For the equilibrium $ \text{Liquid} \rightleftharpoons \text{Vapour} $,which of the following expressions is correct?

Using the data provided,find the value of the equilibrium constant for the following reaction at $298 \ K$ and $1 \ atm$ pressure: $NO_{(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons NO_{2(g)}$
$\Delta_{f} H^0(NO_{(g)}) = 90.4 \ kJ \cdot mol^{-1}$
$\Delta_{f} H^0(NO_{2(g)}) = 32.48 \ kJ \cdot mol^{-1}$
$\Delta S^{\circ} = -70.8 \ J \cdot K^{-1} \cdot mol^{-1}$
$\text{antilog}(6.4) = 2.51 \times 10^6$ (Note: Calculation based on standard thermodynamic relations)

For the reaction $A + B \rightleftharpoons 2C$,the value of equilibrium constant is $100$ at $298 \ K$. If the initial concentration of all the three species is $1 \ M$ each,then the equilibrium concentration of $C$ is $X \times 10^{-1} \ M$. The value of $X$ is $.....$ (Nearest integer)

Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per the following endothermic reaction:
$CH_{4(g)} + H_2O_{(g)} \rightleftharpoons CO_{(g)} + 3H_{2(g)}$
$(a)$ Write an expression for $K_p$ for the above reaction.
$(b)$ How will the values of $K_p$ and the composition of the equilibrium mixture be affected by:
$(i)$ increasing the pressure
$(ii)$ increasing the temperature
$(iii)$ using a catalyst?

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 .......... $atm$.

For the equilibrium:
$CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$; $K_{p} = 1.64 \ atm$ at $1000 \ K$.
$50 \ g$ of $CaCO_{3}$ in a $10 \ L$ closed vessel is heated to $1000 \ K$. The percentage of $CaCO_{3}$ that remains unreacted at equilibrium is:
(Given $R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1}$)