Solutions · Lesson 5 of 11
Ideal Solutions, Deviations and Azeotropes
“Explain real mixture behaviour using molecular interactions and interpret the limits of separation by distillation.”
• State the defining properties of an ideal solution. • Explain positive and negative deviations from Raoult’s law. • Relate interaction changes to mixing enthalpy and volume in the simple model. • Interpret measured pressure data and distinguish both types of azeotrope.
What ideality means at molecular and visible scales
Raoult’s law is a useful benchmark because it predicts an entire pressure curve from pure-component pressures and liquid composition. An ideal solution follows that benchmark for each component across the full composition range. At the molecular scale, unlike A–B contacts have approximately the same energetic effect as the A–A and B–B contacts replaced during mixing. Mixing does not substantially favour or disfavor escape into vapour compared with that reference.
Zero mixing enthalpy means the ideal mixing process absorbs or releases no net heat at constant pressure. Zero mixing volume means component volumes add. Neither condition means molecules do not interact: they interact before and after mixing, with similar average effects. Mixing can still be favoured because the components become dispersed among one another. Real examples such as benzene–toluene, n-hexane–n-heptane and chloroethane–bromoethane are often approximately ideal, rather than perfect at every measurable precision.
Positive deviation: escaping becomes easier
A positive deviation occurs when a component’s actual partial vapour pressure exceeds xᵢpᵢ° at the same temperature and composition. In the usual simple interaction picture, unlike contacts are less favourable on average than the contacts disrupted. Molecules then have a greater escaping tendency. The total pressure lies above the ideal sum when both component deviations are positive. Mixing commonly absorbs heat and can increase volume in such systems.
In ethanol–acetone mixtures, adding acetone disrupts part of the ethanol hydrogen-bond network. New contacts form too, but their overall effect can be weaker than the interactions replaced. Acetone–carbon disulfide is another positive-deviation example: adding a non-polar component weakens the average network of dipolar contacts in acetone. A molecule’s ability to make one kind of attraction is not enough to predict the net deviation without comparing both pure liquids with the mixture.
Negative deviation: unlike contacts are more favourable
A negative deviation occurs when actual component pressure is below the ideal prediction. Stronger average A–B attractions make escape less favourable, commonly releasing heat on mixing and contracting the liquid. Phenol and aniline can form a strong hydrogen bond between phenol’s O–H group and the nitrogen lone pair. Chloroform and acetone provide another example: the polarised C–H bond of chloroform can interact with the carbonyl oxygen of acetone.
A dashed O···H contact between acetone and chloroform represents an intermolecular attraction, not a newly formed O–H covalent bond or a reaction converting the liquids into one compound. Atom identities and connectivity remain unchanged in this physical mixing picture.
| Feature | Ideal model | Positive-deviation example | Negative-deviation example |
|---|---|---|---|
| Pressure relative to Raoult prediction | Equal | Higher | Lower |
| Average unlike contacts | Comparable to replaced contacts | Less favourable | More favourable |
| Typical ΔmixH | Zero | Positive | Negative |
| Typical ΔmixV | Zero | Often positive | Often negative |
| Examples | Benzene–toluene | Ethanol–acetone; acetone–CS₂ | Phenol–aniline; acetone–CHCl₃ |
The signs of volume changes and pressure deviations are not universal substitutes for measured data. The simple picture explains many mixtures in this chapter; real mixtures may show more complex composition and temperature dependence. Define the pressure deviation by comparison with Raoult’s law, not by assuming a volume-change sign.
Problem
At 328 K, pure acetone and chloroform pressures are 741.8 and 632.8 mm Hg. At liquid acetone fraction 0.508, measured component pressures are 322.7 and 257.7 mm Hg. Determine the deviation.
- 1.Ideal acetone pressure =0.508×741.8=376.8344 mm Hg. Ideal chloroform pressure =0.492×632.8=311.3376 mm Hg.
- 2.Ideal total=688.1720 mm Hg, while measured total=322.7+257.7=580.4 mm Hg.
- 3.Both measured component pressures and their sum lie below the ideal predictions: this composition shows negative deviation.
- 4.Plot the liquid fraction on the horizontal axis and pressure in mm Hg on the vertical axis. Join measured points only as an aid to seeing the trend; do not label an invented interpolation as additional measurements.
| x(acetone) | Measured p(acetone) / mm Hg | Measured p(chloroform) / mm Hg | Measured total / mm Hg |
|---|---|---|---|
| 0 | 0 | 632.8 | 632.8 |
| 0.118 | 54.9 | 548.1 | 603.0 |
| 0.234 | 110.1 | 469.4 | 579.5 |
| 0.360 | 202.4 | 359.7 | 562.1 |
| 0.508 | 322.7 | 257.7 | 580.4 |
| 0.582 | 405.9 | 193.6 | 599.5 |
| 0.645 | 454.1 | 161.2 | 615.3 |
| 0.721 | 521.1 | 120.7 | 641.8 |
Why an azeotrope stops ordinary fractional separation
Distillation enriches a collected vapour when its composition differs from the boiling liquid. At an azeotropic composition, vapour and liquid have the same composition at the chosen pressure. Boiling then removes the components in the same ratio as they remain in the liquid, so ordinary fractional distillation cannot separate that composition further. An azeotrope is a mixture, not a pure compound with a fixed chemical formula; its composition can depend on pressure.
A liquid mixture that boils at a constant temperature at a specified pressure with equilibrium vapour and liquid of the same composition.
A sufficiently strong positive deviation may produce an interior maximum in total vapour pressure at fixed temperature. Such enhanced volatility corresponds to a minimum-boiling azeotrope at fixed pressure. A sufficiently strong negative deviation may produce a pressure minimum and a maximum-boiling azeotrope. A small deviation need not produce either: the existence of an azeotrope requires a special composition at which vapour and liquid fractions coincide.
Ethanol–water has a minimum-boiling azeotrope that limits the ethanol enrichment achievable by ordinary fractional distillation at atmospheric pressure. Its composition is near the high-ethanol end; approximate percentages must state whether they are by mass or volume. Nitric acid–water has a maximum-boiling azeotrope near 68% nitric acid by mass, boiling near 393.5 K at atmospheric pressure. These opposite examples connect interaction strength to phase behaviour.
Problem
At a specified pressure, a liquid has x(A)=0.40. Its equilibrium vapour has y(A)=0.65 in one experiment and y(A)=0.40 in another. Interpret the two observations.
- 1.In the first experiment, vapour is richer in A, so collecting and condensing it changes composition. That observation is not azeotropic.
- 2.In the second, vapour and liquid compositions match. If the mixture boils at that constant composition and pressure, it exhibits azeotropic behaviour.
- 3.A boiling temperature by itself cannot establish an azeotrope; composition equality is the decisive condition.
Quick Quiz
Quiz
Which set describes ideal mixing?
Explanation: Ideal mixing replaces contacts with energetically comparable contacts and obeys Raoult’s law; interactions remain present.
Measured total pressure is below the Raoult prediction at the same temperature and composition. This is:
Explanation: Negative deviation is defined by lower measured pressure relative to the ideal prediction.
Which attraction helps explain acetone–chloroform negative deviation?
Explanation: The O···H contact strengthens unlike attractions without changing the molecules into a single compound.
What defines an azeotropic boiling mixture at a given pressure?
Explanation: Composition equality means that vapour removal does not enrich either component at that composition.
A strong positive deviation can produce which azeotrope?
Explanation: Enhanced escaping tendency can create a total-pressure maximum at fixed temperature and a minimum-boiling azeotrope at fixed pressure.
Practice Problems
- Explain why a mixture can be approximately ideal even though its molecules attract one another.
- At x(acetone)=0.360 and 328 K, measured pressures are 202.4 and 359.7 mm Hg. Use pure pressures 741.8 and 632.8 mm Hg to determine the deviation.
- How does the sign of mixing enthalpy help explain common positive and negative deviations?
- Why can repeated ordinary fractional distillation not purify an azeotropic mixture into either component at the same pressure?
- Compare ethanol–water and nitric acid–water azeotropes and explain why “all non-ideal solutions form azeotropes” is incorrect.
Ideality compares the energetic effects of unlike and like contacts; it does not remove attractions. When A–B contacts replace A–A and B–B contacts with approximately equal effects, mixing enthalpy and volume changes are near zero and Raoult behaviour is approached.
Key Takeaways
• An ideal solution follows Raoult’s law for each component across the full composition range. • Ideal mixing has zero enthalpy and volume change without implying zero interactions. • Positive deviation means higher vapour pressure than the ideal prediction. • Negative deviation means lower pressure, often explained by stronger unlike contacts. • Measured pressure data should be compared at the same temperature and composition. • An azeotrope has identical vapour and liquid composition at its boiling condition. • Strong positive or negative deviation can yield minimum- or maximum-boiling azeotropes respectively.