For the reactions $NO_{(g)} + 1/2 O_{2(g)} \rightleftharpoons NO_{2(g)}$ and $2NO_{2(g)} \rightleftharpoons 2NO_{(g)} + O_{2(g)}$,the equilibrium constants at a given temperature are $K_1$ and $K_2$ respectively. If the value of $K_1$ is $4 \times 10^{-3}$,then the value of $K_2$ will be ....

For the reaction $2HI \rightleftharpoons H_2 + I_2$,which of the following is true?

For the reversible reaction $A + B \rightleftharpoons C + D$,the equilibrium concentrations of $C$ and $D$ are $0.8 \ mol/L$ each. If the initial concentrations of $A$ and $B$ were $1 \ mol/L$ each,calculate the equilibrium constant $K_c$.

When $3 \ mol$ of $A$ and $1 \ mol$ of $B$ are mixed in a $1 \ L$ vessel,the following reaction takes place: $A_{(g)} + B_{(g)} \rightleftharpoons 2C_{(g)}$. If $1.5 \ mol$ of $C$ are formed at equilibrium,the equilibrium constant $(K_c)$ for the reaction is:

Consider the following equilibrium,$CO_{(g)} + 2H_{2(g)} \rightleftharpoons CH_3OH_{(g)}$. $0.1 \ mol$ of $CO$ along with a catalyst is present in a $2 \ dm^3$ flask maintained at $500 \ K$. Hydrogen is introduced into the flask until the pressure is $5 \ bar$ and $0.04 \ mol$ of $CH_3OH$ is formed. The $K_{p}^0$ is $......... \times 10^{-3}$ (nearest integer). Given: $R = 0.08 \ dm^3 \ bar \ K^{-1} \ mol^{-1}$. Assume only methanol is formed as the product and the system follows ideal gas behaviour.

Equilibrium constants $K_1$ and $K_2$ for the following equilibria:
$(a)$ $NO_{(g)} + \frac{1}{2}O_{2(g)} \rightleftharpoons NO_{2(g)}$
$(b)$ $2NO_{2(g)} \rightleftharpoons 2NO_{(g)} + O_{2(g)}$
are related as: