For a reaction $2 A \rightleftharpoons B + C$,$K_c$ is $2 \times 10^{-3}$. At a given time,the reaction mixture has $[A] = [B] = [C] = 3 \times 10^{-4} \ M$. Which of the following options is correct?

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

At $473 \ K$,the equilibrium constant $K_{c}$ for the decomposition of phosphorus pentachloride is $8.3 \times 10^{-3}$. If the decomposition is depicted as:
$PCl_{5(g)} \longleftrightarrow PCl_{3(g)} + Cl_{2(g)} \quad \Delta_{r}H^{\circ} = 124.0 \ kJ \ mol^{-1}$
$(a)$ Write an expression for $K_{c}$ for the reaction.
$(b)$ What is the value of $K_{c}$ for the reverse reaction at the same temperature?
$(c)$ What would be the effect on $K_{c}$ if:
$(i)$ more $PCl_{5}$ is added?
$(ii)$ pressure is increased?
$(iii)$ the temperature is increased?

An equilibrium shifts towards reactants at higher temperatures. Find the correct graph.

$0.6 \ mol$ of $NH_3$ in a reaction vessel of $2 \ dm^3$ capacity was brought to equilibrium. The vessel was then found to contain $0.15 \ mol$ of $H_2$ formed by the reaction $2NH_{3(g)} \rightleftharpoons N_{2(g)} + 3H_{2(g)}$. Which of the following statements is true?

The equilibrium constants for the following reactions are $K_1$ and $K_2$,respectively.
$2 P_{(g)} + 3 Cl_{2(g)} \rightleftharpoons 2 PCl_{3(g)}$
$PCl_{3(g)} + Cl_{2(g)} \rightleftharpoons PCl_{5(g)}$
Then,the equilibrium constant for the reaction,$2 P_{(g)} + 5 Cl_{2(g)} \rightleftharpoons 2 PCl_{5(g)}$ is