$15$ moles of $H_2$ and $5.2$ moles of $I_2$ are mixed and allowed to attain equilibrium at $500 \, ^oC$. At equilibrium,the concentration of $HI$ is found to be $10$ moles. The equilibrium constant for the formation of $HI$ is

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

From equations $1$ and $2$,
$CO_2 \rightleftharpoons CO + \frac{1}{2} O_2 \, [K_{C_1} = 9.1 \times 10^{-12} \, \text{at} \, 1000^{\circ} C] \, \text{(Eq. } i\text{)}$
$H_2O \rightleftharpoons H_2 + \frac{1}{2} O_2 \, [K_{C_2} = 7.1 \times 10^{-12} \, \text{at} \, 1000^{\circ} C] \, \text{(Eq. } ii\text{)}$
The equilibrium constant for the reaction,$CO_2 + H_2 \rightleftharpoons CO + H_2O$ at the same temperature,is

For the gaseous reactions $(I)$ and $(II)$,the equilibrium constants are $X$ and $Y$,respectively.
$I. \frac{1}{2} N_{2(g)} + O_{2(g)} \rightleftharpoons NO_{2(g)}$
$II. 2 NO_{2(g)} \rightleftharpoons N_2O_{4(g)}$
Using the above reactions,the equilibrium constant $Z$ for the reaction $(III)$ given below is:
$III. N_2O_{4(g)} \rightleftharpoons N_{2(g)} + 2 O_{2(g)}$

The equilibrium constant for the reaction $SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$ is $5 \times 10^{-2} \ atm^{-1/2}$. The equilibrium constant of the reaction $2 SO_{3(g)} \rightleftharpoons 2 SO_{2(g)} + O_{2(g)}$ would be

In the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,the equilibrium concentrations of $PCl_5$ and $PCl_3$ are $0.4 \ mol/L$ and $0.2 \ mol/L$ respectively. If the value of $K_c$ is $0.5$,what is the concentration of $Cl_2$ in $mol/L$?