$A$ mixture of $0.3 \ mol$ of $H_2$ and $0.3 \ mol$ of $I_2$ is allowed to react in a $10 \ L$ evacuated flask at $500 \ ^oC$. The reaction is $H_2 + I_2 \rightleftharpoons 2HI$,and the equilibrium constant $K_c$ is found to be $64$. The amount of unreacted $I_2$ at equilibrium is $...... \ mol$.

If $2 \ mol$ of $H_2$ and $I_2$ are taken initially in a $1 \ L$ vessel,and the equilibrium concentration of $HI$ is $2 \ mol/L$,find the $K_p$ for the reaction $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$.

For the reaction $CO_{(g)} + Cl_{2(g)} \rightleftharpoons COCl_{2(g)}$,$\frac{K_p}{K_c}$ is equal to

For the reaction $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$,$0.4 \ mol$ of $H_2$ and $I_2$ each are taken in a $2 \ L$ vessel. If $0.5 \ mol$ of $HI$ is formed at equilibrium,calculate the equilibrium constant $K_c$ and $K_p$.

For the reaction $CO_{(g)} + 1/2 O_{2(g)} \rightleftharpoons CO_{2(g)}$,the value of $K_p/K_c$ 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.