At $T$ $(K)$,$K_c$ for the dissociation of $PCl_5$ is $2 \times 10^{-2} \ mol \ L^{-1}$. The number of moles of $PCl_5$ that must be taken in a $1.0 \ L$ flask at the same temperature to get $0.2 \ mol$ of chlorine at equilibrium is:

Solid $KClO_3$ is taken in a container maintained at a constant pressure of $1 \ atm$. Upon heating,the following equilibrium is obtained:
$2KClO_{3(s)} \rightleftharpoons 2KCl_{(s)} + 3O_{2(g)}$
If $\Delta H^o = 25 \ kcal/mol$ and $\Delta S^o = 50 \ cal/K$,at what temperature will equilibrium be established in the container? (Ignore variation of $\Delta H^o$ and $\Delta S^o$ with temperature.) $......K$

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)
$30$	$300$
$\infty$	$600$

In the reaction $2P_{(g)} + Q_{(g)} \rightleftharpoons 3R_{(g)} + S_{(g)}$,if $2 \text{ moles}$ of each $P$ and $Q$ are taken initially in a $1 \text{ L}$ flask,which of the following is true at equilibrium?

For the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$,the equilibrium constant is $K_1$. For the reaction $2NO_{(g)} + O_{2(g)} \rightleftharpoons 2NO_{2(g)}$,the equilibrium constant is $K_2$. The equilibrium constant $K$ for the reaction $NO_{2(g)} \rightleftharpoons \frac{1}{2}N_{2(g)} + O_{2(g)}$ will be:

If $8 \, \text{mol}$ of $PCl_5$ is heated in a closed vessel of $10 \, L$ capacity and $25\%$ of it dissociates into $PCl_3$ and $Cl_2$ at equilibrium,then the value of $K_p$ is .....