One mole of $N_2O_4(g)$ is taken in a closed container at $1 \ atm$ and $300 \ K$. When it is heated to $600 \ K$,$20 \%$ of $N_2O_4(g)$ dissociates into $NO_2(g)$. The resulting pressure is .......... $atm$.

Which of the following statements is/are true about equilibrium?
$(a)$ Equilibrium is possible only in a closed system at a given temperature.
$(b)$ All the measurable properties of the system remain constant at equilibrium.
$(c)$ Equilibrium constant for the reverse reaction is the inverse of the equilibrium constant for the reaction in the forward direction.

At high temperature,$2 \, \text{mol}$ of $NH_3$ is placed in a $500 \, \text{mL}$ vessel. For the decomposition reaction $2NH_{3(g)} \rightleftharpoons N_{2(g)} + 3H_{2(g)}$,if $1 \, \text{mol}$ of $NH_3$ remains at equilibrium,then $K_c$ is equal to:

$AB_{3(g)}$ dissociates as:
$AB_3(g) \rightleftharpoons AB_2(g) + \frac{1}{2}B_2(g)$
When the initial pressure of $AB_3$ is $800 \ torr$ and the total pressure developed at equilibrium is $900 \ torr$,what fraction of $AB_{3(g)}$ is dissociated? .....$\%$

For a reaction $A_{(s)} \rightleftharpoons B_{(s)} + C_{(g)}$,the set of all correct statements are:
$(a) \ K$ is independent of $[A]$.
$(b) \ K$ is dependent on partial pressure of $C$ at a given temperature.
$(c) \ \Delta H$ will be independent of temperature.
$(d) \ \Delta H$ is independent of the catalyst addition.

Solid carbon, $CaO$ and $CaCO_3$ are mixed and allowed to attain equilibrium at $T \text{ K}$. $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$ $K_{p1} = 0.08 \text{ atm}$. $C(s) + CO_2(g) \rightleftharpoons 2CO(g)$ $K_{p2} = 2 \text{ atm}$. The partial pressure of $CO$ is . . . . . . $\times 10^{-1} \text{ atm}$.