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

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 $2\,A \rightleftharpoons B + C$, $K_c = 4 \times 10^{-3}$. 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?

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 $M$)

In a chemical equilibrium $A + B \rightleftharpoons C + D$,when $1 \, mol$ each of two reactants are mixed,$0.5 \, mol$ each of the products are formed. The equilibrium constant is

$K_{a_1}, K_{a_2}$ and $K_{a_3}$ are the respective ionization constants for the following reactions $(a), (b),$ and $(c)$.
$(a)$ $H_2C_2O_4 \rightleftharpoons H^{+} + HC_2O_4^-$
$(b)$ $HC_2O_4^- \rightleftharpoons H^{+} + C_2O_4^{2-}$
$(c)$ $H_2C_2O_4 \rightleftharpoons 2H^{+} + C_2O_4^{2-}$
The relationship between $K_{a_1}, K_{a_2}$ and $K_{a_3}$ is given as