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

Calculate the partial pressure of carbon monoxide from the following data:
$CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}, K_p = 8 \times 10^{-2}$
$CO_{2(g)} + C_{(s)} \rightleftharpoons 2CO_{(g)}, K_p = 2$

At equilibrium for the reaction $A_{2(g)} + B_{2(g)} \rightleftharpoons 2 AB_{(g)}$,the concentrations of $A_2$,$B_2$,and $AB$ respectively are $1.5 \times 10^{-3} \ M$,$2.1 \times 10^{-3} \ M$,and $1.4 \times 10^{-3} \ M$ in a sealed vessel at $800 \ K$. What will be $K_p$ for the decomposition of $AB$ at the same temperature?

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:

$A$ plot of $\ln K$ against $\frac{1}{T}$ ($x$-axis) is expected to be a straight line,with intercept on $Y$-axis equal to

Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as:
$CH_3COOH_{(l)} + C_2H_5OH_{(l)} \longleftrightarrow CH_3COOC_2H_{5(l)} + H_2O_{(l)}$
$(i)$ Write the concentration ratio (reaction quotient),$Q_c$,for this reaction (note: water is not in excess and is not a solvent in this reaction).
$(ii)$ At $293 \ K$,if one starts with $1.00 \ mol$ of acetic acid and $0.18 \ mol$ of ethanol,there is $0.171 \ mol$ of ethyl acetate in the final equilibrium mixture. Calculate the equilibrium constant.
$(iii)$ Starting with $0.5 \ mol$ of ethanol and $1.0 \ mol$ of acetic acid and maintaining it at $293 \ K$,$0.214 \ mol$ of ethyl acetate is found after sometime. Has equilibrium been reached?