Colligative properties
Colligative properties depend mainly on how many dissolved particles are present, not on their chemical identity. The common mechanism is a lowering of the solvent’s chemical potential when solute is mixed into it.
Vapor-pressure lowering and Raoult law
For an ideal solution containing a nonvolatile solute:
Psolvent = xsolventP°solvent
Because xsolvent < 1, the solvent vapor pressure is lower than for the pure liquid. Real solutions can show positive or negative deviations when intermolecular interactions differ strongly from ideal mixing.
Boiling-point elevation and freezing-point depression
Lower vapor pressure means the solution must be heated to a higher temperature before its vapor pressure reaches the external pressure. Conversely, the liquid solution remains stable to a lower temperature before freezing.
ΔTb = iKbm ΔTf = iKfm
m is molality and i is the van ’t Hoff factor, the effective number of dissolved particles per formula unit.
Osmotic pressure
π = iMRT
For sufficiently dilute solutions, osmotic pressure follows an ideal-gas-like equation. It is especially useful for estimating molar masses of large molecules because the pressure can be measurable even at low concentration.
Reverse osmosis applies a pressure greater than the osmotic pressure to drive solvent in the opposite direction, a basis of desalination technology.
Electrolytes and the van ’t Hoff factor
NaCl ideally gives two ions and might suggest i ≈ 2; CaCl₂ suggests i ≈ 3. Real values can be smaller because ions interact and are not always independent particles, especially at higher concentration.
For nonelectrolytes such as sucrose, i is close to 1 if the molecules neither associate nor dissociate.
Molality, not molarity, for temperature-change formulas
Molality is moles of solute per kilogram of solvent. It is used because mass does not change with temperature, whereas solution volume does. This makes Kbm and Kfm thermodynamically cleaner than formulas based on molarity.
Colligative equations assume dilute or near-ideal behavior; concentrated solutions require activities rather than raw concentrations.
Using colligative effects as measurements
Molar mass from freezing-point depression
If a known mass of unknown nonelectrolyte is dissolved in a known mass of solvent, ΔTf gives the molality. From molality, the moles of solute can be recovered, and mass divided by moles gives molar mass.
The method works best when the solution remains dilute and the solute does not associate, dissociate or react with the solvent.
Antifreeze is a thermodynamic compromise
Ethylene glycol lowers the freezing point and raises the boiling point of water, widening the liquid operating range of an engine coolant. Its usefulness is colligative, but real coolant formulation also depends on corrosion inhibitors, viscosity and heat-transfer performance.
Adding ever more solute is not automatically better: concentrated solutions depart from ideal equations and can have undesirable physical properties.
Osmosis and cells
Cell membranes are selectively permeable, so osmotic gradients can move water and change cell volume. An isotonic solution has an effective osmotic pressure similar to that of the cell interior; hypotonic and hypertonic solutions drive water in opposite directions.
Biological membranes are not perfect semipermeable membranes, so permeability to specific ions and solutes matters alongside simple π = iMRT estimates.
Worked example: freezing-point depression
Dissolve 0.100 mol of a nonelectrolyte in 0.500 kg of water. The molality is 0.200 mol kg⁻¹. With Kf(water) = 1.86 K kg mol⁻¹ and i = 1:
ΔTf = 1×1.86×0.200 = 0.372 K. The predicted freezing point is about −0.372 °C.
If the same ideal particle concentration came from a fully dissociated 1:1 electrolyte, i would be near 2 and the depression roughly twice as large. Real ionic solutions depart from the ideal value as ion interactions grow.
Distillation and vapor composition
Raoult’s law also explains why distillation can separate volatile liquids. A component with the larger vapor pressure contributes disproportionately to the vapor, so vapor composition differs from liquid composition. Repeated vaporization and condensation enriches the more volatile component.
Colligative freezing and boiling equations are simpler because they usually treat the solute as nonvolatile. When both components are volatile, a full vapor–liquid equilibrium description is needed.
Associating solutes can give i below 1
The van ’t Hoff factor is not restricted to values above one. If solute molecules associate—for example by dimerization—the number of independently moving solute particles can fall below the number of formula units added, making the effective i less than 1.
Exercises
Particle count
At the same molality, which ideally depresses freezing point more: glucose or NaCl?
Solution
NaCl, because it dissociates into roughly two particles per formula unit.
Molality
Why is molality preferred to molarity in ΔTf calculations?
Solution
Molality uses solvent mass, which is essentially independent of temperature.
Osmosis
What is osmotic pressure?
Solution
The external pressure required to stop net solvent flow through a semipermeable membrane.