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Thermodynamic Properties of Ideal Solutions

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In an ideal solution, each component’s standard state is its pure form at the same temperature and pressure, which serves as the reference for measuring changes in its thermodynamic properties upon mixing.

The chemical potentials of these components in the ideal solution can be compared to those of the pure substances in their standard states.

Mixing quantities of the ideal solution refers to the thermodynamic properties, like change in Gibbs free energy, volume, and enthalpy during mixing. It describes the changes that occur when two or more substances are mixed to form a solution.

As a measurable thermodynamic property, vapor pressure connects mixing behavior to phase equilibrium. It is the pressure exerted by the vapor phase of a substance when in equilibrium with its liquid phase.

In an ideal solution, vapor pressure is the sum of the partial pressures of the components in the solution.

Further, Raoult’s law states that the partial pressure of a component in the vapor phase is equal to the product of its mole fraction in the liquid phase and the vapor pressure of the pure component at the same temperature

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For an ideal liquid solution, the standard state of each component is defined as the pure liquid at the temperature and pressure of the solution. Similarly, for solid solutions, the standard state is the pure solid. The chemical potentials of the components in the ideal solution are compared to the chemical potentials of the pure substances in their standard states. These standard states provide a reference point for calculating the thermodynamic properties of ideal solutions.

For ideal solutions, the change in enthalpy of mixing (ΔH_mix) and change in volume of mixing (ΔV_mix) are zero, while the change in Gibbs free energy of mixing (ΔG_mix) is negative due to the increase in entropy upon mixing, reflecting that ideal solutions involve molecules of similar size and intermolecular interactions, with no enthalpic or volumetric change but a favorable entropy change upon mixing.

Calculating mixing quantities helps to understand the thermodynamic properties of ideal solutions and how they change when different substances are mixed together.

If the pressure applied to an ideal liquid solution is reduced until it vaporizes, it becomes a two-phase system in equilibrium with its vapor. Then the vapor pressure (p) of an ideal solution is the sum of the partial pressures (p_n) of the components in the solution (p = p₁ + p₂.. +... + p_n).

In an ideal solution, the chemical potential of the component equals the chemical potential of its vapor phase at equilibrium.

Raoult's law is a relationship that describes the vapor pressure of an ideal solution. According to Raoult's law, the partial pressure of a component in the vapor phase of an ideal solution is equal to the product of its mole fraction in the solution and the vapor pressure of the pure component.

p_i = x_i^l p*_i

where p_i is the partial pressure of substance i in the vapor in equilibrium with an ideal liquid solution at temperature T, x_i^l is the mole fraction of i in the ideal solution, and p*_i is the vapor pressure of pure liquid i at the same temperature T as the solution.

This law assumes ideal behavior of both the solution and the vapor phase, and it holds true for ideal solutions.

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Ideal Solutions

Thermodynamic Properties

Chemical Potential

Enthalpy of Mixing

Gibbs Free Energy

Entropy of Mixing

Pure Substances