Colligative Properties: Principles and Applications

Colligative Properties

Definition and General Principles

Colligative properties are physical properties of solutions that depend on the concentration of solute particles, not their chemical identity. These properties change when a non-volatile solute is added to a solvent, and are crucial in understanding solution behavior in both chemical and biological contexts.

• Key Point: Colligative properties depend on the number of solute particles present, not the type of particles.

• Example: Adding sugar (a non-electrolyte) or NaCl (an electrolyte) to water will affect its freezing and boiling points, but the effect is proportional to the number of particles formed in solution.

Classification of Solutes

Electrolytes vs Non-Electrolytes

Solutes are classified based on their ability to ionize in solution:

• Electrolytes: Substances that dissociate into ions in water, conducting electricity. They can be:

  • Strong electrolytes: Completely ionized (e.g., HCl, NaCl)

  • Weak electrolytes: Partially ionized (e.g., acetic acid, HAc)

• Non-electrolytes: Do not ionize in solution and do not conduct electricity (e.g., sugar, urea).

Main Colligative Properties

• Freezing Point Depression

• Vapor Pressure Depression

• Boiling Point Elevation

• Osmotic Pressure

Freezing Point Depression

Principle and Formula

When a solute is added to a solvent, the freezing point of the solution is lower than that of the pure solvent. This occurs because solute particles disrupt the formation of the solid structure, making it harder for the solvent to freeze.

• Formula: $\Delta T_f = K_f \cdot m$

• $K_f$: Molal freezing point depression constant (for water, $K_f = 1.86\ ^\circ\mathrm{C}/m$)

• $m$: Molality of the solution (moles of solute per kg of solvent)

• Example: Adding salt to icy roads in winter lowers the freezing point, preventing ice formation.

Vapor Pressure Depression

Principle and Formula

The addition of a non-volatile solute to a solvent lowers the vapor pressure of the solution compared to the pure solvent. Solute particles attract solvent molecules, reducing their tendency to escape into the vapor phase.

• Raoult's Law: $P_1 = P_1^0 X_1$

• $P_1$: Vapor pressure of solvent in solution

• $P_1^0$: Vapor pressure of pure solvent

• $X_1$: Mole fraction of solvent

• Key Point: The more solute present, the lower the vapor pressure.

• Example: Sugar solution has lower vapor pressure than pure water.

Boiling Point Elevation

Principle and Formula

Boiling point elevation occurs because the vapor pressure of a solution is lower than that of the pure solvent, requiring a higher temperature to reach atmospheric pressure.

• Formula: $\Delta T_b = K_b \cdot m$

• $K_b$: Molal boiling point elevation constant (for water, $K_b = 0.51\ ^\circ\mathrm{C}/m$)

• $m$: Molality of the solution

• Example: Adding salt to water increases its boiling point, useful in cooking.

Osmotic Pressure

Principle and Formula

Osmosis is the movement of solvent through a semi-permeable membrane from a region of low solute concentration to high solute concentration. Osmotic pressure is the pressure required to stop this flow.

• Van't Hoff Equation: $\pi = MRT$

• $\pi$: Osmotic pressure

• $M$: Molarity of the solution

• $R$: Gas constant ($0.082$ L·atm/mol·K)

• $T$: Absolute temperature (K)

• Example: Calculation for 1 g of sucrose in 100 mL solution at 25°C:

  • $\pi = \frac{1}{342 \times 0.1} \times 62.4 \times (25+273)$

  • $\pi = 543.72$ mm Hg

Tonicity and Isotonic Solutions

Biological Applications

Tonicity describes the effect of a solution on cell volume. An isotonic solution has the same osmotic pressure as blood, preventing net movement of water into or out of cells.

• Isotonic: 0.9% NaCl solution; cells retain normal size.

• Hypertonic: >0.9% NaCl; cells shrink.

• Hypotonic: <0.9% NaCl; cells swell and may burst (hemolysis).

Colligative Properties of Electrolyte Solutions

Van't Hoff Factor and Particle Counting

Electrolytes dissociate into multiple ions, increasing the number of particles and thus magnifying colligative effects. The Van't Hoff factor ($i$) accounts for the number of particles produced per formula unit.

• For non-electrolytes: $i = 1$

• For strong electrolytes: $i$ equals the number of ions produced (e.g., NaCl: $i = 2$; CaCl2: $i = 3$)

• Modified formulas:

  • $\Delta T_f = K_f \cdot m \cdot i$

  • $\Delta T_b = K_b \cdot m \cdot i$

• Example: 1 mole of NaCl yields 2 moles of particles; 1 mole of CaCl2 yields 3 moles of particles.

Worked Example: Freezing Point Depression Calculation

Step-by-Step Solution

• Given: 195 g sucrose (C12H22O11), 200 mL water ($K_f = 1.86\ ^\circ\mathrm{C}/m$)

• Calculate moles: $195\ g / 342\ g/mol = 0.570$ moles

• Calculate molality: $0.570\ mol / 0.200\ kg = 2.85$ molal

• Apply formula: $\Delta T_f = -1.86 \times 2.85 = -5.301\ ^\circ\mathrm{C}$

• Result: Water will freeze 5.301°C below its normal freezing point.

Comparison Table: Ionic vs Molecular Solutes

Solute Type	Number of Particles Produced	Effect on Colligative Properties	Examples
Molecular (Non-electrolyte)	1 per formula unit	Lower effect	Glucose, Sucrose
Ionic (Electrolyte)	2 or more per formula unit	Higher effect (proportional to number of ions)	NaCl (2), CaCl2 (3)

Summary of Key Equations

• Freezing Point Depression: $\Delta T_f = K_f m i$

• Boiling Point Elevation: $\Delta T_b = K_b m i$

• Vapor Pressure (Raoult's Law): $P_1 = P_1^0 X_1$

• Osmotic Pressure (Van't Hoff): $\pi = MRT$

Additional info: These notes expand on the original slides by providing definitions, formulas, and worked examples for each colligative property, as well as a comparison table for solute types and their effects.