Boiling-point elevation

Boiling-point elevation is the increase in temperature of the boiling point of a liquid that contains non-volatile solute. It is a colligative property: for dilute solutions of non-electrolytes, the difference in boiling point from that of the pure solvent is proportional to the amount of solute.

Ebullioscopy is the experimental technique that uses boiling-point elevation to measure the molecular weight of compounds. Tonometry is a related technique that directly measures the reduction in vapour pressure of the solution compared to that of the pure solvent. Both techniques are of historical interest only, although their development led to the formulation of Raoult's law.

Description

The boiling-point elevation ΔT_b is proportional to the molality of the solution m: the proportionality constant is called the ebullioscopic constant K_eb.

ΔT_b = K_ebm

The molality of the solution is the amount of solute divided by the mass of solvent. For dilute solutions, where the mass of the solution can be approximated by the mass of solvent, the molality is equal to the mass fraction w of solute divided by its molar mass M. Hence, the molar mass of a solute can be calculated from the boiling-point elevation by

M = K_ebw/ΔT_b

The same phenomenon can be described in terms of vapour pressure for any given temperature. If p₀ is the vapour pressure of the pure solvent and p is the vapour pressure of the solution:

(p₀ − p)/p₀ = K′_Rm

where K′_R is a constant that is specific for each solvent and m is the molality of the solution. French physical chemist François-Marie Raoult (1830–1901) investigated this relation in the 1880s, and found in 1887 that a single constant (K_R) for all solvents could be obtained by replacing the molality with the amount fraction of solute x, that is by dividing the molality by the molar mass of the solvent:

(p₀ − p)/p₀ = K_Rx

where K_R ≈ 1 (Raoult found a value of 1.05).

See also

• Freezing-point depression