Chemistry

Chemistry

Problem

An aqueous solution of urea has freezing point of −0.52θC-0.52^{ \theta }\text{C} . Calculate the osmotic pressure of solution at 27θC27^{ \theta }\text{C} . Assume molarity and molality be same. KfK_f for H2O\text{H}_2\text{O} is 1.86 K mol−1 kg1.86 \text{ K mol}^{-1} \text{ kg} .
Intuitive explanation

The key is recognizing that freezing point depression tells you the solution's molality, which you can then convert to molarity (given the assumption). Once you know the concentration, osmotic pressure follows directly from the van 't Hoff equation Π=MRT\Pi = MRT—the same colligative property framework that governs freezing point, just expressed differently. Both phenomena stem from how solute particles disrupt the solvent's behavior.

Intuitive explanation

The key is recognizing that freezing point depression tells you the solution's molality, which you can then convert to molarity (given the assumption). Once you know the concentration, osmotic pressure follows directly from the van 't Hoff equation Π=MRT\Pi = MRT—the same colligative property framework that governs freezing point, just expressed differently. Both phenomena stem from how solute particles disrupt the solvent's behavior.

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