In the reaction $A + 2B \rightleftharpoons 2C$,if $2$ moles of $A$,$3.0$ moles of $B$ and $2.0$ moles of $C$ are placed in a $2.0 \ L$ flask and the equilibrium concentration of $C$ is $0.5 \ mol/L$. The equilibrium constant $K_c$ for the reaction is:

For the reaction,$0.5 C_{(s)} + 0.5 CO_{2(g)} \rightleftharpoons CO_{(g)}$,the equilibrium pressure is $12 \ atm$. If $CO_2$ conversion is $50 \%$,the value of $K_p$,in $atm$,is:

The amount of $PCl_5$ (in moles) that needs to be added to a $1\,L$ vessel at $250\,^oC$ in order to obtain $0.1\,mol$ of $Cl_2$ for the given reaction is:
$PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$; $K_C = 0.0414\,mol\,L^{-1}$

For the esterification reaction $CH_3COOH_{(l)} + C_2H_5OH_{(l)} \rightleftharpoons CH_3COOC_2H_{5(l)} + H_2O_{(l)}$,the equilibrium constant $K_c$ is $4$. If $4 \ mol$ of each acid and alcohol are taken initially,what will be the concentration of the acid at equilibrium?

For which of the following reactions will $K_p < K_c$?

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