$$ \mathrm{X}_2(\mathrm{~g})+\mathrm{Y}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{Z}(\mathrm{~g}) $$

$\mathrm{X}_2(\mathrm{~g})$ and $\mathrm{Y}_2(\mathrm{~g})$ are added to a 1 L flask and it is found that the system attains the above equilibrium at $\mathrm{T}(\mathrm{K})$ with the number of moles of $\mathrm{X}_2(\mathrm{~g}), \mathrm{Y}_2(\mathrm{~g})$ and $\mathrm{Z}(\mathrm{g})$ being 3,3 and 9 mol respectively (equilibrium moles). Under this condition of equilibrium, 10 mol of $\mathrm{Z}(\mathrm{g})$ is added to the flask and the temperature is maintained at $\mathrm{T}(\mathrm{K})$. Then the number of moles of $\mathrm{Z}(\mathrm{g})$ in the flask when the new equilibrium is established is $\_\_\_\_$ . (Nearest integer)

For the following gas phase equilibrium reaction at constant temperature,

$$ \mathrm{NH}_3(\mathrm{~g}) \rightleftharpoons 1 / 2 \mathrm{~N}_2(\mathrm{~g})+3 / 2 \mathrm{H}_2(\mathrm{~g}) $$

if the total pressure is $\sqrt{3} \mathrm{~atm}$ and the pressure equilibrium constant $\left(K_p\right)$ is 9 atm , then the degree of dissociation is given as $\left(x \times 10^{-2}\right)^{-1 / 2}$. The value of $x$ is $\_\_\_\_$ . (nearest integer)

Dissociation of a gas $\mathrm{A}_2$ takes place according to the following chemical reaction. At equilibrium, the total pressure is 1 bar at 300 K .

$$ \mathrm{A}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{~A}(\mathrm{~g}) $$

The standard Gibbs energy of formation of the involved substances has been provided below:

$$ \begin{array}{|c|c|} \hline \text { Substance } & \Delta \mathrm{G}_{\mathrm{f}}^{\circ} / \mathrm{kJ} \mathrm{~mol}^{-1} \\ \hline \hline \mathrm{~A}_2 & -100.00 \\ \hline \mathrm{~A} & -50.832 \\ \hline \end{array} $$

The degree of dissociation of $\mathrm{A}_2(\mathrm{~g})$ is given by $\left(x \times 10^{-2}\right)^{1 / 2}$ where $x=$

$\_\_\_\_$ . (Nearest integer).

[ Given : $\mathrm{R}=8 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}, \log 2=0.3010, \log 3=0.48$ ]

Assume degree of dissociation is not negligible.

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]