Colligative properties check:\r Which of the following is <em>not</em> a colligative property of solutions?

Introduction:
Colligative properties depend only on the number of solute particles in a solution, not their identity (within ideal approximations). Recognizing these properties is key in molecular weight determination, antifreeze design, and desalination studies.

Given Data / Assumptions:

• Ideal or dilute solutions are assumed for the concept.
• Solute is nonvolatile and nonassociating unless noted.
• We identify which listed property is not colligative.

Concept / Approach:
The standard colligative properties are: lowering of vapor pressure, elevation of boiling point, depression of freezing point, and osmotic pressure. All four arise from the same thermodynamic basis—dilution of solvent chemical potential by solute particles—and scale with molality or molarity through proportionality constants (Kb, Kf, or van ’t Hoff factor for electrolytes). Therefore, options (a), (b), (c), and (e) are all genuine colligative properties. As the question asks for what is not a colligative property, the correct response is “none of these.”

Step-by-Step Solution:
List canonical colligative properties.Match each option to the list and confirm inclusion.Conclude that all provided are colligative; hence “none of these.”

Verification / Alternative check:
Textbook equations: ΔTb = Kb * m, ΔTf = Kf * m, π = i * M * R * T, and Raoult’s law for vapor pressure lowering all show dependency only on particle number (with i for electrolytes).

Why Other Options Are Wrong:

• Each listed property (a), (b), (c), (e) is indeed colligative and thus not the correct “not” choice.

Common Pitfalls:
Confusing density or refractive index (not strictly colligative) with the classic four; these are not listed here.

Final Answer:
none of these.