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?

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1. Step 1: Understand the van't Hoff factor (i) and its effect on freezing point depression. The van't Hoff factor represents the number of particles a compound dissociates into in solution. Substance A has i = 1, meaning it does not dissociate, while substance B has i = 3, indicating it dissociates into three particles.
2. Step 2: Analyze the phase diagram. The line with the greater freezing point depression (lower temperature) corresponds to the solution with the higher van't Hoff factor. Therefore, identify which line (red or blue) shows a greater depression to determine which represents substance B.
3. Step 3: Determine the melting point of the pure solvent. On the phase diagram, locate the point where the solid and liquid phases of the pure solvent meet. This is the melting point of the pure solvent.
4. Step 4: Use the freezing point depression formula to find the molal concentration of each solution. The formula is \( \Delta T_f = i \cdot K_f \cdot m \), where \( \Delta T_f \) is the change in freezing point, \( K_f \) is the cryoscopic constant, and \( m \) is the molality. Rearrange the formula to solve for \( m \).
5. Step 5: Calculate the molal concentration for each solution. Use the freezing point depression values from the phase diagram and the given \( K_f \) value to find the molality for both solutions A and B.