The correct option for free expansion of an ideal gas under adiabatic condition is:

The standard enthalpy of formation of $$\mathrm{CH}_4$$, the standard enthalpy of sublimation of Carbon and the bond dissociation enthalpy of Hydrogen gas are $$-74.8,+719.6$$ and $$436 \mathrm{~kJ} / \mathrm{mol}$$ respectively. What is the bond enthalpy of $$\mathrm{C}-\mathrm{H}$$ bond in Methane?

Given: $$\Delta \mathrm{G}^0{ }_{\mathrm{f}}$$ of $$\mathrm{C}_2 \mathrm{H}_2$$ is $$2.09 \times 10^5 \mathrm{~J} / \mathrm{mol}$$ and $$\Delta \mathrm{G}_{\mathrm{f}}^0$$ of $$\mathrm{C}_6 \mathrm{H}_6$$ is $$1.24 \times 10^5 \mathrm{~J} / \mathrm{mol}$$. Calculate the equilibrium constant for the cyclic polymerisation of Ethyne to Benzene at $$27^{\circ} \mathrm{C}$$. $$(\mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1})$$

If the enthalpy of formation of a diatomic molecule $$\mathrm{AB}$$ is $$-400 \mathrm{~kJ} / \mathrm{mol}$$ and the bond dissociation energies of $$\mathrm{A}_2$$ and $$\mathrm{B}_2$$ and $$\mathrm{AB}$$ are in the ratio $$2: 1: 2$$, what is the bond dissociation enthalpy of $$\mathrm{B}_2$$ ?