The equilibrium constant for decomposition of $\text{H}_2\text{O(g)}$

$ \text{H}_2\text{O(g)} \rightleftharpoons \text{H}_2\text{(g)} + \frac{1}{2}\text{O}_2\text{(g)} \quad (\Delta G^\circ = 92.34 \, \text{kJ mol}^{-1}) $

is $8.0 \times 10^{-3}$ at 2300 K and total pressure at equilibrium is 1 bar. Under this condition, the degree of dissociation ($\alpha$) of water is _________ $\times 10^{-2}$ (nearest integer value).

[Assume $\alpha$ is negligible with respect to 1]

Consider the following equilibrium,

$$\mathrm{CO}(\mathrm{~g})+2 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_3 \mathrm{OH}(\mathrm{~g})$$

0.1 mol of CO along with a catalyst is present in a $2 \mathrm{dm}^3$ flask maintained at 500 K . Hydrogen is introduced into the flask until the pressure is 5 bar and 0.04 mol of $\mathrm{CH}_3 \mathrm{OH}$ is formed. The $K_p^\theta$ is __________ $\times 10^{-3}$ (nearest integer).

Given : $\mathrm{R}=0.08 \mathrm{~dm}^3$ bar $\mathrm{K}^{-1} \mathrm{~mol}^{-1}$

Assume only methanol is formed as the product and the system follows ideal gas behaviour.

$37.8 \mathrm{~g} \mathrm{~N}_2 \mathrm{O}_5$ was taken in a 1 L reaction vessel and allowed to undergo the following reaction at 500 K

$$2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightleftharpoons 2 \mathrm{~N}_2 \mathrm{O}_{4(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})}$$

The total pressure at equilibrium was found to be 18.65 bar.

Then, $\mathrm{Kp}=$ _________ $\times 10^{-2}$ [nearest integer]

Assume $\mathrm{N}_2 \mathrm{O}_5$ to behave ideally under these conditions.

Given: $\mathrm{R}=0.082$ bar $\mathrm{L} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$

The following concentrations were observed at $$500 \mathrm{~K}$$ for the formation of $$\mathrm{NH}_3$$ from $$\mathrm{N}_2$$ and $$\mathrm{H}_2$$. At equilibrium ; $$\left[\mathrm{N}_2\right]=2 \times 10^{-2} \mathrm{M},\left[\mathrm{H}_2\right]=3 \times 10^{-2} \mathrm{M}$$ and $$\left[\mathrm{NH}_3\right]=1.5 \times 10^{-2} \mathrm{M}$$. Equilibrium constant for the reaction is ________.