The reaction,$2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$ is carried out in a $1 \ dm^3$ vessel and $2 \ dm^3$ vessel separately. The ratio of the reaction velocities will be

The equilibrium constants for the following three reactions $(i)$,$(ii)$,and $(iii)$ are given as:
$(i)$ $CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2(g)} + H_{2(g)} \quad K_1$
$(ii)$ $CH_{4(g)} + H_2O_{(g)} \rightleftharpoons CO_{(g)} + 3H_{2(g)} \quad K_2$
$(iii)$ $CH_{4(g)} + 2H_2O_{(g)} \rightleftharpoons CO_{2(g)} + 4H_{2(g)} \quad K_3$
Which of the following relations 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

For a reaction $A_{(s)} \rightleftharpoons B_{(s)} + C_{(g)}$,the set of all correct statements are:
$(a) \ K$ is independent of $[A]$.
$(b) \ K$ is dependent on partial pressure of $C$ at a given temperature.
$(c) \ \Delta H$ will be independent of temperature.
$(d) \ \Delta H$ is independent of the catalyst addition.

Consider the following chemical equilibrium of the gas phase reaction at a constant temperature: $A_{(g)} \rightleftharpoons B_{(g)} + C_{(g)}$. If $p$ is the total pressure,$K_p$ is the equilibrium constant,and $\alpha$ is the degree of dissociation,then which of the following is true at equilibrium?

Solid $NH_4HS$ is placed in a flask containing $NH_3$ gas at a certain temperature and a pressure of $0.50 \ atm$. The $NH_4HS$ decomposes to form $NH_3$ gas and $H_2S$ gas. When equilibrium is established in the flask,the total pressure increases to $0.84 \ atm$. What is the equilibrium constant $(K_p)$ for the decomposition of $NH_4HS$ at this temperature?