At $600 \ K$,ammonium carbamate decomposes in a closed vessel: $NH_2COONH_{4(s)} \rightleftharpoons 2NH_{3(g)} + CO_{2(g)}$. At equilibrium,the total pressure is $3 \ bar$. Calculate $K_p$. (in $bar^3$)

The equilibrium constants of the following are
$N_2 + 3H_2 \rightleftharpoons 2NH_3 \,; \quad K_1$
$N_2 + O_2 \rightleftharpoons 2NO \,; \quad K_2$
$H_2 + \frac{1}{2} O_2 \rightleftharpoons H_2O \,; \quad K_3$
The equilibrium constant $(K)$ of the reaction:
$2NH_3 + \frac{5}{2} O_2 \rightleftharpoons 2NO + 3H_2O$ is:

The two substances $A$ and $B$ are in equilibrium with $C$ and $D$ as $2A + B \rightleftharpoons 3C + 2D$. If the initial pressure of $A$ and $B$ are in the ratio of $4:1$ and at equilibrium,the partial pressures of $A$ and $D$ are equal,find the correct relation.

$PCl_{5}$ dissociates as $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$. $5 \, \text{moles}$ of $PCl_{5}$ are placed in a $200 \, L$ vessel which contains $2 \, \text{moles}$ of $N_{2}$ and is maintained at $600 \, K$. The equilibrium pressure is $2.46 \, atm$. The equilibrium constant $K_{p}$ for the dissociation of $PCl_{5}$ is $...... \times 10^{-3}$. (nearest integer) (Given: $R = 0.082 \, L \, atm \, K^{-1} \, mol^{-1}$: Assume ideal gas behaviour)

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?

Which of the following statements is correct?