Colligative Properties and Solution Behavior (Ch. 13.6–13.7)

Colligative Properties of Solutions

Introduction to Solutions and Colligative Properties

Solutions are homogeneous mixtures composed of a solvent and one or more solutes. The physical properties of solutions, especially those known as colligative properties, depend primarily on the ratio of solute particles to solvent particles, not on the chemical identity of the solute. Colligative properties include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

• Colligative properties depend on the number of solute particles, not their type.

• Examples: Salt water freezes at a lower temperature than pure water.

• Adding solute "dilutes" the solvent, affecting phase changes.

Enthalpy and Entropy in Solution Formation

The formation of a solution is generally entropically favorable due to increased disorder. The enthalpy of solution ($\Delta H_{\text{soln}}$) determines whether a solution forms spontaneously:

• Exothermic ($\Delta H_{\text{soln}} < 0$): Solutions always form (energy-driven).

• Athermic ($\Delta H_{\text{soln}} \approx 0$): Solutions always form (entropy-driven).

• Endothermic ($\Delta H_{\text{soln}} > 0$): Solutions form only if $\Delta H_{\text{soln}}$ is moderate.

Temperature and pressure also affect solubility:

• Increasing temperature increases solubility of solids, decreases solubility of gases.

• Increasing pressure increases solubility of gases (Henry’s law: solubility $\propto$ pressure).

Vapor Pressure Lowering

Raoult’s Law and Dilution Effect

Adding a non-volatile, non-electrolyte solute to a solvent lowers its vapor pressure. The effect is proportional to the mole fraction of the solvent, as described by Raoult’s Law:

• Solvent molecules are "diluted" by solute, lowering vapor pressure.

• Solute type does not matter; only the number of particles matters.

Raoult’s Law:

$P_{\text{solution}} = \chi_{\text{solvent}} P_{\text{solvent}}$

Where $\chi_{\text{solvent}}$ is the mole fraction of the solvent:

$\chi_{\text{solvent}} = \frac{n_{\text{solvent}}}{n_{\text{solvent}} + n_{\text{solute}}}$

Ideal Solutions and Deviations

In ideal solutions, solvent–solvent, solute–solute, and solvent–solute interactions are identical. Deviations from ideality occur when these interactions differ:

• Strong solvent–solute interactions: $P_{\text{solution}} < \chi_{\text{solvent}} P_{\text{solvent}}$ (evaporation is harder).

• Weak solvent–solute interactions: $P_{\text{solution}} > \chi_{\text{solvent}} P_{\text{solvent}}$ (evaporation is easier).

For mixtures of two volatile liquids, Raoult’s Law applies to both components:

• $P_A = \chi_A P_A^\circ$

• $P_B = \chi_B P_B^\circ$

• $P_{\text{tot}} = P_A + P_B = (P_A^\circ - P_B^\circ) \chi_A + P_B^\circ$

Boiling Point Elevation

Principle and Calculation

Adding a non-volatile solute raises the boiling point of a solvent. This is a direct consequence of vapor pressure lowering, requiring a higher temperature to reach atmospheric pressure.

• Boiling point elevation is proportional to solution concentration.

• Different solvents have different boiling point elevation constants ($K_b$).

Boiling point elevation equation:

$\Delta T_b = m \times K_b$

Where $m$ is molality and $K_b$ is the boiling point elevation constant.

Example Table: Boiling Point Elevation Constants

Solvent	Normal b.p. (°C)	Kb (°C / m)
Benzene (C6H6)	80.1	2.53
Carbon tetrachloride (CCl4)	76.7	5.03
Chloroform (CHCl3)	61.2	3.63
Ethanol (C2H5OH)	78.3	1.22
Water (H2O)	100.0	0.512

Freezing Point Depression

Principle and Calculation

Solutions have lower freezing points than pure solvents. The effect is explained by the dilution of solvent molecules, making it harder for the solid phase to form.

• Freezing point depression is proportional to solution concentration.

• Different solvents have different freezing point depression constants ($K_f$).

Freezing point depression equation:

$\Delta T_f = m \times K_f$

Where $m$ is molality and $K_f$ is the freezing point depression constant.

Example Table: Freezing Point Depression Constants

Solvent	Normal f.p. (°C)	Kf (°C / m)
Benzene (C6H6)	5.5	5.12
Carbon tetrachloride (CCl4)	-22.9	29.9
Chloroform (CHCl3)	-63.5	4.70
Ethanol (C2H5OH)	-114.1	1.99
Water (H2O)	0.00	1.86

Electrolytes and the van’t Hoff Factor

Electrolytes vs. Non-Electrolytes

Electrolytes dissociate into ions in solution, increasing the number of solute particles. The van’t Hoff factor ($i$) quantifies the effective number of particles produced per formula unit:

• Non-electrolytes: $i = 1$

• Electrolytes: $i > 1$ (depends on dissociation)

• Ion pairing can reduce the measured $i$ below the expected value.

Van’t Hoff Factor Table

The table below compares expected and measured van’t Hoff factors for various solutes:

Solute	i Expected	i Measured
Nonelectrolyte	1	1
NaCl	2	1.9
MgSO4	2	1.3
MgCl2	3	2.7
K2SO4	3	2.6
FeCl3	4	3.4

Modified Colligative Property Equations for Electrolytes

For electrolyte solutions, the colligative property equations are modified to include the van’t Hoff factor:

• Vapor pressure lowering: $P_{\text{solution}} = \chi_{\text{solvent}} P_{\text{solvent}}$ with $\chi_{\text{solvent}} = \frac{n_{\text{solvent}}}{n_{\text{solvent}} + i \times n_{\text{solute}}}$

• Boiling point elevation: $\Delta T_b = i \times m \times K_b$

• Freezing point depression: $\Delta T_f = i \times m \times K_f$

Summary of Colligative Properties

• Colligative properties depend on the number of solute particles, not their identity.

• Key properties: vapor pressure lowering, boiling point elevation, freezing point depression.

• Electrolytes increase the effect due to dissociation (van’t Hoff factor).