For the reaction $CH_{4(g)} + 2O_{2(g)} \rightleftharpoons CO_{2(g)} + 2H_{2}O_{(g)}$ with $\Delta H = -170.8 \ kJ \ mol^{-1}$,which of the following statements is incorrect?

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

Dissociation of a gas $A_2$ takes place according to the following chemical reaction. At equilibrium, the total pressure is $1 \ bar$ at $300 \ K$.
$A_{2(g)} \rightleftharpoons 2A_{(g)}$
The standard Gibbs energy of formation of the involved substances has been provided below:

Substance	$\Delta G_f^{\circ} / kJ \ mol^{-1}$
$A_2$	$-100.00$
$A$	$-50.832$

The degree of dissociation of $A_{2(g)}$ is given by $(x \times 10^{-2})^{1/2}$ where $x =$ . . . . . . . (Nearest integer).
[Given: $R = 8.3 \ J \ mol^{-1} \ K^{-1}$, $\ln 2 = 0.693$]

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

The reaction $2H_2S_{(g)} \rightleftharpoons 2H_{2_{(g)}} + S_{2_{(g)}}$ is in equilibrium. If $0.5 \ mol$ of $H_2S$,$0.10 \ mol$ of $H_2$,and $0.4 \ mol$ of $S_2$ are taken in a $1 \ L$ vessel,the value of the equilibrium constant $(K)$ is .... $mol \ L^{-1}$.

In a $10 \ L$ vessel,$1 \ mol$ each of $PCl_5$ and $PCl_3$ are present. If the vessel is heated,some $PCl_5$ dissociates. What are the concentrations of $PCl_5$,$PCl_3$,and $Cl_2$ at equilibrium,respectively?