Ideal and Non-Ideal Solutions

So far, we have been applying Raoult’s law as though every liquid mixture obeys it perfectly. But does every mixture really follow Raoult’s law across all compositions? Some do, and those well-behaved mixtures earn the label “ideal solutions.” Most real mixtures, however, break the rules to some degree. Understanding why certain solutions deviate from Raoult’s law, and what consequences those deviations bring, is the focus of this topic.

What Makes a Solution Ideal

A solution qualifies as ideal when it obeys Raoult’s law over the entire range of concentration, from pure component A all the way to pure component B.

Beyond obeying Raoult’s law, an ideal solution has two additional signature properties:

• Zero enthalpy of mixing: $\Delta_{\text{mix}}H = 0$. No heat is absorbed or released when the two pure liquids are combined. The mixing process is energetically neutral.
• Zero volume of mixing: $\Delta_{\text{mix}}V = 0$. The volume of the solution equals the sum of the volumes of the two pure components. There is no expansion or contraction.

$\Delta_{\text{mix}}H = 0, \qquad \Delta_{\text{mix}}V = 0 \qquad \text{(1.21)}$

These two conditions follow directly from what is happening at the molecular level.

The Molecular Picture Behind Ideal Behaviour

Consider two liquids, A and B. In their pure forms, the intermolecular attractions are A-A (between molecules of A) and B-B (between molecules of B). When the two are mixed, a new type of interaction appears: A-B.

An ideal solution forms when the A-B attractive forces are nearly equal in strength to the A-A and B-B forces. In this situation, a molecule of A surrounded by molecules of B feels roughly the same pull as it would feel if surrounded by other A molecules. From the molecule’s perspective, the environment has barely changed.

Because the forces are balanced:

• No energy is needed to break old interactions, and no energy is released forming new ones, so $\Delta_{\text{mix}}H = 0$.
• Molecules pack together in the mixture the same way they pack in the pure liquids, so $\Delta_{\text{mix}}V = 0$.
• Each component escapes from the surface at exactly the rate Raoult’s law predicts.

A perfectly ideal solution is rare in practice, but some pairs of liquids come very close:

• $n$-hexane and $n$-heptane (both are straight-chain alkanes with similar London dispersion forces)
• Bromoethane and chloroethane (nearly identical molecular shapes and polarities)
• Benzene and toluene (structurally similar aromatic hydrocarbons)

The common thread is that these pairs are chemically and structurally similar, so their intermolecular forces match up well.

When Solutions Break the Rules: Non-Ideal Behaviour

A non-ideal solution is any solution that does not obey Raoult’s law across the full concentration range. Its actual vapour pressure is either higher or lower than what Raoult’s law predicts.

• If the actual vapour pressure is higher than predicted, the solution shows positive deviation.
• If the actual vapour pressure is lower than predicted, the solution shows negative deviation.

Fig 1.6: (a) A solution showing positive deviation: the actual vapour pressure curves (solid lines) lie above the ideal Raoult’s law lines (dashed). (b) A solution showing negative deviation: the actual curves dip below the ideal lines

The reason behind each type of deviation lies in how the A-B intermolecular forces compare with the A-A and B-B forces.

Positive Deviation: Weaker A-B Forces

Positive deviation occurs when the A-B interactions are weaker than the A-A or B-B interactions. In this scenario, molecules in the mixture are held less tightly than they were in their respective pure liquids. They find it easier to escape from the liquid surface into the vapour phase, which pushes the vapour pressure above the Raoult’s law prediction.

Ethanol and Acetone: A Classic Example

In pure ethanol, molecules are held together by hydrogen bonds (the $O{-}H$ group on one molecule forms a hydrogen bond with the oxygen on a neighbouring molecule). These are relatively strong intermolecular forces.

When acetone is added to ethanol, the acetone molecules get in between the ethanol molecules. Acetone cannot form hydrogen bonds with ethanol as effectively as ethanol molecules do with each other. As a result, some of the ethanol-ethanol hydrogen bonds are broken without being replaced by equally strong interactions.

The net effect: molecules escape more easily, the vapour pressure rises above the ideal value, and the solution shows positive deviation from Raoult’s law.

Carbon Disulphide and Acetone: Another Positive Deviation Pair

In pure acetone, dipole-dipole interactions hold the molecules together. In pure carbon disulphide ($CS_2$), the molecules interact through London dispersion forces. When the two are mixed, the cross-interactions between acetone and $CS_2$ molecules are weaker than either set of like-interactions. The result is the same: easier escape, higher vapour pressure, positive deviation.

