Chapter 5: Colligative Properties

5.1 Introduction

• Colligative Properties: Depend on the number of molecules, not type.
  • Includes boiling point elevation, freezing point depression, and osmotic pressure.
  • Used historically to determine molecular weights of unknown compounds.
• Focus on molecular weight measurement of polymers using colligative properties.

5.2 Boiling Point Elevation

• Vapor Pressure: Lowered in solutions compared to pure solvents.
• Boiling Point: Increases when a solute is dissolved (boiling point elevation).
  • Formula: (\Delta T_b = K_bm) where (m) is molality and (K_b) is the coefficient depending on solvent.
• Used to determine molecular weight (M_B) of unknown compounds.
• Application to Polymers:
  • Assumes ideal solutions: Chemical potential of vapor equals liquid.
  • Boiling point elevation for polymer solutions described by mole fractions.
• Limitations: Not sensitive enough for high molecular weight polymers.

5.3 Freezing Point Depression

• Similar analysis to boiling point elevation.
• Formula: (\Delta T_f = \frac{RT^2_f}{l_f}M_N)
• Limited utility for high molecular weight polymers due to small effect size.

5.4 Osmotic Pressure

• Concept: Pressure needed to equalize chemical potential across a semipermeable membrane.
• Thermodynamics: At equilibrium, chemical potentials on both sides are equal.
• Pressure Formula: (\Pi = \frac{cRT}{M_N})
• Example: Polystyrene in benzene demonstrates measurable osmotic pressure, suitable for molecular weights up to 2,000,000 g/mol.

5.5 Practical Aspects of Osmotic Pressure

• Osmotic pressure useful for determining number average molecular weights in polymers.
• Deviations from Ideal Behavior: Requires corrections through extrapolation techniques like virial expansions.
  • Virial Coefficients: Account for non-ideal interactions.
  • Flory-Huggins Theory: Helps interpret non-ideal interactions.
  • Theta Solvents: Conditions where excluded volume effect disappears, identified by zero slope in data.
• Approaches:
  • Linear fits for simple analysis.
  • Inclusion of higher-order virial coefficients for complex data.

5.6 Experimental Aspects of Membrane Osmometry

• Block Type Osmometer: Measures osmotic pressure using semipermeable membranes.
  • Static osmometers rely on natural equilibrium development.
  • Dynamic osmometers use applied pressure to reach equilibrium faster.
• Membrane Requirements:
  • Must be permeable to solvent, impermeable to polymers.
  • Common materials: Gel cellulose, cellulose derivatives, polyurethanes.

Problems

• Considerations in osmotic pressure data analysis.
• Practical exercises in plotting and finding molecular weights using osmometry.
• Theoretical exploration of alternative boiling point elevation formulations.