For the reaction $A_{(g)} + B_{(g)} \rightleftharpoons 2 C_{(g)}$; $K_{c} = 4$. If equilibrium concentration of $A_{(g)}$ and $B_{(g)}$ are found to be $0.1 \ M$ and $0.4 \ M$ respectively. Determine equilibrium concentration of $C_{(g)}$. (in $M$)

For the reaction $N_2O_2 \rightleftharpoons 2NO$,the value of the concentration equilibrium constant is .......

For the reaction $CO_{(g)} + 2H_{2_{(g)}} \rightleftharpoons CH_3OH_{(g)}$,the equilibrium constant $K_c$ is $0.5$. If the concentrations of $CO$ and $H_2$ at equilibrium are $0.18 \ M$ and $0.22 \ M$ respectively,what is the concentration of $CH_3OH$?

The equilibrium of formation of phosgene is represented as:
$CO_{(g)} + Cl_{2(g)} \rightleftharpoons COCl_{2(g)}$
The reaction is carried out in a $500 \ mL$ flask. At equilibrium,$0.3 \ mol$ of phosgene,$0.1 \ mol$ of $CO,$ and $0.1 \ mol$ of $Cl_2$ are present. The equilibrium constant $(K_c)$ of the reaction is:

For the reaction $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$,the equilibrium constant $K_p$ is $16$. If the volume of the container is reduced to $\frac{1}{2}$ of its original value,what will be the value of $K_p$ at the same temperature?

Write the applications of equilibrium constants.