When $20 \ g$ of $CaCO_3$ are subjected to decomposition at $227 \ ^oC$ in a closed container of $10 \ L$ capacity,$50 \%$ of $CaCO_3$ remained unreacted at equilibrium. Calculate $K_P$ for $CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$ in $atm$.

For the reaction $A_{(g)} \rightleftharpoons B_{(g)} + C_{(g)}$,$A$ is $33 \%$ dissociated at a total pressure $P$. The correct relation between $P$ and $K_{p}$ is

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?

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

At $783 \, K$ in the reaction,$H_{2(g)} + I_{2(g)} \rightleftharpoons 2 HI_{(g)}$,the molar concentrations $(mol \, L^{-1})$ of $H_2, I_2$ and $HI$ at some instant of time are $0.1, 0.2$ and $0.4$,respectively. If the equilibrium constant is $46$ at the same temperature,then as the reaction proceeds:

One mole of $O_{2(g)}$ and two moles of $SO_{2(g)}$ were heated in a closed vessel of $1 \, L$ capacity at $1098 \, K$. At equilibrium,$1.6 \, moles$ of $SO_{3(g)}$ were found. The equilibrium constant $K_c$ of the reaction would be