For the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$,the equilibrium constant is $K_1$. For the reaction $2NO_{(g)} + O_{2(g)} \rightleftharpoons 2NO_{2(g)}$,the equilibrium constant is $K_2$. The equilibrium constant $K$ for the reaction $NO_{2(g)} \rightleftharpoons \frac{1}{2}N_{2(g)} + O_{2(g)}$ will be:

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 $0.8$

Fill in the blanks:
$a$. If a reaction is in equilibrium,then the rate of the forward reaction and the rate of the backward reaction will be ....... .
$b$. If $\Delta G$ is negative,then thermodynamically the reaction takes place in the ...... direction.
$c$. The equilibrium constant gives ........ information for a reaction.

For the reactions $X \rightleftharpoons 2Y$ and $Z \rightleftharpoons P + Q$,the equilibrium constants $K_p$ and $K_q$ are in the ratio $1:9$. If the degree of dissociation of $X$ and $Z$ is the same,then the ratio of their total pressures is:

$A$ vessel at $1000 \ K$ contains $CO_2$ with a pressure of $0.5 \ atm$. Some of $CO_2$ is converted into $CO$ on addition of graphite. If total pressure at equilibrium is $0.8 \ atm$,then $K_P$ is : (in $atm$)

For the reaction $A_{(g)} + 3B_{(g)} \rightleftharpoons 2C_{(g)}$ at $27 \, ^oC$,$2 \, moles$ of $A$,$4 \, moles$ of $B$ and $6 \, moles$ of $C$ are present in a $2 \, litre$ vessel. If $K_C$ for the reaction is $1.2$,the reaction will proceed in