Colligative Properties in Solution

1. Colligative Properties in Solution • Colligative properties - physical properties that depend on the number but not the kind of solute particles • 4 important colligative properties for solutions: • 1) Vapour pressure depression • 2) Boiling point elevation • 3) Freezing point depression • 4) Osmotic pressure

2. Vapour Pressure Depression • The addition of a non-volatile solute (i.e. sugar) to a volatile solvent lowers the vapour pressure of that system. • Raoult’s Law PSolvent = XSolventP oSolvent • where, PSolvent = vapour pressure of the solvent in the solution • XSolvent = mole fraction of solvent in the solution • P oSolvent = vapour pressure of pure solvent PSolvent P oSolvent

3. Vapour Pressure Depression • The total vapour pressure may decrease or increase if two volatile liquids (A & B) are mixed together. PTotal = PA + PB • Raoult’s Law is still obeyed because the partial pressure of A decreases with the addition of B and the partial pressure of B decreases with the addition of A. PA = XAPAo PB = XBPBo P = PA + PB PAo PBo PA PB

4. Deviations from ideal behavior • Positive deviation is due to the association • between solute-solute and solvent-solvent • (differences in polarity between the solute • and the solvent) • Negative deviation is due to the • association between solute-solvent • (strong intermolecular interactions • between solute and solvent molecules)

5. Boiling Point Elevation • The boiling point of a solvent increases with the addition of a non-volatile solute. • Boiling point - The point at which the vapour pressure of a liquid/solution is equal to the external pressure. • Raoult’s law says that the vapour pressure of a solvent will decrease with the addition of a non-volatile solute therefore, the boiling point of the solution must be higher than the pure solvent. • Tb = Kbm • Tb = Tb - Tbo • Kb = molal boiling point constant • (Kb depends on the solvent, oC/m) • m = molality of the solute • (mol solute/kg solvent)

6. Freezing Point Depression • Tf = Kfm • Tf = Tfo- Tf • Kf = molal freezing point constant • (Kf depends on the solvent, oC/m) • m = molality of the solute • (mol solute/kg solvent)

7. Van’t Hoff Factor, i • colligative properties depend on the number of particles and not their identity therefore, we need to take into account the dissociation of electrolytes • van’t hoff factor, i- a measure of the extent of dissociation of an electrolyte • electrolyte ideal i Actual i • 1.00m 0.10m • Sucrose 1 1 1 • NaCl 2 1.83 1.87 • K2CO3 3 2.39 2.45 • K3[Fe(CN)6] 4 - 2.85

8. Osmotic Pressure • Osmotic Pressure - the pressure necessary to stop osmosis • Osmosis - the spontaneous flow of a solvent from an area of low concentration of solute to an area of high concentration of solute. •  = MRT (dilute solution) • if 1.00 g/ml then •  = mRT • for a non-electrolyte •  = ? for a strong electrolyte •  = iMRT

9. For a 1.25m sucrose solution: • vapour pressure depression = 0.524 torr • boiling point elevation = 0.640oC • freezing point depression = 2.32oC • osmotic pressure = 28.6 atm (2174 torr) • Osmotic pressure is used to find the Molecular Weight of small quantities of sparingly soluble proteins.