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

At $400 \ K$ in a closed vessel,the reaction $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$ takes place. At equilibrium,the concentration of $H_2$ is $0.6 \ mol \ L^{-1}$,the concentration of $I_2$ is $0.8 \ mol \ L^{-1}$,and the concentration of $HI$ is $0.14 \ mol \ L^{-1}$. Calculate the equilibrium constant $(K_c)$.

If the equilibrium constant for the reaction $2AB \rightleftharpoons A_2 + B_2$ is $49$,what is the equilibrium constant for $AB \rightleftharpoons \frac{1}{2}A_2 + \frac{1}{2}B_2$?

At $780 \ K$ and $10 \ atm$ pressure,the equilibrium constant for the reaction $2 \ A_{(g)} \rightleftharpoons B_{(g)} + C_{(g)}$ is $3.52$. At the same temperature and $7.04 \ atm$ pressure,the equilibrium constant for the same reaction is:

The equilibrium constants for some reactions are given below:
$(1)$ $x \rightleftharpoons y ; K = 10^{-1}$
$(2)$ $y \rightleftharpoons z ; K = 2 \times 10^{-2}$
$(3)$ $p \rightleftharpoons Q ; K = 3 \times 10^{-4}$
$(4)$ $R \rightleftharpoons S ; K = 2 \times 10^{-3}$
The initial concentrations of reactants are taken to be the same for each reaction. Which of the above reactions indicate that the reaction mixture contains high concentrations of reactants and products respectively?

At $T \ K$,the equilibrium constant for the reaction $a A_{(g)} \rightleftharpoons b B_{(g)}$ is $K_c$. If the reaction takes place in the following form $2a A_{(g)} \rightleftharpoons 2b B_{(g)}$,its equilibrium constant is $K_c^{\prime}$. The correct relationship between $K_c$ and $K_c^{\prime}$ is