Colligative Properties of Solutions: Vapor Pressure Lowering and Boiling Point Elevation

Chapter 12: Solutions

Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles present, not their identity. These properties are crucial in understanding how solutes affect the behavior of solvents, especially in liquid solutions.

• Vapor pressure lowering

• Boiling point elevation

• Freezing point depression

• Osmotic pressure

Definition: Colligative properties are solution properties that depend only on the quantity (concentration) of solute particles (atoms, ions, or molecules) and not on their chemical nature.

Vapor Pressure Lowering

Vapor Pressure and Dynamic Equilibrium

The vapor pressure of a liquid is the pressure exerted by its vapor when the liquid and vapor are in dynamic equilibrium. At this point, the rate at which molecules leave the liquid equals the rate at which they return from the vapor phase.

• Dynamic equilibrium: The state where the rate of evaporation equals the rate of condensation.

• Vapor pressure: The pressure exerted by the vapor above a liquid in a closed system at equilibrium.

Example: Water in a closed container will reach a certain vapor pressure at a given temperature.

Effect of Solute Addition

When a nonvolatile solute is added to a pure solvent, the vapor pressure of the solution is lowered compared to the pure solvent. This is because the solute particles occupy surface sites, reducing the number of solvent molecules that can escape into the vapor phase.

• Nonvolatile solute: A solute that does not readily evaporate into the gas phase.

• Result: The rate of vaporization decreases, and the equilibrium vapor pressure is reduced.

Example: Adding salt to water lowers its vapor pressure.

Raoult's Law

Raoult's Law quantifies the vapor pressure lowering in ideal solutions:

$P_{\text{solution}} = X_{\text{solvent}} P^0_{\text{solvent}}$

• $P_{\text{solution}}$ = vapor pressure of the solution

• $X_{\text{solvent}}$ = mole fraction of the solvent

• $P^0_{\text{solvent}}$ = vapor pressure of the pure solvent

Units: Any pressure unit (atm, torr, mm Hg, bar) may be used.

Example Calculation: If $X_{\text{solvent}} = 0.710$ and $P^0_{\text{solvent}} = 1.070$ bar, then:

$P_{\text{solution}} = 0.710 \times 1.070 = 0.760$ bar

Vapor Pressure of Solutions with Two Volatile Components

For solutions containing two volatile liquids, the total vapor pressure is the sum of the partial pressures of each component:

$P_{\text{total}} = P_A + P_B = X_A P^0_A + X_B P^0_B$

• $X_A$, $X_B$ = mole fractions of components A and B

• $P^0_A$, $P^0_B$ = vapor pressures of pure A and B

Example: Mixing acetone and methanol, calculate the total vapor pressure using their mole fractions and pure vapor pressures.

Deviations from Raoult's Law

Real solutions may deviate from Raoult's Law due to differences in intermolecular forces:

Type of Deviation	Intermolecular Forces	Vapor Pressure	Example
Positive	Weaker A-B than A-A or B-B	Higher than ideal	Acetone + Carbon disulfide
Negative	Stronger A-B than A-A or B-B	Lower than ideal	Acetone + Methanol

Example: If the measured vapor pressure of an acetone-methanol solution is lower than calculated, this indicates negative deviation due to strong interactions between acetone and methanol molecules.

Boiling Point Elevation

Definition and Explanation

The boiling point of a liquid is the temperature at which its vapor pressure equals the external pressure. When a nonvolatile solute is added, the vapor pressure is lowered, so a higher temperature is required to reach the boiling point. This phenomenon is called boiling point elevation.

• Nonvolatile solute: Raises the boiling point of the solvent.

• Application: Adding salt to water increases its boiling point.

Mathematical Expression

The increase in boiling point ($\Delta T_b$) is given by:

$\Delta T_b = m \cdot K_b$

• $\Delta T_b$ = increase in boiling point (°C)

• $m$ = molality of the solute (mol/kg solvent)

• $K_b$ = molal boiling point elevation constant (°C·kg/mol)

Table: Boiling Point Elevation Constants

The following table summarizes normal boiling points and $K_b$ values for common solvents:

Solvent	Normal Boiling Point (°C)	$K_b$ (°C·kg/mol)
Benzene	80.1	2.53
Carbon tetrachloride	76.8	5.03
Chloroform	61.2	3.63
Ether (diethyl)	34.6	2.02
Water	100.0	0.512

Example Problem

Which of the following solutions has the highest boiling point?

• 0.05 m NaCl

• 0.05 m C6H12O6

• 0.02 m Al(NO3)3

• 0.05 m CO2

• 0.02 m NH4Cl

Key Point: The solution with the greatest number of dissolved particles (considering dissociation) will have the highest boiling point elevation.

Summary Table: Colligative Properties

Property	Effect of Nonvolatile Solute	Equation
Vapor Pressure	Lowered	$P_{\text{solution}} = X_{\text{solvent}} P^0_{\text{solvent}}$
Boiling Point	Elevated	$\Delta T_b = m K_b$

Additional info: Freezing point depression and osmotic pressure are also colligative properties, but are not covered in detail in these notes.