# Colligative Properties of Solutions

## Colligative Properties Definition

Colligative properties are properties of solutions that depend on the number of particles in a volume of solvent (the concentration) and not on the mass or identity of the solute particles. Colligative properties are also affected by temperature. Calculation of the properties only works perfectly for ideal solutions. In practice, this means the equations for colligative properties should only be applied to dilute real solutions when a nonvolatile solute is dissolved in a volatile liquid solvent. For any given solute to solvent mass ratio, any colligative property is inversely proportional to the molar mass of the solute. The word "colligative" comes from the Latin word colligatus, which means "bound together", referring to how the properties of a solvent are bound to the concentration of solute in a solution.

## How Colligative Properties Work

When a solute is added to a solvent to make a solution, the dissolved particles displace some of the solvent in the liquid phase. This reduces the concentration of the solvent per unit of volume. In a dilute solution, it doesn't matter what the particles are, just how many of them are present. So, for example, dissolving CaCl2 completely would yield three particles (one calcium ion and two chloride ions), while dissolving NaCl would only produce two particles (a sodium ion and a chloride ion). The calcium chloride would have a greater effect on colligative properties than the table salt. This is why calcium chloride is a more effective de-icing agent at lower temperatures than ordinary salt.

## What Are the Colligative Properties?

Examples of colligative properties include vapor pressure lowering, freezing point depression, osmotic pressure, and boiling point elevation. For example, adding a pinch of salt to a cup of water makes the water freeze at a lower temperature than it normally would, boil at a higher temperature, have a lower vapor pressure, and changes its osmotic pressure. While colligative properties are generally considered for nonvolatile solutes, the effect also applies to volatile solutes (although it may be harder to calculate). For example, adding alcohol (a volatile liquid) to water lowers the freezing point below that ordinarily seen for either pure alcohol or pure water. This is why alcoholic beverages tend not to freeze in a home freezer.

## Freezing Point Depression and Boiling Point Elevation Equations

Freezing point depression may be calculated from the equation:

ΔT = iKfm
where
ΔT = Change in temperature in °C
i = van 't Hoff factor
Kf = molal freezing point depression constant or cryoscopic constant in °C kg/mol
m = molality of the solute in mol solute/kg solvent

Boiling point elevation may be calculated from the equation:

ΔT = Kbm

where
Kb = ebullioscopic constant (0.52°C kg/mol for water)
m = molality of the solute in mol solute/kg solvent

## Ostwald's Three Categories of Solute Properties

Wilhelm Ostwald introduced the concept of colligative properties in 1891. He actually proposed three categories of solute properties:

1. Colligative properties depend only on solute concentration and temperature, not on the nature of the solute particles.
2. Constitutional properties depend on the molecular structure of the solute particles in a solution.
3. Additive properties are the sum of all the properties of the particles. Additive properties are dependent on the molecular formula of the solute. An example of an additive property is mass.
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