Colligative properties are physical properties derived solely from the number of particles present, not the nature of those particles. These properties are usually associated with dilute solutions.
Pure water (H2O) freezes at 0°C; however, for every mole of solute particles dissolved in 1 L of water, the freezing point is lowered by 1.86°C. This is because the solute particles interfere with the process of crystal formation that occurs during freezing; the solute particles lower the temperature at which the molecules can align themselves into a crystalline structure.
The formula for calculating this freezing-point depression is:
where ΔTf is the freezing-point depression, Kf is a proportionality constant characteristic of a particular solvent, m is the molality of the solution (mol solute/kg solvent), and i is the van ’t Hoff factor, which accounts for the number of particles that dissociate from the original molecule. For example, NaCl dissociates into two ions in water, Na+ and Cl−, so its i = 2 to represent that 1 mol NaCl becomes 2 mol solute particles.
One of the best examples of this principle is when salt is sprinkled on roads to make ice melt. This thawing occurs because the salt depresses the freezing point of the water.
A liquid boils when its vapor pressure equals the atmospheric pressure. If the vapor pressure of a solution is lower than that of the pure solvent, more energy (and consequently a higher temperature) will be required before its vapor pressure equals atmospheric pressure. The extent to which the boiling point of a solution is raised relative to that of the pure solvent is given by the following formula:
where ΔTb is the boiling-point elevation, Kb is a proportionality constant characteristic of a particular solvent, m is the molality of the solution, and i is the van ’t Hoff factor.
One commonly misunderstood example of this principle is the addition of salt (NaCl) to a boiling pot of water on the stove, such as before cooking pasta, supposedly to speed cooking by raising the temperature of the water. Although adding Na+ and Cl− ions does increase the boiling point, the molality of salt normally added only results in an increase in boiling point of approximately 0.1°C (in fact, the main values of adding salt are to decrease sticking and add flavor).
Consider a container separated into two compartments by a semipermeable membrane (which, by definition, selectively permits the passage of only certain molecules). One compartment contains pure water, while the other contains water with dissolved solute. The membrane allows water but not solute to pass through. Because substances tend to flow, or diffuse, from higher to lower concentrations (which increases entropy), water will diffuse from the compartment containing pure water to the compartment containing the water-solute mixture. This net flow will cause the water level in the compartment containing the solution to rise above the level in the compartment containing pure water.
However, the pressure exerted by the water level in the solute-containing compartment due to gravity will eventually oppose the influx of water due to diffusion, and the water will stop flowing once this point is reached. This pressure is defined as the osmotic pressure (Π) of the solution and is given by the formula:
where M is the molarity of the solution, R is the ideal gas constant, T is the temperature on the Kelvin scale, and i is the van ’t Hoff factor. This equation shows that molarity and osmotic pressure are directly proportional (i.e., as the concentration of the solution increases, the osmotic pressure also increases). Thus, the osmotic pressure depends only on the amount of solute, not its identity.
When solute B is added to pure solvent A, the vapor pressure of A above the solvent decreases. If the vapor pressure of A above pure solvent A is designated by P°A and the vapor pressure of A above the solution containing B is PA, the vapor pressure decreases as follows:
In the late 1800s, the French chemist François Marie Raoult determined that this vapor pressure decrease is also equivalent to:
where XB is the mole fraction of the solute B in solvent A (mol B/total moles). Because XB= 1 −XA and ΔP = P°A−PA, substitution into the above equation leads to the common form of Raoult’s law:
Similarly, the expression for the vapor pressure of the solute in solution (assuming it is volatile) is given by:
Raoult’s law holds only when the attraction between molecules of the different components of the mixture is equal to the attraction between the molecules of any one component in its pure state. When this condition does not hold, the relationship between mole fraction and vapor pressure will deviate from Raoult’s law. Solutions that obey Raoult’s Law are called ideal solutions.