One mole of $N_2O_4(g)$ is taken in a closed vessel at $300 \, K$ under $1 \, atm$ pressure. When it is heated to $600 \, K$,$20 \%$ of $N_2O_4(g)$ dissociates into $NO_2(g)$. What is the final pressure in $atm$?

Match List-$I$ (Equations) with List-$II$ (Type of processes) and select the correct option.

List-$I$ (Equations)	List-$II$ (Type of processes)
$A. K_p > Q$	$(i)$ Non-spontaneous
$B. \Delta G^\circ < RT \ln Q$	$(ii)$ Equilibrium
$C. K_p = Q$	$(iii)$ Spontaneous and endothermic
$D. T > \frac{\Delta H}{\Delta S}$	$(iv)$ Spontaneous

Equivalent amounts of $H_2$ and $I_2$ are heated in a closed vessel till equilibrium is obtained. If $80\%$ of the hydrogen is converted to $HI$,the $K_c$ at this temperature is

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?

Consider the following reversible first-order reaction of $X$ at an initial concentration $[X]_{0}$. The values of the rate constants are $K_{f} = 2 \ s^{-1}$ and $K_{b} = 1 \ s^{-1}$.
$X \underset{K_{b}}{\stackrel{K_{f}}{\rightleftharpoons}} Y$
Which of the following plots correctly represents the concentration of $X$ and $Y$ as a function of time?

For the reaction $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$,the value of $K_c$ at $440 \ ^oC$ is $50$. If the reaction is initiated in a $1 \ L$ flask with $1 \ mol$ of $H_2$,$2 \ mol$ of $I_2$,and $3 \ mol$ of $HI$,then the equilibrium concentration of $HI$ will be .......... $M$.