For the equilibrium reaction $A + B \rightleftharpoons C + D$,if we start with equal concentrations of $A$ and $B$,at equilibrium,the concentration of $C$ is $2$ times that of $A$. Find the value of $K_c$.

Which of the following is true for the reaction $H_2O_{(l)} \rightleftharpoons H_2O_{(g)}$ at $100 \ ^\circ C$ and $1 \ \text{atm}$ pressure?

Which of the following is correct for the equilibrium shown below?
$2CH_3COOH \rightleftharpoons (CH_3COOH)_2$
(Equilibrium constants for the reaction in water and benzene are $K_{Water}$ and $K_{Benzene}$ respectively.)

For the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,at equilibrium,the mole fraction of $PCl_5$ is $0.4$ and the mole fraction of $Cl_2$ is $0.3$. What will be the mole fraction of $PCl_3$?

At $550 \ K$,the $K_c$ for the following reaction is $10^4 \ mol^{-1} \ L$: $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$. At equilibrium,it was observed that $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$. What is the value of $[Z]$ (in $mol \ L^{-1}$) at equilibrium?

Solid $KClO_3$ is taken in a container maintained at a constant pressure of $1 \ atm$. Upon heating,the following equilibrium is obtained:
$2KClO_{3(s)} \rightleftharpoons 2KCl_{(s)} + 3O_{2(g)}$
If $\Delta H^o = 25 \ kcal/mol$ and $\Delta S^o = 50 \ cal/K$,at what temperature will equilibrium be established in the container? (Ignore variation of $\Delta H^o$ and $\Delta S^o$ with temperature.) $......K$