At $400 \ K$ for the reaction $2NO_{2(g)} \rightleftharpoons N_{2}O_{4(g)}$,the concentration of $NO_{2}$ is $0.710 \ M$ and $N_{2}O_{4}$ is $0.145 \ M$. Find the equilibrium constant $K_{c}$. (in $M^{-1}$)

If the equilibrium constant for the reaction $2AB \rightleftharpoons A_2 + B_2$ is $49$,what is the equilibrium constant for $AB \rightleftharpoons \frac{1}{2}A_2 + \frac{1}{2}B_2$?

For the following equilibrium,$K_{C} = 6.3 \times 10^{14}$ at $1000 \ K$:
$NO_{(g)} + O_{3(g)} \longleftrightarrow NO_{2(g)} + O_{2(g)}$
Both the forward and reverse reactions in the equilibrium are elementary bimolecular reactions. What is $K_{C}$ for the reverse reaction?

If the equilibrium constant for $A \rightleftharpoons B + C$ is $K_{eq}^{(1)}$ and that of $B + C \rightleftharpoons P$ is $K_{eq}^{(2)}$,the equilibrium constant for $A \rightleftharpoons P$ is :-

Consider the following gaseous equilibria with equilibrium constants $K_{1}$ and $K_{2}$ respectively:
$SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$
$2 SO_{3(g)} \rightleftharpoons 2 SO_{2(g)} + O_{2(g)}$
The equilibrium constants are related as:

At $T \ (K)$,$K_{p}$ value for the reaction,$2 \ AO_{2(g)} + O_{2(g)} \rightleftharpoons 2 \ AO_{3(g)}$ is $4 \times 10^{10}$. What is the $K_{p}^{\prime}$ value for $3 \ AO_{2(g)} + \frac{3}{2} \ O_{2(g)} \rightleftharpoons 3 \ AO_{3(g)}$ at $T \ (K)$?