Colligative properties are all about how dissolved stuff affects a solution's behavior. They depend on how many particles are floating around, not what those particles are. This is key to understanding how solutions work in chemistry.

Vapor pressure, boiling point, freezing point, and osmotic pressure all change when you add solutes. These changes can be calculated using formulas that relate to the concentration of dissolved particles. It's like a recipe for predicting solution behavior.

Colligative Properties and Solute Concentration

Definition and Examples

• Colligative properties depend on the concentration of solute particles in a solution, not the identity of the solute particles
• Examples include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure
• As the concentration of solute particles increases, the magnitude of the colligative property effect also increases

Expressing Solute Concentration

• Molality expresses the concentration as moles of solute per kilogram of solvent
• Mole fraction is the ratio of moles of solute to total moles of solution
• For non-electrolyte solutions, the concentration of solute particles equals the molarity of the solute
• For electrolyte solutions, the concentration of solute particles is greater than the molarity due to the dissociation of the solute into ions (NaCl dissociates into Na⁺ and Cl⁻)

Calculating Colligative Property Changes

Vapor Pressure Lowering

• Vapor pressure lowering (ΔP) is the difference between the vapor pressure of the pure solvent (P₀) and the vapor pressure of the solution (P)
• Calculate using the formula ΔP = P₀ - P = P₀ × χₛₒₗᵤₜₑ, where χₛₒₗᵤₜₑ is the mole fraction of the solute
• Example: A solution of glucose in water has a lower vapor pressure than pure water

Boiling Point Elevation

• Boiling point elevation (ΔTb) is the increase in the boiling point of a solution compared to the pure solvent
• Calculate using the formula ΔTb = Kb × m × i, where:
  • Kb is the molal boiling point elevation constant (specific to the solvent)
  • m is the molality of the solute
  • i is the van 't Hoff factor (the number of particles formed per formula unit of solute)
• Example: A solution of sodium chloride in water boils at a higher temperature than pure water

Freezing Point Depression

• Freezing point depression (ΔTf) is the decrease in the freezing point of a solution compared to the pure solvent
• Calculate using the formula ΔTf = Kf × m × i, where:
  • Kf is the molal freezing point depression constant (specific to the solvent)
  • m is the molality of the solute
  • i is the van 't Hoff factor
• Example: A solution of ethylene glycol in water freezes at a lower temperature than pure water, making it useful as an antifreeze

Raoult's Law for Vapor Pressure

Raoult's Law Equation

• Raoult's law states that the vapor pressure of a solution (P) equals the vapor pressure of the pure solvent (P₀) multiplied by the mole fraction of the solvent in the solution (χₛₒₗᵥₑₙₜ): P = P₀ × χₛₒₗᵥₑₙₜ
• The mole fraction of the solvent (χₛₒₗᵥₑₙₜ) is the ratio of the moles of solvent to the total moles of the solution (solvent + solute)

Assumptions and Limitations

• Raoult's law assumes that the solute is non-volatile (does not contribute to the vapor pressure) and that the solution is ideal (no interactions between solute and solvent molecules)
• For ideal solutions containing two volatile components, the total vapor pressure is the sum of the partial vapor pressures of each component, calculated using Raoult's law for each component
• Example: In a solution of ethanol and water, both components contribute to the total vapor pressure according to their respective mole fractions

Osmotic Pressure and Colligative Properties

Osmotic Pressure Definition

• Osmotic pressure (π) is the pressure that must be applied to a solution to prevent the net flow of solvent molecules across a semipermeable membrane from a region of high solvent concentration (pure solvent or less concentrated solution) to a region of low solvent concentration (more concentrated solution)
• Osmotic pressure is a colligative property, as it depends on the concentration of solute particles in the solution

Calculating Osmotic Pressure

• The osmotic pressure of a solution can be calculated using the van 't Hoff equation: π = MRT, where:
  • M is the molarity of the solute
  • R is the ideal gas constant
  • T is the absolute temperature
• Example: A 1 M solution of sucrose in water at room temperature has an osmotic pressure of approximately 24.6 atm

Osmosis and Osmotic Pressure

• Osmosis is the net movement of solvent molecules across a semipermeable membrane from a region of high solvent concentration to a region of low solvent concentration
• Osmosis is driven by the difference in osmotic pressure between the two sides of the membrane
• When a solution and pure solvent are separated by a semipermeable membrane, the solvent will flow from the pure solvent side to the solution side until the osmotic pressure is balanced by the hydrostatic pressure difference between the two sides
• Example: In a U-tube apparatus, water will flow from the pure water side to the solution side until the height difference between the two sides generates a hydrostatic pressure equal to the osmotic pressure of the solution