 16 . In a closed 1 L flask, one mole each of $A \mathrm{O}_2, B \mathrm{O}_2, A \mathrm{O}_3$ and $B \mathrm{O}$ are taken and heated to $T(\mathrm{~K})$.

What is the concentration (in $\mathrm{mol} \mathrm{L}^{-1}$ ) of $\mathrm{AO}_3$ at equilibrium?

At 298 K , the value of $K_c$ for the following reaction is $x \mathrm{~mol} \mathrm{~L}^{-1}$.

What is the approximate $K_{\mathrm{P}}$ value for this reaction?

$$ \begin{array}{r} \left(R=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right) \\ \mathrm{A}_2 \mathrm{O}_4(\mathrm{~g}) \rightleftharpoons 2 \mathrm{AO}_2(\mathrm{~g}) \end{array} $$