Negative Deviation: Stronger A-B Forces

Negative deviation occurs when the A-B interactions are stronger than the A-A and B-B interactions. Molecules in the mixture are held more tightly than they were in the pure liquids. Escaping becomes harder, so the vapour pressure drops below the ideal prediction.

Phenol and Aniline: Forming Stronger Cross-Bonds

In a mixture of phenol and aniline, the hydrogen on phenol’s $-OH$ group forms a hydrogen bond with the lone pair on the nitrogen atom of aniline. This intermolecular hydrogen bond between the two different molecules turns out to be stronger than the hydrogen bonds that exist within pure phenol alone or pure aniline alone.

Because the A-B forces are stronger, molecules are held back more firmly, fewer escape per unit time, and the vapour pressure falls below the Raoult’s law line.

Chloroform and Acetone: A Textbook Case of Negative Deviation

Chloroform ($CHCl_3$) has a hydrogen atom bonded to carbon, and the three chlorine atoms pull electron density away from this hydrogen, making it partially positive. Acetone has a carbonyl group ($C{=}O$) with an electron-rich oxygen atom.

When these two liquids are mixed, the partially positive hydrogen on chloroform forms a hydrogen bond with the partially negative oxygen on acetone. This new A-B hydrogen bond is stronger than the interactions that existed in either pure liquid.

The stronger attraction reduces the escaping tendency of both components, the vapour pressure dips below the ideal curve, and the solution shows negative deviation from Raoult’s law.

Azeotropes: When Deviations Become Extreme

When a solution shows a particularly large deviation from Raoult’s law, something remarkable happens at a specific composition: the liquid and vapour phases end up with exactly the same composition. Such a mixture is called an azeotrope (a binary mixture that has identical liquid and vapour compositions and boils at a constant temperature).

Because the liquid and vapour have the same makeup, boiling the azeotrope simply produces vapour of the same composition. Condensing that vapour gives back the same liquid. Fractional distillation, which relies on composition differences between liquid and vapour, becomes powerless. The two components cannot be separated beyond the azeotropic composition by ordinary distillation.

There are two types of azeotropes, each linked to the type of deviation that produces it.

Minimum Boiling Azeotrope (from Large Positive Deviation)

Solutions with large positive deviation have vapour pressures that bulge significantly above the ideal line. At the azeotropic composition, the vapour pressure reaches a maximum. Since higher vapour pressure means easier boiling, this composition boils at a temperature lower than either pure component. Hence the name “minimum boiling azeotrope.”

Example: The ethanol-water system. When sugars are fermented, the resulting ethanol-water mixture can be fractionally distilled, but the separation stops at about 95% ethanol by volume. At this composition, the mixture reaches its azeotrope. The liquid and vapour have the same composition, and no further enrichment of ethanol is possible through ordinary distillation.

Maximum Boiling Azeotrope (from Large Negative Deviation)

Solutions with large negative deviation have vapour pressures that dip well below the ideal line. At the azeotropic composition, the vapour pressure reaches a minimum. A lower vapour pressure means the liquid resists boiling, so this composition boils at a temperature higher than either pure component. This is a “maximum boiling azeotrope.”

Example: The nitric acid-water system. This pair forms a maximum boiling azeotrope with an approximate composition of 68% nitric acid and 32% water by mass. The boiling point of this azeotrope is 393.5 K, which is higher than the boiling point of either pure water (373 K) or pure nitric acid.

Connecting the Dots

Feature	Ideal solution	Positive deviation	Negative deviation
Raoult’s law	Obeyed across all compositions	Vapour pressure above predicted	Vapour pressure below predicted
A-B vs A-A, B-B forces	Nearly equal	A-B weaker	A-B stronger
$\Delta_{\text{mix}}H$	Zero	Positive (endothermic)	Negative (exothermic)
$\Delta_{\text{mix}}V$	Zero	Positive (expansion)	Negative (contraction)
Azeotrope type (if large deviation)	None	Minimum boiling	Maximum boiling
Example pairs	$n$-hexane + $n$-heptane; benzene + toluene	Ethanol + acetone; $CS_2$ + acetone	Chloroform + acetone; phenol + aniline

The key takeaway is straightforward: how molecules interact with each other determines everything. When A-B forces match the pure-component forces, you get ideal behaviour. When they are weaker, molecules escape too easily (positive deviation). When they are stronger, molecules are held back (negative deviation). Large enough deviations create azeotropes, mixtures that distillation alone cannot fully separate.