The molecular weights determined by using colligative properties of substances which associate or dissociate will be abnormal and are called abnormal molecular weights. Ionic substances like NaCl, BaCl₂, AlCl₃, etc., ionize in solutions. Their colligative properties are high due to increase in number of particles when compared with solutions of non-electrolytes like glucose having equal molecular mass. When molecules of substance like acetic acid in benzene associate as dimers, trimers or polymers, the number of particles decreases and their colligative properties also decrease. The ratio of the observed colligative property and calculated colligative property is called Van’t Hoff factor i.

\[\text{i = }\frac{\text{observed colligative property}}{\text{calculated colligative property}}\]

\[\text{or, i = }\frac{\text{calculated molecular mass}}{\text{observed molecular mass}}\]

The value of Van’t Hoff factor i is greater than 1 for ionic substances while it has lower value than 1 for associated substances.

\[\frac{\text{calculated molecular mass}}{\text{observed molecular mass}} = \frac{\text{Normal number of solute particles}}{\text{Number of solute particles after dissociation or association}}\]

Which of the following will have the highest freezing point at one atmosphere?

0.1 M sugar solution

The correct answer is option 2. 0.1 M sugar solution.

The freezing point of a solution is determined by the molality of the solution. Molality is the number of moles of solute per kilogram of solvent. The higher the molality, the lower the freezing point.

In this case, all of the solutions have the same molality of 0.1 M. However, sugar does not dissociate in solution, so it will have a lower molality than the other solutions, which dissociate into ions. This means that the sugar solution will have the highest freezing point.

NaCl dissociates into Na⁺ and Cl^- ions, so 0.1 M NaCl solution will have a molality of 0.2 M.

BaCl₂ dissociates into Ba²⁺ and 2Cl^- ions, so 0.1 M BaCl2 solution will have a molality of 0.3 M.

FeCl₃ dissociates into Fe³⁺ and 3 Cl^- ions, so 0.1 M FeCl₃ solution will have a molality of 0.4 M.

Therefore, the sugar solution will have the highest freezing point.

Note: The freezing point of a solution is also affected by the nature of the solvent. For example, the freezing point of a solution of sugar in water will be lower than the freezing point of a solution of sugar in ethanol. However, in this case, we are assuming that all of the solutions are in water.