2.4: Entropy and Solvation

The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ ≥ 15); an apolar solvent is one with a low dielectric constant. The dielectric constant is defined by the electrostatic law, which gives the interaction energy E between two ions with respective charges q₁ and q₂ separated by a distance r. A polar solvent effectively separates or shields ions from one another. Therefore, the tendency of oppositely charged ions to associate is less in a polar solvent than it is in an apolar solvent.

In the case of a hydrocarbon and water, one is polar (water), and the other is apolar (hydrocarbon). On the introduction of hydrocarbon molecules in water, the water molecules along the hydrocarbon–water interface form a shell-like arrangement called the solvent shell around each hydrocarbon molecule. The water within these shell-like arrangements is more ordered and has lower entropy compared to the water in the solvent. Since any system in nature tries to achieve a state of maximum entropy, the system tries to minimize the interactions between hydrocarbon and water, resulting in the formation of separate hydrocarbon and water layers. This entropy-driven separation between hydrocarbon and water is termed the hydrophobic effect.

Since entropy is the driving factor of the insolubility of hydrocarbons in water, the system's temperature also influences the process, for example, in gas hydrates or clathrates, one of the largest reserves of natural gas. Gas hydrates are crystalline solid forms of water and gas. They form when methane and water freeze under high pressures and low temperatures. The hydrocarbon molecules are enclosed within stable cages of ice, which has relatively large open spaces within its crystal structure. The hydrocarbon molecules fit within these holes, making it possible to predict the maximum size of the hydrocarbon molecules that can form clathrates.

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.