Conditions for ideal (Raoultian) solutions: when do liquid mixtures behave ideally?\nSelect the statement that correctly identifies the zero-change criteria required for an ideal solution.

Introduction / Context:
In solution thermodynamics, an ideal liquid solution (often called Raoultian) is a reference model used to estimate vapor–liquid equilibrium and colligative properties. Knowing the defining criteria of ideality helps engineers decide when Raoult's law can be applied without activity coefficients.

Given Data / Assumptions:

• We are dealing with liquid mixtures of chemically similar components.
• Question asks for conditions that characterize ideal solutions.
• No phase change other than mixing is considered.

Concept / Approach:
For an ideal solution, intermolecular interactions between unlike molecules are effectively the same as those between like molecules. As a result, mixing neither releases nor absorbs heat and does not cause volume contraction or expansion. Formally, ΔH_mix = 0 and ΔV_mix = 0, and activity coefficients γ_i ≈ 1 across the full composition range.

Step-by-Step Solution:
Identify the hallmark of ideality: no energetic or volumetric driving force upon mixing.Translate to thermodynamic statements: ΔH_mix = 0 and ΔV_mix = 0.Select the option that includes both conditions.

Verification / Alternative check:
Classic near-ideal pairs (e.g., benzene–toluene) show negligible heats and volume changes on mixing, supporting the criteria experimentally.

Why Other Options Are Wrong:
Only heat or only volume being zero is insufficient; claiming neither needs to be zero contradicts the definition; activity coefficients greater than one indicate positive deviation, not ideality.

Common Pitfalls:
Confusing “ideal gas” with “ideal solution”; assuming only ΔH_mix matters but not ΔV_mix.

Final Answer:
both heat of mixing and volume change on mixing equal zero