$37.8 \ g$ $N_2O_5$ was taken in a $1 \ L$ reaction vessel and allowed to undergo the following reaction at $500 \ K$:
$2N_2O_{5(g)} \rightarrow 2N_2O_{4(g)} + O_{2(g)}$
The total pressure at equilibrium was found to be $18.65 \ bar$. Then,$K_p = \text{ . . . . . . } \times 10^{-2}$ [nearest integer].
Assume $N_2O_5$ to behave ideally under these conditions.
Given: $R = 0.082 \ bar \ L \ mol^{-1} \ K^{-1}$

$PCl_{5} \rightleftharpoons PCl_{3} + Cl_{2} \quad K_{c} = 1.844$
$3.0 \ \text{moles}$ of $PCl_{5}$ is introduced in a $1 \ \text{L}$ closed reaction vessel at $380 \ \text{K}$. The number of moles of $PCl_{5}$ at equilibrium is $..... \times 10^{-3}$. (Round off to the Nearest Integer)

For a reaction taking place in a container in equilibrium with its surroundings,the effect of temperature on its equilibrium constant $K$ in terms of change in entropy is described by:

Consider the following gas phase reaction being carried out in a closed vessel at $25^\circ\text{C}$: $2A(g) \rightarrow 4B(g) + C(g)$. The table provides the total pressure of the system at different time intervals. Calculate the pressure of $C(g)$ at $30$ minutes time interval.

Time (min)	Total pressure (mm Hg)
$30$	$300$
$\infty$	$600$

For the reaction $N_2 + O_2 \rightleftharpoons 2NO$ at $300 \, ^\circ C$,the value of $K_c$ is $9 \times 10^{-4}$. If equivalent amounts of $N_2$ and $O_2$ are used,what is the concentration of $NO$ at equilibrium (in terms of $a$) (in $, a$)?

For a reaction,$A \rightleftharpoons P$,the plots of $[A]$ and $[P]$ with time at temperatures $T_1$ and $T_2$ are given below. If $T_2 > T_1$,the correct statement$(s)$ is (are) (Assume $\Delta H^{\ominus}$ and $\Delta S^{\ominus}$ are independent of temperature and ratio of $\ln K$ at $T_1$ to $\ln K$ at $T_2$ is greater than $T_2 / T_1$. Here $H, S, G$ and $K$ are enthalpy,entropy,Gibbs energy and equilibrium constant,respectively.)
$(A)$ $\Delta H^{\ominus} < 0, \Delta S^{\ominus} < 0$
$(B)$ $\Delta G^{\ominus} < 0, \Delta H^{\ominus} > 0$
$(C)$ $\Delta G^{\ominus} < 0, \Delta S^{\ominus} < 0$
$(D)$ $\Delta G^{\ominus} < 0, \Delta S^{\ominus} > 0$