The work done during reversible isothermal expansion of one mole of hydrogen gas at $$25^{\circ} \mathrm{C}$$ from pressure of 20 atmosphere to 10 atmosphere is (Given $$\mathrm{R}=2.0 \mathrm{~cal} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$)

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?