Abnormal Molecular Mass

In chemistry, an abnormal molar mass occurs when the observed molar mass of a substance is either higher or lower than its expected value. This deviation arises due to the association or dissociation of solute molecules in a solution, affecting properties such as boiling point elevation, freezing point depression, relative vapor pressure reduction, and osmotic pressure. The Van’t Hoff factor accounts for these anomalies in molar mass calculations.

The Van’t Hoff factor helps quantify these deviations and correct abnormal molar masses.

Jacobus Henricus Van’t Hoff, a Dutch physical chemist and the first Nobel Prize winner in Chemistry, introduced this factor to explain these anomalies. In electrolytic solutions, the observed Van’t Hoff factor is often lower than expected due to ion pairing, with the deviation increasing as ion charge increases.

1.0Causes of Abnormal Molar Mass

Association in a Solvent

Solute molecules interact with one another in a solution, leading to their association. This decreases the number of solute particles, thereby altering the colligative properties. As colligative properties depend on the number of solute particles rather than their nature, any reduction in particle count increases the molar mass.

For example, due to hydrogen bonding, acetic acid undergoes dimerization in non-polar solvents like benzene. Resultantly, the effective number of solute particles decreases, leading to an abnormally high molar mass. This phenomenon is more common in solvents with low dielectric constants.

Dissociation in a Solvent

When solute molecules dissolve in a solvent, they may dissociate into multiple ions or smaller particles. This increases the number of solute particles in the solution, enhancing colligative properties. Since molar mass is inversely related to colligative properties, an increase in solute particles leads to a lower observed molar mass.

For example, when weak electrolytes like hydrofluoric acid (HF) dissolve in water, they dissociate into hydrogen (H⁺) and fluoride (F⁻) ions, leading to a decrease in the observed molar mass.

2.0Van’t Hoff Factor and Abnormal Molar Mass

To quantify the effect of dissociation or association on molar mass, Jacobus Henricus Van’t Hoff introduced a correction factor known as the Van’t Hoff factor (i). It is defined as:

Alternatively, the factor can be expressed as:

3.0Formula for Abnormal Molar Mass

If n represents the number of dissociated particles and α is the degree of dissociation, then:

$i=1+(n-1)\alpha$

Thus, the corrected molar mass is given by:

Abnormal molar mass= Molar mass ​/ i

4.0Effect on Vapor Pressure and Boiling Point

When a non-volatile solute is added to a solvent, the vapor pressure of the solution decreases. This phenomenon, known as relative vapor pressure reduction, is directly proportional to the solute’s mole fraction. The reduction in vapor pressure is given by:

Reduction in vapor pressure = Pure solvent’s vapor pressure − Solution’s vapor pressure   

$Relativereduction=\frac{Reductioninvaporpressure}{Puresolvent’svaporpressure}$

Since boiling occurs when vapor pressure equals atmospheric pressure, a lower vapor pressure means the solution requires a higher temperature to boil. This leads to an increase in the boiling point, known as boiling point elevation.