$5 \, \text{moles}$ of $PCl_5$ are heated in a closed vessel of $5 \, \text{L}$ capacity. At equilibrium,$40\%$ of $PCl_5$ is found to be dissociated. What is the value of $K_c$ (in $, \text{M}$)?

Match the items in List-$X$ with List-$Y$ and select the correct option.

List-$X$	List-$Y$
$(A)$ Active mass	$(i)$ $\Delta n = 0$
$(B)$ Equilibrium constant	$(ii)$ Molar concentration
$(C)$ $A + \text{Heat} \rightleftharpoons B$	$(iii)$ Van't Hoff equation
$(D)$ $2A_{(g)} + B_{(g)} \rightleftharpoons 3C_{(g)}$	$(iv)$ Favoured by increase in temperature
	$(v)$ Chemical equilibrium

Observe the following equations:
$Ag^{+} + NH_3 \rightleftharpoons [Ag(NH_3)]^{+}$,$K_1 = 1.6 \times 10^3$
$[Ag(NH_3)]^{+} + NH_3 \rightleftharpoons [Ag(NH_3)_2]^{+}$,$K_2 = 6.8 \times 10^3$
The equilibrium constant for the following reaction,$Ag^{+} + 2 NH_3 \rightleftharpoons [Ag(NH_3)_2]^{+}$ is

Given the equilibrium constants for the following three reactions:
$(1) N_2 + 3H_2 \rightleftharpoons 2NH_3; K_1$
$(2) N_2 + O_2 \rightleftharpoons 2NO; K_2$
$(3) H_2 + \frac{1}{2}O_2 \rightleftharpoons H_2O; K_3$
The equilibrium constant for the reaction of $NH_3$ with oxygen to form $NO$ and $H_2O$ is:

$13.8 \,g$ of $N_{2}O_{4}$ was placed in a $1 \,L$ reaction vessel at $400 \,K$ and allowed to attain equilibrium.
$N_{2}O_{4(g)} \rightleftharpoons 2NO_{2(g)}$
The total pressure at equilibrium was found to be $9.15 \,bar$. Calculate $K_{c}$,$K_{p}$,and the partial pressures at equilibrium.

In an alkaline medium,the sulfide ion reacts with solid sulfur to form polysulfide ions. The equilibrium constants for the formation of $S_2^{2-}$ and $S_3^{2-}$ from $S$ and $S^{2-}$ ions are $1.7$ and $5.3$,respectively. The equilibrium constant for the formation of $S_3^{2-}$ from $S_2^{2-}$ and $S$ will be .........