For the system $3A + 2B \rightleftharpoons C$,the expression for equilibrium constant is

At $T \ K$,the $K_C$ value for the reaction $\frac{1}{3} N_{2(g)} + H_{2(g)} \rightleftharpoons \frac{2}{3} NH_{3(g)}$ is $50$. The $K_C$ value for the reaction $2 NH_{3(g)} \rightleftharpoons N_{2(g)} + 3 H_{2(g)}$ at the same temperature is:

Equilibrium constant $(K_c)$ of $2HI_{(g)} \rightleftharpoons H_{2_{(g)}} + I_{2_{(g)}}$ is $5 \times 10^{3}$. What is the equilibrium concentration of $HI$,if equilibrium concentrations of $H_{2_{(g)}}$ and $I_{2_{(g)}}$ respectively are $2.2 \times 10^{-2} \ M$ and $2.2 \times 10^{-4} \ M$?

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

The following equilibrium constants are given:
$N_{2} + 3 H_{2} \rightleftharpoons 2 NH_{3} ; K_{1}$
$N_{2} + O_{2} \rightleftharpoons 2 NO ; K_{2}$
$H_{2} + \frac{1}{2} O_{2} \rightleftharpoons H_{2} O ; K_{3}$
The equilibrium constant for the oxidation of $2 \text{ mole}$ of $NH_{3}$ to give $NO$ is

If $K_1, K_2, K_3$ are equilibrium constants for the formation of $AD, AD_2, AD_3$ respectively as follows: $A + D \rightleftharpoons AD$,$AD + D \rightleftharpoons AD_2$,$AD_2 + D \rightleftharpoons AD_3$. Then the equilibrium constant '$K$' for $A + 3D \rightleftharpoons AD_3$ is related as: