The enthalpy change for the adsorption process and micelle formation respectively are

We need to determine the enthalpy changes for adsorption and micelle formation.

Enthalpy of adsorption ($$\Delta H_{ads}$$).

Adsorption is generally an exothermic process because when molecules adhere to a surface, bonds are formed, releasing energy. Both physical and chemical adsorption are exothermic.

Therefore, $$\Delta H_{ads} < 0$$.

Enthalpy of micelle formation ($$\Delta H_{mic}$$).

Micelle formation is primarily an entropy-driven process. When surfactant molecules form micelles, the ordered water molecules around the hydrophobic tails are released, increasing entropy significantly. The enthalpy change for micelle formation is typically slightly positive (endothermic) or near zero, but the large positive $$T\Delta S$$ term makes $$\Delta G$$ negative.

Therefore, $$\Delta H_{mic} > 0$$.

Match with options.

$$\Delta H_{ads} < 0$$ and $$\Delta H_{mic} > 0$$ corresponds to Option C.

The correct answer is Option C: $$\Delta H_{ads} < 0$$ and $$\Delta H_{mic} > 0$$.