For the reaction $P_{(g)} + 3Q_{(g)} \rightleftharpoons 4R_{(g)}$,the initial concentrations of $P$ and $Q$ are equal. If the equilibrium concentrations of $P$ and $R$ are equal,then the equilibrium constant $K_c$ for the reaction will be .....

In a vessel of volume $1 \, dm^3$,$1 \, mol$ of $N_2$ and $2 \, mol$ of $H_2$ are taken for the reaction. If $0.8 \, mol$ of $NH_3$ is obtained at equilibrium,the concentration of $H_2$ in the vessel will be .......... $mol \, dm^{-3}$.

$56 \, g$ of nitrogen and $8 \, g$ of hydrogen gas are heated in a closed vessel. At equilibrium,$34 \, g$ of ammonia are present. The equilibrium number of moles of nitrogen,hydrogen,and ammonia are respectively:

At $473 \ K$,the equilibrium constant $K_{c}$ for the decomposition of phosphorus pentachloride is $8.3 \times 10^{-3}$. If the decomposition is depicted as:
$PCl_{5(g)} \longleftrightarrow PCl_{3(g)} + Cl_{2(g)} \quad \Delta_{r}H^{\circ} = 124.0 \ kJ \ mol^{-1}$
$(a)$ Write an expression for $K_{c}$ for the reaction.
$(b)$ What is the value of $K_{c}$ for the reverse reaction at the same temperature?
$(c)$ What would be the effect on $K_{c}$ if:
$(i)$ more $PCl_{5}$ is added?
$(ii)$ pressure is increased?
$(iii)$ the temperature is increased?

For the reaction $C_{(s)} + CO_{2(g)} \rightleftharpoons 2CO_{(g)}$,if $25\%$ of $CO_2$ is converted to $CO$ at equilibrium and the total equilibrium pressure is $12 \ atm$,then the partial pressure of $CO_2$ at equilibrium will be............$atm$.

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