The process of a solid dissolving in a liquid to form a solution is governed by the solubility limit, which is the maximum amount of the solid substance, or solute, that can be dissolved in a specific volume of the liquid or solvent. As the solute dissolves, it reaches a point where no more solute can be dissolved at a given temperature - this is known as the saturation point. However, if further solute is added and it manages to dissolve, the solution becomes supersaturated. Supersaturated solutions are unstable and tend to form when a solution is heated to temporarily dissolve an additional solute. Then, perturbation of the solution can cause rapid crystallization of the excess solute as the solution cools.
The concept of chemical potential also comes into play here, with the principle being that in a solution at equilibrium, the chemical potential of the undissolved solute equals that of the dissolved solute.
The mole fraction, which is the ratio of the number of moles of the solute to the total number of moles of all components in the solution, is used to express the concentration of the dissolved solute. Mathematical equations are used to express the mole fraction of the dissolved solute in the solution. This equation can be further refined by replacing the chemical potential difference between the pure solute in its solid and liquid phases with the negative Gibbs energy of fusion, thereby expressing the mole fraction in terms of thermodynamic parameters. Finally, assuming the minimal impact of temperature on enthalpy and entropy simplifies the equation for calculating solid solubilities in solutions. Enthalpy and entropy are thermodynamic properties that significantly influence how much solute can dissolve in a solvent.
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.
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