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Colligative Properties and Related Laws

Objective

In this lesson we will examine colligative properties and the calculations associated with them.

Previously we covered…

  • Completing Ksp and precipitation formation problems; We should be familiar with equilibrium before beginning this lesson.
  • Describing the interparticle interactions (ion-ion, ion-dipole, dipole-dipole, hydrogen bonds, and London dispersion forces) in solutions
  • Recognizing the difference between diffusion and osmosis
  • Using concentrations, amounts of solutions, and Ksp values to predict if precipitates will form when solutions are mixed

Colligative Properties

Colligative properties are properties of solutions that depend on the concentration of solute particles present. The most common colligative properties examined in chemistry include:

  • Freezing point depression
  • Boiling point elevation
  • Reduction of vapor pressure
  • Osmotic pressure

Freezing point depression

Throwing salt on ice lowers the freezing point of water below its normal freezing point, thus melting the ice. The freezing point depression can be calculated using the following formula

ΔTf = iKfm

ΔTf is the freezing point depression (freezing point of the solution subtracted by the freezing point of the pure solvent), i is the van’t Hoff factor (the number of solute particles per mole of solute), Kf is the freezing point depression constant (this should be negative) and m is the molality.

Boiling point elevation

In a similar way, the boiling point of a solvent can be raised above its normal boiling point by adding solute particles. Boiling point elevation can be calculated using the following formula:

ΔTb = iKbm

ΔTb is the boiling point elevation, i is the van’t Hoff factor (the number of solute particles per mole of solute), Kb is the boiling point elevation constant and m is the molality.

The molar mass of the solute can be calculated from freezing point depression or boiling point elevation values and some additional data.

Raoult’s Law

When nonvolatile solute particles are added, the vapor pressure of a volatile solvent generally decreases proportionally to the concentration. This can be expressed as:

PA is the partial pressure of the solvent’s vapor above a solution, XA is the mole fraction of the solvent in the solution, and P°A is the vapor pressure of the pure solvent.

Henry’s Law

Henry’s Law expresses the directly proportional relationship between the solubility of a gas and its pressure. Using the equation:

Sg = kPg

Sg is the solubility of the gas, k is the proportionality constant (Henry’s law constant), and Pg is the partial pressure of the gas over the solution. The proportionality constant is dependent upon the identities of the solute and solvent as well as the temperature. Henry’s Law can be used to predict the concentration of gases in a mixture.

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