One mole of a compound $AB$ reacts with one mole of a compound $CD$ according to the equation $AB + CD \rightleftharpoons AD + CB$. When equilibrium had been established,it was found that $\frac{3}{4} \ mol$ each of reactant $AB$ and $CD$ had been converted to $AD$ and $CB$. There is no change in volume. The equilibrium constant for the reaction is:

Write the expression for the equilibrium constant,$K_{c}$ for each of the following reactions:
$(i)$ $2 NOCl_{(g)} \longleftrightarrow 2 NO_{(g)} + Cl_{2(g)}$
$(ii)$ $2 Cu(NO_{3})_{2(s)} \longleftrightarrow 2 CuO_{(s)} + 4 NO_{2(g)} + O_{2(g)}$
$(iii)$ $CH_{3}COOC_{2}H_{5(aq)} + H_{2}O_{(l)} \longleftrightarrow CH_{3}COOH_{(aq)} + C_{2}H_{5}OH_{(aq)}$
$(iv)$ $Fe^{3+}_{(aq)} + 3 OH^{-}_{(aq)} \longleftrightarrow Fe(OH)_{3(s)}$
$(v)$ $I_{2(s)} + 5 F_{2(g)} \longleftrightarrow 2 IF_{5(g)}$

For the reaction $2\,A \rightleftharpoons B + C$, $K_c = 4 \times 10^{-3}$. At a given time, the composition of the reaction mixture is: $[A] = [B] = [C] = 2 \times 10^{-3} \ M$. Then, which of the following is correct?

How can you predict the direction of a reaction by comparing the values of the equilibrium constant $K_{c}$ and the reaction quotient $Q_{c}$?
$(i)$ Net reaction proceeds in the forward direction,
$(ii)$ Net reaction proceeds in the backward direction,
$(iii)$ No net reaction occurs.

For the reaction $CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$,which of the following expressions for the equilibrium constant $K_p$ is correct?

$A$ quantity of $PCl_5$ was heated in a $10 \ L$ vessel at $250 \ ^oC$; $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$. At equilibrium,the vessel contains $0.1 \ mol$ of $PCl_5$,$0.20 \ mol$ of $PCl_3$,and $0.2 \ mol$ of $Cl_2$. The equilibrium constant $(K_c)$ of the reaction is: