The following phase diagram shows a very small part of the solid–liquid phase-transition boundaries for two solutions of equal concentration. Substance A has i = 1, and substance B has i = 3. (a) Which line, red or blue, represents a solution of A, and which represents a solution of B? (b) What is the approximate melting point of the pure liquid solvent? (c) What is the approximate molal concentration of each solution, assuming the solvent has Kf = 3.0 °C/m?

Colligative properties are physical properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. In this question, the van 't Hoff factor (i) indicates how many particles a solute dissociates into, which directly affects the freezing point of the solution.

The van 't Hoff factor (i) is a dimensionless number that represents the number of particles into which a solute dissociates in solution. For example, a non-electrolyte like substance A, which does not dissociate, has i = 1, while a substance like B, which dissociates into three particles, has i = 3. This factor is crucial for calculating changes in colligative properties, such as freezing point depression, in the context of the phase diagram.

Freezing point depression is a colligative property that describes the decrease in the freezing point of a solvent when a solute is added. The extent of this depression can be calculated using the formula ΔTf = i * Kf * m, where ΔTf is the change in freezing point, Kf is the freezing point depression constant of the solvent, and m is the molal concentration of the solution. Understanding this concept is essential for determining the melting points of the solutions in the phase diagram.