For the reaction $2A_{(g)} + B_{(g)} \rightleftharpoons 3C_{(g)} + D_{(g)}$,$2 \ mol$ each of $A$ and $B$ are taken in a flask. Which of the following will always be true when the system reaches equilibrium?

At $T(K)$,the $K_c$ value of the reaction $AO_{2(g)} + BO_{2(g)} \rightleftharpoons AO_{3(g)} + BO_{(g)}$ is $16$. In a closed $1 \ L$ flask,one mole each of $AO_2, BO_2, AO_3$ and $BO$ are taken and heated to $T(K)$. Identify the correct statements about this equilibrium.
$I)$ Total number of moles at equilibrium is $4$
$II)$ At equilibrium,the ratio of moles of $AO_2$ and $AO_3$ is $1:4$
$III)$ Total number of moles of $AO_2$ and $BO_2$ at equilibrium is $0.8$

The equilibrium constants for the reactions $X \rightleftharpoons 2Y$ and $Z \rightleftharpoons P + Q$ are $K_{1}$ and $K_{2}$,respectively. If the initial concentrations and the degree of dissociation of $X$ and $Z$ are the same,the ratio $K_{1} / K_{2}$ is

At $298 \ K$,
$N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g), K_1 = 4 \times 10^5$
$N_2(g) + O_2(g) \rightleftharpoons 2NO(g), K_2 = 1.6 \times 10^{12}$
$H_2(g) + \frac{1}{2}O_2(g) \rightleftharpoons H_2O(g), K_3 = 1.0 \times 10^{-13}$
Based on the above equilibria,the equilibrium constant of the reaction,
$2NH_3(g) + \frac{5}{2}O_2(g) \rightleftharpoons 2NO(g) + 3H_2O(g)$
is $.......... \times 10^{-33}$ (Nearest integer).

At $717 \ K$,$3.2 \ mol$ of $HI$ is heated in a closed tube. $20\%$ of $HI$ decomposes at equilibrium according to the reaction $2HI_{(g)} \rightleftharpoons H_{2_{(g)}} + I_{2_{(g)}}$. Find $K_c$ and the moles of $HI$,$H_2$,and $I_2$ at equilibrium.

The values of $K_p$ for the reactions,
$X \rightleftharpoons Y + Z$ $...(i)$
$A \rightleftharpoons 2B$ $...(ii)$
are in the ratio $9 : 1$. If the degree of dissociation of $X$ and $A$ is equal,then the ratio of total pressure at equilibrium for $(i)$ and $(ii)$ is: