In a closed flask at 600 K , one mole of $\mathrm{X}_2 \mathrm{Y}_4(\mathrm{~g})$ attains equilibrium as given below :

$$ \mathrm{X}_2 \mathrm{Y}_4(\mathrm{~g}) \rightleftharpoons 2 \mathrm{XY}_2(\mathrm{~g}) $$

At equilibrium, $75 \% \mathrm{X}_2 \mathrm{Y}_4(\mathrm{~g})$ was dissociated and the total pressure is 1 atm . The magnitude of $\Delta_{\mathrm{r}} \mathrm{G}^{\ominus}$ (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) at this temperature is $\_\_\_\_$ . (Nearest Integer)

(Given : $\mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} ; \ln 10=2.3, \log 2=0.3, \log 3=0.48, \log 5=0.69, \log 7=0.84$ )

The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$

$$ \begin{array}{|c|c|} \hline \frac{1}{\mathrm{~T}}\left(\mathrm{~K}^{-1}\right) & \log _{10} \mathrm{~K}_{\mathrm{p}} \\ \hline 0.05 & 3.5 \\ \hline 0.06 & 2.5 \\ \hline 0.07 & 1.5 \\ \hline \end{array} $$

The magnitude of $\frac{\Delta \mathrm{H}^{\circ}}{\mathrm{R}}$ calculated from the above data is $\_\_\_\_$ . (Nearest integer)

For the following reaction at $50^{\circ} \mathrm{C}$ and at 2 atm pressure,

$$ 2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \rightleftharpoons 2 \mathrm{~N}_2 \mathrm{O}_4(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) $$

$\mathrm{N}_2 \mathrm{O}_5$ is $50 \%$ dissociated.

The magnitude of standard free energy change at this temperature is $x$.

$x=$ $\_\_\_\_$ $\mathrm{J} \mathrm{mol}^{-1}$ [Nearest integer].

Given : $\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}, \log 2=0.30, \log 3=0.48, \ln 10=2.303$, ${ }^{\circ} \mathrm{C}+273=\mathrm{K}$

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

$\mathrm{X}_2(\mathrm{~g})$ 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)