Consider the following reaction :-

$$2 \mathrm{H}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{H}_2 \mathrm{O}(\mathrm{g}) \Delta_{\mathrm{r}} \mathrm{H}^{\circ}=-483.64 \mathrm{~kJ} \text {. }$$

What is the enthalpy change for decomposition of one mole of water? (Choose the right option).

The equilibrium concentrations of the species in the reaction $$\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}$$ are $$2,3,10$$ and $$6 \mathrm{~mol}$$ $$\mathrm{L}^{-1}$$, respectively at $$300 \mathrm{~K} . \Delta \mathrm{G}^{0}$$ for the reaction is $$(\mathrm{R}=2 \mathrm{cal} / \mathrm{mol} ~\mathrm{K})$$

Which amongst the following options is the correct relation between change in enthalpy and change in internal energy?

One mole of an ideal gas at 300 K is expanded isothermally from 1 L to 10 L volume. $$\Delta$$U for this process is :

(Use R = 8.314 J k^$$-$$1 mol^$$-$$1)