For the reaction $I_{2(g)} \rightleftharpoons 2I_{(g)}$,the equilibrium constant $K_c$ at $1000 \ K$ is $10^{-6}$. If $1 \ mol$ of $I_2$ is added to a $1 \ L$ container,which of the following statements is true at equilibrium?

$A$ gaseous reaction $A_{2(g)} \to B_{(g)} + \frac{1}{2} C_{(g)}$ shows an increase in pressure from $100 \ mm$ of $Hg$ to $120 \ mm$ of $Hg$ in $5 \ min$. What will be the rate of disappearance of $A_2$ in $mm$ of $Hg/min$?

At $T \ K$,$K_c$ for the reaction $AO_{2(g)} + BO_{2(g)} \rightleftharpoons AO_{3(g)} + BO_{(g)}$ is $16$. One mole each of reactants and products are taken in a $1 \ L$ flask and heated to $T \ K$,and equilibrium is established. What is the equilibrium concentration of $BO$ (in $mol \ L^{-1}$)?

$2SO_2 + O_2 \to$ product. If the pressure of the reaction increases $3$ times, then the rate will be (in $\times$)?

$PCl_{5}$ 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 $550 \ K$,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?