$3.00 \ mol$ of $PCl_5$ kept in $1 \ L$ closed reaction vessel was allowed to attain equilibrium at $380 \ K$. If $1.59 \ mol$ of reactant was converted into the product at equilibrium,then $K_c$ is:

Which of the following statements is/are true about equilibrium?
$(a)$ Equilibrium is possible only in a closed system at a given temperature.
$(b)$ All the measurable properties of the system remain constant at equilibrium.
$(c)$ Equilibrium constant for the reverse reaction is the inverse of the equilibrium constant for the reaction in the forward direction.

Which of the following is true for the reaction $H_2O_{(l)} \rightleftharpoons H_2O_{(g)}$ at $100 \ ^\circ C$ and $1 \ \text{atm}$ pressure?

$28 \, g$ of $N_2$ and $6 \, g$ of $H_2$ were kept at $400 \, ^oC$ in a $1 \, L$ vessel. The equilibrium mixture contained $27.54 \, g$ of $NH_3$. The approximate value of $K_c$ for the reaction $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$ is (in $L^2 \, mol^{-2}$):

Ammonia under a pressure of $15 \ atm$ at $27 \ ^{\circ}C$ is heated to $347 \ ^{\circ}C$ in a closed vessel in the presence of a catalyst. Under these conditions,$NH_3$ is partially decomposed according to the equation,$2NH_3 \rightleftharpoons N_2 + 3H_2$. The vessel is such that the volume remains constant,and the pressure increases to $50 \ atm$. Calculate the percentage of $NH_3$ actually decomposed.

Match the items in List-$X$ with List-$Y$ and select the correct option.

List-$X$	List-$Y$
$(A)$ $A_{(g)} \rightleftharpoons B_{(g)} + \text{Heat}$	$(i)$ Equilibrium constant
$(B)$ $r_b/r_f$	$(ii)$ Favored at low temperature
$(C)$ $r_f/r_b$	$(iii)$ [Equilibrium constant]$^{-1}$
$(D)$ $2A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)}$	$(iv)$ $A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)} + D_{(g)}$
$(E)$ Effect of pressure	$(V)$ $\Delta n < 0$