Liquid–Solid Solutions

In a liquid-solid solution, a solid dissolves until it reaches its solubility limit - the maximum amount of solid that can dissolve in a given liquid volume.

When this limit is reached, the solution is said to be saturated. Further dissolution of the solute makes the solution supersaturated.

For an ideal liquid-solid solution at equilibrium, the chemical potential of the undissolved and dissolved solute are equal.

Considering dissolved solute as a component of a liquid-liquid solution, its chemical potential can be expressed using its mole fraction.

Combining these equations and rearranging the expression gives the mole fraction of the dissolved solute.

Replacing the chemical potential difference with the negative Gibbs energy of fusion and incorporating enthalpy and entropy terms expresses the mole fraction in thermodynamic parameters.

Including a term for the solute’s melting point links dissolution to melting, since solutes with higher melting points are less soluble. So, introducing the solute’s melting point separates enthalpic and entropic contributions at different temperatures.

Assuming minimal temperature dependence of enthalpy and entropy leads to the final equation for calculating solid solubility in solutions.