At a certain temperature,$2HI \rightleftharpoons H_2 + I_2$. If only $50\%$ of $HI$ is dissociated at equilibrium,the equilibrium constant $(K_c)$ is:

At $T(K)$,the $K_c$ value of the reaction $AO_{2(g)} + BO_{2(g)} \rightleftharpoons AO_{3(g)} + BO_{(g)}$ is $16$. In a closed $1 \ L$ flask,one mole each of $AO_2, BO_2, AO_3$ and $BO$ are taken and heated to $T(K)$. Identify the correct statements about this equilibrium.
$I)$ Total number of moles at equilibrium is $4$
$II)$ At equilibrium,the ratio of moles of $AO_2$ and $AO_3$ is $1:4$
$III)$ Total number of moles of $AO_2$ and $BO_2$ at equilibrium is $0.8$

For a reaction $X + Y \rightleftharpoons 2 Z$,$1.0 \ mol$ of $X$,$1.5 \ mol$ of $Y$ and $0.5 \ mol$ of $Z$ were taken in a $1 \ L$ vessel and allowed to react. At equilibrium,the concentration of $Z$ was $1.0 \ mol \ L^{-1}$. The equilibrium constant of the reaction is $-\frac{x}{15}$. The value of $x$ is........

One mole each of $He$ and $A(g)$ are taken in a $10 \text{ L}$ closed flask and heated to $400 \text{ K}$ to establish the following equilibrium: $A(g) \rightleftharpoons B(g)$. $K_{c}$ for this reaction at $400 \text{ K}$ is $4.0$. The partial pressures (in $\text{atm}$) of $He$ and $B(g)$ are respectively (at equilibrium) (Assume $He$,$A(g)$ and $B(g)$ behave as ideal gases) (Given: $R = 0.082 \text{ L atm K}^{-1} \text{ mol}^{-1}$)

For the gas phase reaction; $C_2H_{4(g)} + H_{2(g)} \rightleftharpoons C_2H_{6(g)}$,$\Delta H = -32.7 \ kcal$ carried out in a vessel,the equilibrium concentration of $C_2H_4$ can be increased by:

For the reaction $P_{(g)} + 3Q_{(g)} \rightleftharpoons 4R_{(g)}$,the initial concentrations of $P$ and $Q$ are equal. If the equilibrium concentrations of $P$ and $R$ are equal,then the equilibrium constant $K_c$ for the reaction will be .....