Three moles of $PCl_{5}$,three moles of $PCl_{3}$ and two moles of $Cl_{2}$ are taken in a closed vessel. If at equilibrium the vessel has $1.5$ moles of $PCl_{5}$,the number of moles of $PCl_{3}$ present in it is

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

Explain the relationship between the time taken to reach equilibrium and thermodynamics.

In a $20 \ L$ vessel,if $1 \ mol$ each of $CO$,$H_2O$,and $CO_2$ are initially present,then for the equilibrium $CO + H_2O \rightleftharpoons CO_2 + H_2$,which of the following is true?

$X_{2(g)} + Y_{2(g)} \rightleftharpoons 2Z_{(g)}$
$X_{2(g)}$ and $Y_{2(g)}$ are added to a $1 \ L$ flask and it is found that the system attains the above equilibrium at $T \ K$ with the number of moles of $X_{2(g)}$,$Y_{2(g)}$ and $Z_{(g)}$ being $3$,$3$ and $9 \ mol$ respectively (equilibrium moles). Under these conditions of equilibrium,$10 \ mol$ of $Z_{(g)}$ is added to the flask and the temperature is maintained at $T \ K$. Then the number of moles of $Z_{(g)}$ in the flask when the new equilibrium is established is . . . . . . . (Nearest integer).

$PCl_{5}$ dissociates as $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$. $5 \, \text{moles}$ of $PCl_{5}$ are placed in a $200 \, L$ vessel which contains $2 \, \text{moles}$ of $N_{2}$ and is maintained at $600 \, K$. The equilibrium pressure is $2.46 \, atm$. The equilibrium constant $K_{p}$ for the dissociation of $PCl_{5}$ is $...... \times 10^{-3}$. (nearest integer) (Given: $R = 0.082 \, L \, atm \, K^{-1} \, mol^{-1}$: Assume ideal gas behaviour)