Summary

Raoult's law gives a method of estimating the composition and pressure of the vapour above a liquid mixture. This article describes the basis of Raoult's law and provides an example of how to apply it.

Definitions

Dh:Hydraulic Diameter
:Partial Pressure
:Pure Partial Pressure
:Pressure
:Mole Fraction in Liquid


Raoult's law

Raoult's law states that the partial vapour pressure of a component above a liquid mixture is equal to the vapour pressure of the pure component multiplied by the mole fraction of the component in the liquid:

The total vapour pressure above a solution can then be estimated using Dalton's Law by taking the sum of the partial pressures for the individual components (as estimated by Raoult's Law).

Assumptions

In the form presented in this article Rauolt's relies on two assumptions of ideality:

  • the vapours form an ideal gas
  • the liquids form an ideal mixture
Vapour Pressure of a Mixture

Where the solution is not ideal, Raoult's law is most accurate for very high concentrations of a given component, see line section C-D on the graph above. For low concentrations, Henry's Law is better for approximating vapour pressure.

It should be noted that there can be both positive deviation and negative deviation from Raoult's law. Positive deviation as shown in the figure above indicates that cohesive forces between like molecules are greater than the adhesive forces between dissimilar molecules. Correspondingly negative deviation indicates that adhesive forces between dissimilar molecules are greater than cohesive forces between like molecules. Mixtures exhibiting this deviation from Raoult's law are said to be constant boiling point or azeotropic mixtures.



Examples

Basic Mixture

For a simple mixture with weak interaction we can expect Raoult's law to be a reasonably accurate approximation of vapor pressure. In this case we look at propane-butane mixture, as might be found in automotive LPG, for this example we assume a 50:50 ratio at 40°C:




This blend puts us comfortably in the middle of the of typical automotive LPG vapor pressure specifications.

Mixture with non-volatile solute

Where one component of the mixture is essentially non-volatile, for example salt or sugar in water, we can use Raoult's law to understand why the vapour pressure of the water is depressed.

For a solution which is 95 mol% water and 5 mol% sugar:






From this we can see that as we add additional sugar to the solution the vapor pressure of the water will be further depressed.



Further Reading

  1. Chemical Engineering Volume 2, Fifth Edition
  2. Perry’s Chemical Engineers’ Handbook, Eighth Edition