For the reaction $PCl_5(g) \rightleftarrows PCl_3(g) + Cl_2(g)$,which condition is correct?

In a $10 \ L$ vessel,$SO_3, SO_2$,and $O_2$ gases are present at a definite temperature with $K_c = 100$. For the reaction $2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$,if $SO_3$ and $SO_2$ are present in the same number of moles at equilibrium,find the moles of $O_2$. If $SO_3$ is double the moles of $SO_2$,what is the number of moles of $O_2$?

For the reaction,$H_{2(g)} + I_{2(g)} \rightleftharpoons 2 HI_{(g)}$,the attainment of equilibrium is predicted correctly by:

At $550 \ K$,the $K_c$ for the following reaction is $10^4 \ mol^{-1} \ L$: $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$. At equilibrium,it was observed that $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$. What is the value of $[Z]$ (in $mol \ L^{-1}$) at equilibrium?

Two solids dissociate as follows:
$A_{(s)} \rightleftharpoons B_{(g)} + C_{(g)}$; $K_{p_1} = x \, atm^2$
$D_{(s)} \rightleftharpoons C_{(g)} + E_{(g)}$; $K_{p_2} = y \, atm^2$
The total pressure when both the solids dissociate simultaneously is:

Reaction between $N_{2}$ and $O_{2}$ takes place as follows:
$2 N_{2(g)} + O_{2(g)} \longleftrightarrow 2 N_{2}O_{(g)}$
If a mixture of $0.482 \ mol$ of $N_{2}$ and $0.933 \ mol$ of $O_{2}$ is placed in a $10 \ L$ reaction vessel and allowed to form $N_{2}O$ at a temperature for which $K_{c} = 2.0 \times 10^{-37}$,determine the composition of the equilibrium mixture.