# Colligative Properties (with Formulas)

The  colligative property  is any property of a substance that depends on, or varies according to, the number of particles present in it (in the form of molecules or atoms), without depending on the nature of those particles.

In other words, these can also be explained as properties of solutions that depend on the relationship between the number of solute particles and the number of solvent particles. This concept was introduced in 1891 by the German chemist Wilhelm Ostwald, who classified the properties of solute into three categories. These categories claimed that the colligative properties depended solely on the concentration and temperature of the solute and not on the nature of its particles.

Furthermore, additive properties such as mass depended on the composition of the solute, and constitutional properties depended more on the molecular structure of the solute.

## Colligative properties

Colligative properties are studied mainly for dilute solutions (due to their almost ideal behavior), and are as follows:

### Decrease in vapor pressure

It can be said that the vapor pressure of a liquid is the equilibrium pressure of the vapor molecules with which that liquid is in contact.

Likewise, the relationship of these pressures is explained by Raoult’s law, which expresses that the partial pressure of a component is equal to the product of the mole fraction of the component by the vapor pressure of the component in its pure state:

P A = X A . Pº A

In this expression:

P A = Partial vapor pressure of component A in the mixture.

X A = Molar fraction of component A.

A = Vapor pressure of pure component A.

In the case of the decrease in the vapor pressure of a solvent, this occurs when a non-volatile solute is added to form a solution. As is known and by definition, a non-volatile substance has no tendency to evaporate.

For this reason, the more of this solute is added to the volatile solvent, the lower the vapor pressure will be and the less solvent can escape to become a gaseous state .

Thus, when the solvent evaporates naturally or forcibly, an amount of solvent will finally remain without evaporating along with the non-volatile solute.

This phenomenon can be better explained with the concept of entropy: when the molecules make transition from the liquid phase to the gas phase, the entropy of the system increases.

This means that the entropy of this gas phase will always be greater than that of the liquid state , because the gas molecules occupy a greater volume.

Then, if the entropy of the liquid state increases by dilution, even though it is linked to a solute, the difference between the two systems decreases. For this reason, the decrease in entropy also decreases the vapor pressure.

### Boiling temperature rise

The boiling point is that temperature at which there is equilibrium between the liquid and gas phases. At this point, the number of gas molecules becoming liquid (condensing) equals the number of liquid molecules evaporating to gas.

The aggregation of a solute causes the concentration of liquid molecules to dilute, causing the rate of evaporation to decrease. This generates a change in the boiling point , to compensate for the change in solvent concentration.

In other simpler words, the boiling temperature in a solution is higher than that of the solvent in its pure state. This is expressed by a mathematical expression shown below:

ΔT b = i. K b . m

In this expression:

ΔT b = T b (solution) – T b (solvent) = Variation of the boiling temperature.

i = Van’t Hoff factor.

K b = Boiling constant of the solvent (0.512 ºC / molal for water).

m = Molality (mol / kg).

### Lowering the freezing temperature

The freezing temperature of a pure solvent will decrease when a quantity of solute is added, since it is affected by the same phenomenon that the vapor pressure decreases.

This happens because, as the vapor pressure of the solvent is decreased by diluting a solute, a lower temperature will be required to make it freeze.

The nature of the freezing process can also be taken into account to explain this phenomenon: for a liquid to become frozen, it must reach an ordered state in which it ends up forming crystals.

If there are impurities within the liquid in the form of solutes, the liquid will be less ordered. For this reason, the solution will have greater difficulties to freeze than a solvent without impurities.

This reduction is expressed as:

ΔT f = -i. K f . m

In the above expression:

ΔT f = T (solution) – T (solvent) = Freezing temperature variation.

i = Van’t Hoff factor.

K f = Freezing constant of the solvent (1.86 ºC kg / mol for water).

m = Molality (mol / kg). ### Osmotic pressure

The process known as osmosis is the tendency of a solvent to pass through a semi-permeable membrane from one solution to another (or from a pure solvent to a solution).

This membrane represents a barrier through which some substances can pass and others cannot, as in the case of semipermeable membranes in the cell walls of animal and plant cells.

Osmotic pressure is then defined as the minimum pressure that must be applied to a solution to stop the passage of its pure solvent through a semi-permeable membrane.

It is also known as the measure of the tendency of a solution to receive the pure solvent due to the effect of osmosis. This property is colligative since it depends on the concentration of solute in the solution, which is expressed as a mathematical expression:

Π. V = n. R. T, or also π = M. R. T

In these expressions:

n = Number of moles of particles in the solution.

R = Universal gas constant (8.314472 J. K -1 . Mol -1 ).

T = Temperature in Kelvin.

M = Molarity.