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)

A vessel contains 3.2 g of dioxygen gas at STP (273.15 K and 1 atm pressure). The gas is now transferred to another vessel at constant temperature, where pressure becomes one third of the original pressure. The volume of new vessel in L is : (Given : molar volume at STP is 22.4 L)