$CH_3COCH_{3(g)} \rightleftharpoons C_2H_{6(g)} + CO_{(g)}$. The initial pressure of $CH_3COCH_3$ is $100 \ mm$. When equilibrium is set up,the mole fraction of $CO_{(g)}$ is $\frac{1}{4}$. Hence,the partial pressure of $CO$ is:

$13.8 \,g$ of $N_{2}O_{4}$ was placed in a $1 \,L$ reaction vessel at $400 \,K$ and allowed to attain equilibrium.
$N_{2}O_{4(g)} \rightleftharpoons 2NO_{2(g)}$
The total pressure at equilibrium was found to be $9.15 \,bar$. Calculate $K_{c}$,$K_{p}$,and the partial pressures at equilibrium.

Match the items in List-$X$ with List-$Y$ and select the correct option.

List-$X$	List-$Y$
$(A)$ Active mass	$(i)$ $\Delta n = 0$
$(B)$ Equilibrium constant	$(ii)$ Molar concentration
$(C)$ $A + \text{Heat} \rightleftharpoons B$	$(iii)$ Van't Hoff equation
$(D)$ $2A_{(g)} + B_{(g)} \rightleftharpoons 3C_{(g)}$	$(iv)$ Favoured by increase in temperature
	$(v)$ Chemical equilibrium

For the reversible reaction $2NO_2 \leftrightarrow[K_2]{K_1} N_2O_4$,the rate of disappearance of $NO_2$ is given by:

For the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,the value of $K_c$ is $0.04$ at $250 \ ^oC$ in a $3 \ L$ vessel. If the concentration of $Cl_2$ at equilibrium is $0.15 \ M$,then the initial moles of $PCl_5$ will be ...........

The thermal dissociation equilibrium of $CaCO_{3(s)}$ is studied under different conditions.
$CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$
For this equilibrium,the correct statement$(s)$ is (are):
$(A)$ $\Delta H$ is dependent on $T$
$(B)$ $K$ is independent of the initial amount of $CaCO_{3}$
$(C)$ $K$ is dependent on the pressure of $CO_{2}$ at a given $T$
$(D)$ $\Delta H$ is independent of the catalyst,if any