Which of the following expressions is true regarding the formation of $PCl_{5(g)}$?
$PCl_{3(g)} + Cl_{2(g)} \rightleftharpoons PCl_{5(g)}$

Equilibrium constants $K_1$ and $K_2$ for the following equilibria:
$(a)$ $NO_{(g)} + \frac{1}{2}O_{2(g)} \rightleftharpoons NO_{2(g)}$
$(b)$ $2NO_{2(g)} \rightleftharpoons 2NO_{(g)} + O_{2(g)}$
are related as:

For the following three equilibria $X, Y$,and $Z$ in the gaseous state at $300 \ K$,the increasing order of the ratio of $K_p$ to $K_c$ is:
$X: 2SO_2 + O_2 \rightleftharpoons 2SO_3$
$Y: PCl_5 \rightleftharpoons PCl_3 + Cl_2$
$Z: 2HI \rightleftharpoons H_2 + I_2$

In the synthesis of $HI$,the amounts of $H_{2(g)}$,$I_{2(g)}$,and $HI_{(g)}$ at equilibrium were found to be $0.8 \ mol$,$0.8 \ mol$,and $2.4 \ mol$ respectively in a $10 \ L$ vessel. Calculate the equilibrium constant $(K_c)$ for the reaction $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$ and the equilibrium constant for the reverse reaction.

$2 \ mol$ of $PCl_5$ is heated in a closed vessel of $2 \ L$ capacity. When equilibrium is attained,$PCl_5$ is $40\%$ dissociated. The equilibrium constant $K_c$ for the reaction will be ........... $mol/L$.

For the reaction $2NO_{2(g)} \rightleftharpoons 2NO_{(g)} + O_{2(g)}$,$K_c = 1.8 \times 10^{-6}$ at $184 \, ^\circ C$. Given $R = 0.0831 \, kJ/(mol \cdot K)$,when $K_p$ and $K_c$ are compared at $184 \, ^\circ C$,it is found that: