11.3 Solubility

Factors Affecting Solubility

Solubility describes how much of a substance (the solute) can dissolve in a given amount of solvent at specific conditions. Two major factors control solubility: temperature and pressure. Knowing how each one works lets you predict whether more or less solute will dissolve when conditions change.

Temperature and Pressure Effects on Solubility

Temperature effects depend on whether the solute is a solid or a gas:

• Solids in liquids — Solubility usually increases with temperature. Think of stirring sugar into hot tea versus iced tea. Dissolving most solids is an endothermic process (it absorbs heat), so adding heat shifts the process forward and lets more solute dissolve.
• Gases in liquids — Solubility decreases with temperature. A warm soda goes flat faster than a cold one because the dissolved $CO_2$ escapes more readily at higher temperatures. Dissolving a gas is typically exothermic (it releases heat), so raising the temperature works against that process.

Pressure effects are mostly relevant for gases:

• Solids and liquids — Pressure has very little effect on their solubility because these phases are nearly incompressible.
• Gases in liquids — Solubility increases with pressure. The higher the gas pressure above the liquid, the more gas molecules get pushed into solution. This relationship is described quantitatively by Henry's law.

Henry's Law for Gas Solubility

Henry's law gives you a simple equation to calculate how much gas dissolves in a liquid:

$C = k_H \times P$

• $C$ = concentration (solubility) of the dissolved gas, in mol/L
• $k_H$ = Henry's law constant, in mol/(L·atm), specific to a particular gas-liquid pair at a given temperature
• $P$ = partial pressure of the gas above the solution, in atm

The constant $k_H$ captures how easily a particular gas dissolves in a particular liquid. A larger $k_H$ means the gas is more soluble at the same pressure.

Using Henry's law step-by-step:

1. Look up (or be given) the Henry's law constant $k_H$ for the specific gas-liquid pair at the temperature you're working with.
2. Identify the partial pressure $P$ of the gas above the solution.
3. Multiply: $C = k_H \times P$ to get the gas solubility in mol/L.

For example, if $k_H$ for $O_2$ in water at 25 °C is $1.3 \times 10^{-3}$ mol/(L·atm) and the partial pressure of $O_2$ is 1.0 atm, then $C = 1.3 \times 10^{-3} \times 1.0 = 1.3 \times 10^{-3}$ mol/L.

Liquid-Liquid Solubility

Spectrum of Liquid-Liquid Solubility

Miscibility is the ability of two liquids to mix and form a homogeneous solution. Not all liquid pairs behave the same way, and they fall along a spectrum:

• Fully miscible — The two liquids dissolve in each other in any proportion, forming a single phase. Ethanol and water are a classic example; you can mix them in any ratio and still get one uniform layer.
• Partially miscible — The liquids dissolve in each other only to a limited extent. Beyond that limit, two separate layers form, each containing some of both liquids. Diethyl ether and water behave this way.
• Immiscible — The liquids essentially do not mix at all, forming two distinct layers. Oil and water are the everyday example; hexane and water behave similarly.

The guiding principle here is "like dissolves like." Factors that determine where a pair falls on this spectrum include:

• Polarity — Liquids with similar polarity tend to be miscible. Two polar liquids mix well; two nonpolar liquids mix well. A polar and a nonpolar liquid usually don't.
• Hydrogen bonding — Liquids that can form hydrogen bonds with each other (like ethanol and water) are more likely to be miscible.
• Temperature — Raising the temperature can sometimes increase miscibility for partially miscible pairs.

Solubility Dynamics

These three terms describe what happens as solute enters or leaves a solution:

• Dissolution is the process of a solute dissolving into a solvent. At the molecular level, solvent molecules surround and pull apart solute particles.
• Saturation is the point where a solution holds the maximum amount of dissolved solute at a given temperature and pressure. At saturation, the rate of dissolution equals the rate of solute coming back out of solution (a dynamic equilibrium).
• Precipitation occurs when a solution becomes supersaturated, meaning it temporarily contains more dissolved solute than the saturation limit. The excess solute comes out as a solid. You can trigger this by cooling a hot, saturated solution or by adding a seed crystal.