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 crucial in understanding how solutes affect the behavior of solvents, especially in aqueous solutions.

• Examples of colligative properties:

  • Vapour pressure lowering

  • Boiling point elevation

  • Freezing point depression

  • Osmotic pressure

• Colligative properties are used to analyze and predict the behavior of solutions in both laboratory and real-world contexts.

Concentration Units for Colligative Properties

Molality

Molality (symbol: b or sometimes m) is the amount of solute (in moles) per kilogram of solvent. Unlike molarity, molality is independent of temperature because it is based on mass, not volume.

• Definition: Molality (b) = moles of solute / kilograms of solvent

• Formula:

• Example: Dissolving 4.00 g NaOH (0.10 mol) in 250 g water (0.250 kg):

• Molality is preferred for colligative property calculations because it does not change with temperature.

Mole Fraction

The mole fraction of a component in a solution is the ratio of the number of moles of that component to the total number of moles of all components.

• Definition:

• Mole fraction is also temperature-independent.

• Example: In a solution with 1 mol A, 2 mol B, and 3 mol C:

Vapour Pressure and Raoult's Law

Vapour Pressure of Solutions

Vapour pressure is the pressure exerted by a vapor in equilibrium with its liquid in a closed container. The presence of a nonvolatile solute lowers the vapour pressure of the solvent.

• Vapour pressure increases with temperature.

• At the boiling point, vapour pressure equals external (atmospheric) pressure.

Raoult's Law

Raoult's Law quantifies the lowering of vapour pressure in a solution containing a nonvolatile solute.

• Formula:

• Where is the vapour pressure of the solution, is the mole fraction of the solvent, and is the vapour pressure of the pure solvent.

Boiling Point Elevation and Freezing Point Depression

Boiling Point Elevation

The boiling point of a solution is higher than that of the pure solvent due to the presence of a nonvolatile solute.

• Formula:

• is the molal boiling point elevation constant (unique for each solvent).

• To find the new boiling point:

• Example: For a 10% (by mass) sugar solution in water:

  • 10 g sugar (C12H22O11) in 90 g water: mol

  • Molality: mol kg–1

  • For water, K mol–1 kg

  • K

  • New boiling point: °C

Freezing Point Depression

The freezing point of a solution is lower than that of the pure solvent.

• Formula:

• is the molal freezing point depression constant (unique for each solvent).

• To find the new freezing point:

Table: Boiling Point Elevation and Freezing Point Depression Constants

Effect of Solute Dissociation

Colligative properties depend on the total number of solute particles. Ionic compounds dissociate in solution, increasing the number of particles and thus the magnitude of colligative effects.

• 1 mol glucose (C6H12O6): 1 mol particles

• 1 mol NaCl: 2 mol particles (Na+ and Cl–)

• 1 mol (NH4)2SO4: 3 mol particles (2 NH4+ and 1 SO42–)

Osmosis and Osmotic Pressure

Osmosis

Osmosis is the movement of solvent molecules through a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration, until equilibrium is reached.

• Semipermeable membranes allow only certain molecules (usually solvent) to pass through.

• Examples:

  • Cucumber in salt solution loses water and becomes a pickle.

  • Limp carrot in water becomes firm as it absorbs water.

  • Salted meat or sugared fruit prevents bacterial growth by dehydrating bacteria.

  • Eating salty food can cause tissue swelling (oedema) due to water retention.

Osmotic Pressure

Osmotic pressure is the pressure required to stop the net flow of solvent through a semipermeable membrane. It is a colligative property, depending on the number of solute particles.

• Osmotic pressure is important in biological systems for maintaining cell water balance.

• Isotonic solution: Osmotic pressure is equal inside and outside the cell; no net water movement.

• Hypertonic solution: Higher solute concentration outside; water leaves the cell, causing it to shrink.

• Hypotonic solution: Lower solute concentration outside; water enters the cell, causing it to swell and possibly burst.

Table: Effects of Different Solutions on Red Blood Cells

Summary: Colligative properties are essential for understanding how solutes affect the physical properties of solutions. Mastery of concepts such as molality, mole fraction, Raoult's Law, boiling point elevation, freezing point depression, and osmosis is fundamental for success in general chemistry.