Thermodynamics of solutions – scope of the Van Laar equation In phase-equilibrium calculations, the Van Laar equation is an empirical model for activity coefficients. For which type of liquid-phase mixtures is it primarily formulated and applied?

Introduction / Context:
The Van Laar equation is a classic excess-Gibbs-energy model that correlates non-ideality in liquid mixtures. It is frequently taught alongside the Margules and Wilson equations in chemical engineering thermodynamics for predicting activity coefficients required in vapor–liquid equilibrium design and extraction calculations.

Given Data / Assumptions:

• The model uses two adjustable interaction parameters.
• It targets deviations from Raoult's law in liquid mixtures.
• Focus is on routine engineering use rather than ab initio prediction.

Concept / Approach:
Van Laar's two-parameter form is derived for two-component (binary) mixtures. The activity coefficients gamma_1 and gamma_2 are expressed as simple functions of composition and two constants fitted to binary data. While extensions exist, the standard form is not directly parameterized for ternary systems without further assumptions or combination rules. Azeotropes may be described if they occur in the binary being modeled, but the equation is not limited to azeotropic compositions; it covers the entire binary composition range when properly regressed.

Step-by-Step Solution:

Verification / Alternative check:
Standard thermodynamics texts tabulate Van Laar parameters for binary pairs (e.g., ethanol–water, acetone–chloroform), confirming its binary focus.

Why Other Options Are Wrong:

• Ternary solutions: Not the native scope without extra mixing rules.
• Azeotropic mixture only: The model is not restricted to azeotropes.
• None of these: Incorrect because a correct choice exists.

Common Pitfalls:
Confusing the Van Laar model with multicomponent-capable models like Wilson or NRTL; assuming a binary model automatically generalizes without re-derivation.

Final Answer:
binary solutions