Ideal and Non-Ideal Solution Models in Thermodynamics: From Henry’s and Raoult’s Laws to Regular Solutions

Overview

In this lecture excerpt, the instructor motivates solution modeling by deriving the ideal solution model from ideal gas mixing and then extends the discussion to non-ideal behavior. The talk emphasizes how partial molar properties combine to give the Gibbs free energy of mixing and how entropy and enthalpy contribute in the ideal case. The session then introduces deviation from ideality using activity coefficients and begins to explore two non-ideal models: the dilute solution model and the regular solution model.

• Derivation of delta G mixing for ideal solutions and its negative sign
• Introduction of partial molar properties and the role of activity coefficients
• Two non-ideal models to be covered: dilute solutions and regular solutions
• Key concepts: Henry’s law, Raoult’s law, and configurational vs non-configurational entropy

Introduction and the Ideal Solution Model

The lecture opens by outlining the plan to explore ideal and non-ideal solution models, starting with the ideal solution model. Pure A and pure B are prepared at the same temperature and pressure, then mixed. For ideal gases, the volumes merely add, and the process can be viewed as two isothermal expansions. The core result is that the change in chemical potential during mixing equals the molar Gibbs free energy change, which can be written as a sum over components of xi times the partial molar Gibbs free energy. From prior work, the log form emerges: delta mu I = RT ln(pI/pT). This is recast as the change in mu during mixing, and, via Dalton’s law, the log argument is expressed in terms of mole fractions. This gives the ideal solution model, a compact form that is extendable to real-world systems, with very few parameters—composition and temperature.

“delta G mix is negative and convex in composition” is a concise way to describe the behavior implied by the ideal solution expression, which is strictly negative for mixing and curved upward (d^2 delta G mix/dx^2 > 0 everywhere). This ensures spontaneous mixing in the ideal case, aligning with long-standing intuition about entropy-driven mixing in non-interacting molecular populations.

The session then details the properties of the ideal solution model, including the partial molar entropy of mixing, which equals -R ln xi for each component and remains positive, reflecting an entropy increase upon mixing. Entropy of mixing is positive, there is no volume of mixing (final volume is the sum of contributions from the pure components), and there are no changes in enthalpy or energy due to mixing. The model thus captures a fundamental thermodynamic picture: mixing is entropy-driven, with no enthalpic contribution in the ideal limit.

In summary, the ideal solution model provides a starting framework that is derived from ideal gas mixing yet is applicable to a broader class of real systems. It is built on few parameters—composition and temperature—and yields a stable thermodynamic description of ideal mixing.