For a reaction $X + Y \rightleftharpoons 2 Z$,$1.0 \ mol$ of $X$,$1.5 \ mol$ of $Y$ and $0.5 \ mol$ of $Z$ were taken in a $1 \ L$ vessel and allowed to react. At equilibrium,the concentration of $Z$ was $1.0 \ mol \ L^{-1}$. The equilibrium constant of the reaction is $-\frac{x}{15}$. The value of $x$ is........

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

For the equilibrium $ \text{Liquid} \rightleftharpoons \text{Vapour} $,which of the following expressions is correct?

If $8 \, \text{mol}$ of $PCl_5$ is heated in a closed vessel of $10 \, L$ capacity and $25\%$ of it dissociates into $PCl_3$ and $Cl_2$ at equilibrium,then the value of $K_p$ is .....

$8 \ mol$ of $AB_{3(g)}$ are introduced into a $1.0 \ dm^3$ vessel. If it dissociates as $2AB_{3(g)} \rightleftharpoons A_{2(g)} + 3B_{2(g)}$. At equilibrium,$2 \ mol$ of $A_2$ are found to be present. The equilibrium constant of this reaction is

Given below are two statements:
Statement $I$: $A$ catalyst cannot alter the equilibrium constant $(K_{C})$ of the reaction,temperature remaining constant.
Statement $II$: $A$ homogenous catalyst can change the equilibrium composition of a system,temperature remaining constant.
In the light of the above statements,choose the correct answer from the options given below: