$8 \, \text{mol}$ of $AB_3$ is added to a $1.0 \, \text{dm}^3$ container. If it dissociates according to the reaction $2AB_{3(g)} \rightleftharpoons A_{2(g)} + 3B_{2(g)}$ and $2 \, \text{mol}$ of $A_2$ are present at equilibrium,what is the equilibrium constant $(K_c)$ for this reaction?

The equilibrium constant for the reaction $SO_{3(g)} \rightleftharpoons SO_{2(g)} + 1/2 O_{2(g)}$ is $4.9 \times 10^{-2}$. Find the equilibrium constant for the reaction $2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$.

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 $2.2 \times 10^{-4} \ M$?

For the reaction ${N_2}_{(g)} + 2{O_2}_{(g)} \rightleftharpoons 2{NO_2}_{(g)}$,the equilibrium constant is $100$. Find the equilibrium constant for the following reactions:
$(1)$ $2{NO_2}_{(g)} \rightleftharpoons {N_2}_{(g)} + 2{O_2}_{(g)}$
$(2)$ ${NO_2}_{(g)} \rightleftharpoons \frac{1}{2}{N_2}_{(g)} + {O_2}_{(g)}$

Consider the imaginary equilibrium $4A + 5B \rightleftharpoons 4X + 6Y$. The equilibrium constant $K_c$ has the unit:

For the reaction $2NO_{2(g)} \rightleftharpoons 2NO_{(g)} + O_{2(g)}$,$K_c = 1.8 \times 10^{-6}$ at $185\,^{\circ}C$. At $185\,^{\circ}C$,the value of $K_c$ for the reaction $NO_{(g)} + \frac{1}{2}O_{2(g)} \rightleftharpoons NO_{2(g)}$ is