Colligative Properties of Solutions: Freezing-Point Depression, Osmosis, and Determination of Molar Mass

Chapter 12: Solutions

Colligative Properties Continued

Colligative properties are physical properties of solutions that depend on the number of solute particles present, not their identity. This section covers freezing-point depression, osmosis, colligative properties of ionic solutions, and the determination of molar mass using colligative properties.

Freezing-Point Depression

Concept and Explanation

When a nonvolatile solute is added to a solvent, the freezing point of the solution decreases compared to the pure solvent. This phenomenon is known as freezing-point depression. The effect is due to the disruption of the equilibrium between the solid and liquid phases, requiring a lower temperature to re-establish equilibrium.

• Nonvolatile solute: A solute that does not easily vaporize and thus does not contribute to the vapor pressure of the solution.

• Equilibrium disruption: The addition of solute particles interferes with the formation of the solid phase, lowering the freezing point.

Example: Adding salt to icy roads lowers the freezing point of water, preventing ice formation at 0°C.

Mathematical Expression

The decrease in freezing point is given by:

$\Delta T_f = m \cdot K_f$

• $\Delta T_f$ = decrease in freezing point (°C)

• $m$ = molality of solute (mol/kg)

• $K_f$ = molal freezing-point depression constant (°C·kg·mol−1)

Vapour Pressure Perspective

The addition of a solute lowers the vapor pressure of the solution, which in turn lowers the freezing point and raises the boiling point. This is illustrated in phase diagrams comparing pure solvent and solution.

Osmosis

Definition and Biological Importance

Osmosis is the net movement of solvent molecules across a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration. This process is vital in biological systems, such as the regulation of water in cells.

• Semipermeable membrane: Allows passage of solvent molecules but not solute particles.

• Osmotic pressure ($\Pi$): The pressure required to halt the net flow of solvent across the membrane.

Example: Red blood cells placed in pure water will swell due to osmosis, while in a concentrated salt solution, they will shrink.

Osmotic Pressure Equation

The osmotic pressure of a solution is given by:

$\Pi = MRT$

• $\Pi$ = osmotic pressure (in bar)

• $M$ = molarity of the solution (mol/L)

• $R$ = gas constant ($0.08314$ L·bar·K−1·mol−1)

• $T$ = temperature in Kelvin

Colligative Properties of Ionic Solutions

Effect of Ion Dissociation

For ionic compounds, colligative properties depend on the total number of ions produced in solution. The van't Hoff factor ($i$) represents the number of particles into which a formula unit dissociates.

• van't Hoff factor ($i$): Number of particles per formula unit in solution.

• For NaCl, $i = 2$ (Na+ and Cl−); for CaCl2, $i = 3$ (Ca2+ and 2 Cl−).

Colligative property equations for ionic solutions:

$\Delta T_b = i K_b m$

$\Delta T_f = i K_f m$

$\Pi = i M R T$

Table: Expected vs. Measured van't Hoff Factors

Solute	Expected $i$	Measured $i$
NaCl	2	1.8
MgCl2	3	2.7
MgSO4	2	2.3
K2SO4	3	2.6
FeCl3	4	3.4

Additional info: The measured $i$ values are often lower than expected due to ion pairing in solution.

Determination of Molar Mass Using Colligative Properties

Principle and Application

Colligative properties can be used to determine the molar mass of an unknown solute. By measuring the change in freezing point, boiling point, or osmotic pressure, and knowing the amount of solute and solvent, the molar mass can be calculated.

• Each colligative property is related to concentration (molality, molarity, or mole fraction).

• By rearranging the relevant equation, the number of moles of solute can be found, and thus the molar mass.

Example: If 0.186 g of an unknown organic substance is dissolved in 2.18 g of camphor and the freezing point depression is measured, the molar mass can be calculated using $\Delta T_f = K_f m$.

Concept Checks and Practice

Sample Multiple Choice

Which of the following solutions will produce the largest increase in boiling point upon addition to 1 kg of water?

• a. 1 mol Co(NO3)2

• b. 2 mol KCl

• c. 3 mol C2H6O2

• d. I don't know

Additional info: The answer depends on the total number of particles produced in solution (colligative effect).

Conceptual Questions

• If solution A has a greater molecular weight than solution B, and equal masses are dissolved in equal volumes of water, which solution will have a higher osmotic pressure? (Answer: Solution B, because it has more moles of solute particles.)

• How does the vapor pressure of a solution compare to that of the pure solvent? (Answer: The vapor pressure of the solution is lower.)