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

Which of the following statements is/are wrong?
$(a)$ At equilibrium,concentrations of reactants and products become constant because the reaction stops.
$(b)$ Addition of catalyst speeds up the forward reaction more than the backward reaction.
$(c)$ Equilibrium constant of an exothermic reaction decreases with increase of temperature.
$(d)$ $K_p$ is always greater than $K_c$.

For the reaction $2P_{(g)} + Q_{(g)} \rightleftharpoons R_{(g)} + S_{(g)}$; $K_C = 10^{12}$. If the initial moles of $P, Q, R, S$ are $2, 1, 7$ and $3$ moles respectively in a $1 \ L$ vessel,find the equilibrium concentration of $P$.

The equilibrium constant at $298 \ K$ for a reaction $A + B \rightleftharpoons C + D$ is $100$. If the initial concentration of all the four species were $1 \ M$ each,then the equilibrium concentration of $D$ (in $mol \ L^{-1}$) will be:

The equilibrium composition for the reaction $PCl_3 + Cl_2 \rightleftharpoons PCl_5$ at $298 \, K$ is given below.
$[PCl_3]_{eq} = 0.2 \, mol \, L^{-1}$
$[Cl_2]_{eq} = 0.1 \, mol \, L^{-1}$
$[PCl_5]_{eq} = 0.40 \, mol \, L^{-1}$
If $0.2 \, mol$ of $Cl_2$ is added at the same temperature,the equilibrium concentration of $PCl_5$ is $.... \times 10^{-2} \, mol \, L^{-1}$. Given: $K_c$ for the reaction at $298 \, K$ is $20$.

Given three reactions and their equilibrium constants:
$N_2 + 3H_2 \rightleftharpoons 2NH_3 ; k_1$
$N_2 + O_2 \rightleftharpoons 2NO ; k_2$
$H_2 + \frac{1}{2}O_2 \rightleftharpoons H_2O ; k_3$
The equilibrium constant for the reaction $2NH_3 + \frac{5}{2}O_2 \rightleftharpoons 2NO + 3H_2O$ in terms of $k_1, k_2,$ and $k_3$ is: