In the reaction $PCl_5 \rightleftharpoons PCl_3 + Cl_2$,one mole of $PCl_5$ is started in a $5 \ L$ vessel. If $0.3 \ mol$ of $PCl_5$ is present at equilibrium,find the concentration of $PCl_3$,total moles,and the value of $K_c$.

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

Ammonia under a pressure of $15 \ atm$ at $27 \ ^{\circ}C$ is heated to $347 \ ^{\circ}C$ in a closed vessel in the presence of a catalyst. Under these conditions,$NH_3$ is partially decomposed according to the equation,$2NH_3 \rightleftharpoons N_2 + 3H_2$. The vessel is such that the volume remains constant,and the pressure increases to $50 \ atm$. Calculate the percentage of $NH_3$ actually decomposed.

Write a relation between $\Delta G$ and $Q$ and define the meaning of each term and answer the following:
$(a)$ Why a reaction proceeds forward when $Q < K$ and no net reaction occurs when $Q = K$.
$(b)$ Explain the effect of increase in pressure in terms of reaction quotient $Q$.
For the reaction: $CO_{(g)} + 3H_{2(g)} \rightleftharpoons CH_{4(g)} + H_{2}O_{(g)}$

$\Delta _f G^o$ at $500 \, K$ for substance '$S$' in liquid state and gaseous state are $+100.7 \, kcal \, mol^{-1}$ and $+103 \, kcal \, mol^{-1}$,respectively. The vapour pressure of liquid '$S$' at $500 \, K$ is approximately equal to $(R = 2 \, cal \, K^{-1} \, mol^{-1}) \dots \dots \text{atm}$.

$A$ gaseous reaction $A_{2(g)} \to B_{(g)} + \frac{1}{2} C_{(g)}$ shows an increase in pressure from $100 \ mm$ of $Hg$ to $120 \ mm$ of $Hg$ in $5 \ min$. What will be the rate of disappearance of $A_2$ in $mm$ of $Hg/min$?