Limits of Raoult’s law:\nRaoult’s law is <em>not</em> applicable under which conditions?

Introduction / Context:
Raoult’s law is the foundation for modeling the vapor pressure of ideal solutions, but practitioners must know its limits to avoid large design errors in distillation and evaporation. Deviations are common when molecular interactions differ significantly from like–like interactions or when composition moves far from dilute or ideal ranges.

Given Data / Assumptions:

• We seek conditions where Raoult’s law fails or becomes inaccurate.
• Focus on liquid-phase nonideality due to association/dissociation and high concentrations.

Concept / Approach:
Raoult’s law assumes activity coefficients γ_i ≈ 1. Association (e.g., carboxylic acid dimerization) or dissociation (e.g., electrolytes) changes effective species counts and interactions, leading to γ_i ≠ 1. At higher concentrations, many solutions exhibit strong nonideality due to specific interactions, size disparity, or hydrogen bonding, again violating Raoult’s assumptions. In contrast, dilute solutions of non-volatile solutes used for colligative properties often approximate Raoult’s behavior for the solvent.

Step-by-Step Solution:
Identify non-ideal mechanisms: association/dissociation → non-unity activity coefficients.Recognize composition effect: concentrated solutions magnify deviations.Therefore, conditions (a) and (b) are where Raoult’s law is not applicable.

Verification / Alternative check:
Electrolyte solutions require activity coefficient models (e.g., Debye–Hückel, Pitzer). Strongly non-ideal nonelectrolytes use Margules, NRTL, or UNIQUAC—not Raoult’s law.

Why Other Options Are Wrong:
Low-concentration non-volatile solute in a similar solvent often follows Raoult’s law for the solvent; an ideal binary of similar molecules is precisely the scenario where Raoult’s law performs well.

Common Pitfalls:
Applying Raoult’s law to electrolytes or associating systems; ignoring temperature/composition dependence of γ_i.

Final Answer:
both (a) and (b)