Entropy and Solvation

Entropy, S, reflects the probability of achieving a given state in a system. In an isolated system, a process occurs spontaneously when it causes an increase in total entropy.

The change in entropy resulting from solution formation called the entropy of mixing, or ΔS_mixing, is independent of any intermolecular interactions.

During solution formation, the solute and the solvent undergo mixing, and the solute disperses into the solvent. The solvent molecules that directly interact with the solute molecules are collectively called the solvent shell or solvent cage.

Due to the formation of solvent shells, the solvent has fewer energetically equivalent configurations than the solute, and the solute gains entropy at the expense of energy from the solvent.

When a hydrocarbon is dissolved in water, the water molecules at the water–hydrocarbon interface rearrange to maximize the number of hydrogen bonds they make with one another. Some solvent water is transformed into the water of the solvent shells resulting in a solvent cage around each hydrocarbon molecule.

The water in the solvent shell has a more ordered arrangement and reduced motional freedom compared to the solvent water. This lowers the entropy of the water in the solvent shell compared to that of the solvent water. Thus, dissolution is accompanied by a reduction in entropy.

Alternatively, if the hydrocarbon molecules clump together, the low entropy solvation water is released to become higher entropy solvent water, thus increasing the entropy.

This entropy-driven separation of hydrocarbon and water molecules is referred to as the hydrophobic effect. The clumping of hydrocarbons is favored because of the associated increase in entropy, resulting in separate hydrocarbon and water layers.