In solution thermodynamics, which relation is obeyed by an ideal (Raoultian) liquid solution over the entire composition range?

Introduction / Context:
An ideal liquid solution is a cornerstone model in chemical engineering thermodynamics. It assumes that intermolecular interactions between unlike molecules are the same as those between like molecules, so escaping tendencies scale directly with composition. Knowing which law characterizes such solutions helps in vapor–liquid equilibrium (VLE) calculations, distillation design, and solvent selection.

Given Data / Assumptions:

• Binary or multicomponent liquid mixture with chemically similar components.
• Temperature and pressure are such that components behave ideally in the liquid phase.
• Vapor phase is near ideal so the basic form of the law applies.

Concept / Approach:
For an ideal liquid solution, the partial pressure of each component i is p_i = x_i * P_i^sat at the system temperature, where x_i is the liquid mole fraction and P_i^sat is the pure-component saturation pressure. This is Raoult's law. Other listed relations have different scopes: Boyle's law is for gases (P ∝ 1/V at constant T), Amagat's law concerns additive volumes of gas mixtures, and Trouton's rule gives approximate latent heat–boiling point trends for many liquids. Henry's law applies for dilute solutes in non-ideal (or solvent-dominated) systems, not for ideal solutions over the full composition range.

Step-by-Step Solution:
Identify the definition of an ideal liquid solution: activity coefficients ≈ 1 for all components.Match to the constitutive relation: p_i = x_i * P_i^sat → Raoult's law.Conclude that Raoult's law is the appropriate answer.

Verification / Alternative check:
Experimental VLE data of near-ideal pairs (e.g., benzene–toluene) closely follow Raoult's predictions, validating the model under similarity in molecular interactions.

Why Other Options Are Wrong:
Boyle's law and Amagat's law apply to gases, not liquids; Trouton's rule is an empirical boiling/latent heat correlation; Henry's law handles dilute, not full-range ideality.

Common Pitfalls:
Confusing Raoult's and Henry's domains; assuming ideality for highly dissimilar molecules.

Final Answer:
Raoult's law