Chapter 14 lecture 3

Colligative Properties of Solutions

Introduction to Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles present, not their chemical identity. These properties are influenced by whether the solute is an electrolyte (dissociates into ions) or a nonelectrolyte (does not dissociate).

• Key Colligative Properties: Vapor pressure lowering, boiling point elevation, freezing point depression, osmotic pressure, and the van’t Hoff factor.

• Electrolyte vs. Nonelectrolyte: Electrolytes produce more particles in solution, affecting colligative properties more strongly than nonelectrolytes.

Vapor Pressure Lowering

Raoult’s Law and the Effect of Nonvolatile Solutes

The addition of a nonvolatile solute to a solvent lowers the vapor pressure of the solution compared to the pure solvent. This occurs because fewer solvent molecules are present at the surface to escape into the vapor phase.

• Raoult’s Law: $P_{\text{solution}} = P_{\text{solvent}}^\circ X_{\text{solvent}}$

• Vapor Pressure Lowering: $\Delta P = P_{\text{solvent}}^\circ X_{\text{solute}}$

• Entropy Explanation: The solution is more disordered than the pure solvent, so the difference in entropy between solution and vapor is less, reducing the tendency for solvent molecules to vaporize.

• Example: Calculating vapor pressure lowering for solutions of glycerin and glucose in water.

Vapor Pressure of Solutions with Volatile Solutes

In solutions with two volatile components, both contribute to the vapor pressure. Raoult’s Law applies to each component, and the total vapor pressure is the sum of the partial pressures.

• Raoult’s Law for Each Component: $P_A = X_A P_A^\circ$, $P_B = X_B P_B^\circ$

• Total Pressure: $P_T = P_A + P_B$

• Deviations from Raoult’s Law: Strong solute-solvent interactions cause negative deviations (lower vapor pressure), while weak interactions cause positive deviations (higher vapor pressure).

Boiling Point Elevation

Phase Diagram and Boiling Point Changes

The addition of a nonvolatile solute lowers the vapor pressure, requiring a higher temperature to reach boiling. Thus, the boiling point of the solution is elevated compared to the pure solvent.

• Boiling Point Elevation Equation: $\Delta T_b = k_b m$

• Molality (m): Moles of solute per kilogram of solvent.

• Boiling Point Elevation Constant (k_b): Depends only on the solvent, units are °C/m.

• Example: Calculating boiling point elevation for glucose in water.

Freezing Point Depression

Phase Diagram and Freezing Point Changes

The addition of a nonvolatile solute lowers the freezing point of the solution compared to the pure solvent. This is because the solute disrupts the formation of the solid phase.

• Freezing Point Depression Equation: $\Delta T_f = k_f m$

• Molal Freezing Point Depression Constant (k_f): Depends only on the solvent, units are °C/m.

• Example: Calculating freezing point depression for glucose in water.

• Application: Cryoscopy is used to determine molar mass by measuring freezing point depression.

Osmotic Pressure

Osmosis and Osmotic Pressure

Osmosis is the movement of solvent through a semipermeable membrane to equalize solute concentration. Osmotic pressure is the pressure required to stop this flow.

• Osmotic Pressure Equation: $\pi = M R T$

• Variables: $\pi$ = osmotic pressure (atm), $M$ = molarity, $R$ = gas constant (0.0821 L·atm/K·mol), $T$ = temperature (K).

• Applications: Reverse osmosis for desalination, biological cell environments (hypertonic, hypotonic, isotonic).

van’t Hoff Factor (i)

Electrolyte Solutions and Colligative Properties

The van’t Hoff factor accounts for the number of particles produced by dissociation of electrolytes in solution. Colligative property equations are modified by multiplying by i.

• van’t Hoff Factor Equation: $i = \frac{\text{moles of ions in solution}}{\text{moles of formula units dissolved}}$

• Modified Colligative Property Equations:

  • $\Delta P = i P_{\text{solvent}}^\circ X_{\text{solute}}$

  • $\Delta T_b = i k_b m$

  • $\Delta T_f = i k_f m$

  • $\pi = i M R T$

• Example: Freezing point depression for CuCl2 in water, with i = 3.

• Experimental vs. Theoretical i: Ion pairing at higher concentrations reduces the effective number of particles, causing deviations from the theoretical value.

Summary Table: Freezing Point Depression and Boiling Point Elevation Constants

The following table summarizes the freezing point depression and boiling point elevation constants for several common solvents:

Solvent	Normal Freezing Point (°C)	kf (°C/m)	Normal Boiling Point (°C)	kb (°C/m)
Benzene (C6H6)	5.5	5.12	80.1	2.53
Carbon tetrachloride (CCl4)	-22.9	29.9	76.7	5.03
Chloroform (CHCl3)	-63.5	4.70	61.2	3.63
Ethanol (C2H5OH)	-114.1	1.99	78.3	1.22
Diethyl ether (C4H10O)	-116.3	1.79	34.6	2.02
Water (H2O)	0.00	1.86	100.0	0.512

Summary Table: van’t Hoff Factors for Several Substances

The following table shows van’t Hoff factors for several substances at different concentrations:

Compound	0.100 m	0.0100 m	0.00100 m	Limiting Value
Sucrose	1.00	1.00	1.00	1.00
NaCl	1.87	1.94	1.97	2.00
K2SO4	2.32	2.70	2.84	3.00
MgSO4	1.21	1.53	1.82	2.00

Additional info: This study guide expands on lecture notes with full academic explanations, equations, and relevant examples for each colligative property. All included images and tables directly reinforce the concepts discussed.