# Raoult’s Law and Phase Equilibria

## Raoult's Law

Raoult’s law states that the vapour pressure of a solvent above a solution is equal to the vapour pressure of the pure solvent at the same temperature ´ the mole fraction of the solvent present.

Any liquid is involved in the equilibrium X(l) e X(g). This also happens to a lesser degree on the surface of a solid. This is called phase equilibrium, because the only thing changing is the phase that the substance is in. This leads to the conclusion that there is a vapour present above any liquid or solid. This can be observed with a bottle of ethanol – the smell of the alcohol is noticeable when the bottle is opened.

The vapour pressure of a liquid is the pressure exerted by the vapour above the liquid. This is affected by the volatility of the liquid in question (a more volatile liquid will have a higher vapour pressure) and the temperature (the vapour pressure increases with temperature). Boiling point can be related to vapour pressure – a lower boiling point means that the liquid is more volatile and therefore has a greater vapour pressure.

Ideal mixtures show a straight line on a (composition, vapour pressure) graph – i.e. they obey Raoult’s law. They tend to be liquids with similar intermolecular bonding – i.e. ones with similar structure. Examples of ideal mixtures are hexane and pentane, or propan-1-ol and propan-2-ol. A graph of boiling point against composition looks similar, but the line slopes in the opposite direction.

## Deviations from Raoult’s Law

### Positive Deviations

For a positive deviation, the vapour pressure for a given mixture is greater than would be expected (and therefore the boiling point is lower). Because the vapour pressure is higher, the liquid is evaporating more easily than would be expected. This means that some of the intermolecular bonds in the liquid must have been broken when the liquids were mixed. Examples:

ethanol and water – the ethanol molecules have an average of 1 hydrogen bond per molecule, whereas the water molecules have 2. The ethanol molecules interfere with the hydrogen bonds and therefore make the liquid more volatile.

ethanol and benzene – the hydrogen bonding in the ethanol is reduced by the presence of the benzene.

### Negative Deviations

The vapour pressure is lower than would be expected from Raoult’s Law – i.e. the intermolecular forces increase when the liquids are mixed. This is generally because molecules where no hydrogen bonding is present are mixed to form a liquid with hydrogen bonds. Examples:

trichloromethane and ethoxyethane – CHCl3 has a polar hydrogen atom but no lone pairs and therefore cannot form hydrogen bonds. C2H5-O-C2H5 has lone pairs on the oxygen but no polar hydrogen atom and therefore cannot form hydrogen bonds. When mixed, hydrogen bonds form, decreasing the vapour pressure.

## Vapour and mixture composition in boiling mixtures

### Ideal Mixtures

If mixture X is boiled, the vapour has composition Y and the liquid remaining in the flask has composition Z. The upper line represents the composition of the vapour of different mixtures of the two liquids and the lower line shows the composition of the remaining liquid from each of the boiling liquids.

### Fractional Distillation

Fractional distillation consists of repeated evaporations followed by condensations. Each evaporation and condensation of the vapour results in an enrichment of component B (the more volatile component). Therefore, the vapour produces pure B. Repeated evaporations and condensations will also result in the liquid being enriched with component A. Thus the liquid produces pure A.

### Mixtures with a negative deviation

The point marked Z (the mixture with the highest boiling point) is referred to as the azeotropic mixture or azeotrope. At this point, the composition of the vapour is equal to the composition of the liquid left (and thus both are the azeotrope). If fractional distillation is carried out on a mixture with negative deviation, then the vapour produces pure product, the nature depending on the side of the azeotropic point where the initial mixture is located (see diagram). Fractional distillation of X leads to pure B product, whereas the liquid is left as pure azeotrope. Distillation of Y leads to pure A product in the vapour and the azeotrope in the liquid.

### Positive deviation

Again, the point with the lowest boiling point is the azeotropic point. If X is distilled, the vapour produces the azeotrope and the liquid pure B, whereas when Y is distilled, the vapour produces azeotrope and the liquid pure A.

It is also possible to draw composition lines on the graphs for vapour pressure. These are on the other side of the curve for those for boiling point, but otherwise are the same. The diagrams show the same products from fractional distillation that would be shown on the boiling point graphs. This confirms the result given above.