Positive Deviations from Raoult's Law

Introduction

An ideal mixture follows a straight Raoult-law pressure line between pure-component endpoints. Some real mixtures have higher vapour pressure than that line at intermediate compositions. This is a positive deviation. A common qualitative explanation is that unlike A–B attractions are, on average, less favourable than the like–like contacts they replace, so molecules escape the mixed liquid more readily. The measured curve, not the slogan, establishes the deviation.

Core explanation

At a specified temperature, calculate the ideal reference ptotal,ideal = xA pA° + xB pB°. Measure the actual equilibrium total vapour pressure for a liquid at the same composition and temperature. If ptotal,actual > ptotal,ideal, the total pressure shows positive deviation. One or both component partial pressures may contribute to the excess; a total pressure comparison alone does not reveal each partial pressure separately. At pure endpoints the actual and reference pressure coincide by definition, so a positive-deviation curve rises above the line mainly at intermediate mixtures.

For instance, pA° = 60 kPa and pB° = 20 kPa at a stated temperature. At xA = 0.50, the ideal total is 0.50(60) + 0.50(20) = 40 kPa. If the measured equilibrium pressure is 46 kPa, the excess is 6 kPa. This is a positive total-pressure deviation. It would be wrong to assign all 6 kPa to A without separate vapour-composition or component-pressure data.

The interaction picture begins with pure liquids having A–A and B–B contacts. Mixing replaces some with A–B contacts. If the new contacts are weaker on average, molecules can be less tightly retained by the liquid than the ideal model anticipates, making vapour escape thermodynamically more favourable. Mixing may absorb heat and expand in many such systems, but neither sign should be announced as a universal theorem based solely on one pressure measurement. A full thermodynamic description may need enthalpy, volume, composition and temperature data.

Ethanol–water is a widely discussed example of positive deviation from Raoult's law over relevant composition ranges. The explanation is not simply that ethanol and water cannot hydrogen-bond; they can. Rather, mixing disrupts networks and changes the balance of interactions and molecular organisation. An actual ethanol–water vapour-pressure curve must be used for precise distillation predictions, because treating this system as ideal can miss its azeotropic behaviour.

At suitable pressure, a strong positive deviation can create a maximum in total vapour pressure at a particular composition. Because boiling occurs when vapour pressure reaches the external pressure, that pressure maximum corresponds to a local minimum in boiling temperature. If vapour and liquid compositions are equal there, the mixture is a minimum-boiling azeotrope. Not every positive deviation produces an azeotrope: the pressure curve must have a suitable extremum. The next azeotrope page examines this in detail.

Deviation is defined relative to a model under controlled conditions. An apparently high gauge pressure because a closed flask contains air, or because the actual temperature is warmer, does not prove positive deviation. Compare component-compatible equilibrium measurements at identical temperature and specified liquid composition. Likewise evaporation rate is not the definition; pressure at equilibrium is.

Step-by-step reasoning

1. Read pA° and pB° at the mixture temperature and calculate the ideal pressure at the given liquid x values. 2. Compare with the measured equilibrium pressure after accounting for other gases. 3. Call the deviation positive only if actual pressure exceeds the ideal reference. 4. Use weaker average unlike interactions as a qualitative interpretation, not as a measured bond-energy value. 5. Check whether the curve has a pressure maximum before discussing a minimum-boiling azeotrope.

Visual explanation

Draw a composition axis from pure B to pure A. Connect pB° and pA° with a straight ideal line. Above it draw an actual curve that touches the endpoints and arches upward in the middle. Mark one x value where vertical separation is +6 kPa. Add a note “same temperature, liquid composition, equilibrium” so the plotted difference is a real model deviation.

Real-world analogy

Imagine two teams whose members work smoothly within each team but coordinate less effectively when intermixed. The mixed arrangement is easier to disrupt than a simple average would predict. That resembles weaker unlike molecular attraction and easier vapour escape, although real molecules have energies and configurations rather than social preferences.

Real-world example

An engineer measuring a solvent blend finds a vapour pressure higher than the mole-fraction-weighted average of the pure-liquid pressures at the same temperature. Designing a distillation from the ideal straight line would underestimate vapour pressure at that composition. The engineer uses measured vapour–liquid equilibrium data, especially if a pressure maximum or azeotrope might limit separation.

Why?

Why does a pressure maximum matter for boiling? At a fixed external pressure, a liquid boils when its equilibrium vapour pressure reaches that pressure. A composition with unusually high vapour pressure at a given temperature can reach the boiling condition at a lower temperature than nearby compositions.

Common misconception

“Positive deviation means both liquids are individually more volatile after mixing by a fixed percentage.” The deviation may vary strongly with composition, and total-pressure data do not by themselves show each component's separate contribution. It is a comparison with an ideal reference, not a constant multiplier.

Worked example

At 300 K, pure A has pA° = 50 kPa and pure B pB° = 30 kPa. At liquid xA = 0.40, ideal ptotal = 0.40(50) + 0.60(30) = 20 + 18 = 38 kPa. A measured equilibrium total vapour pressure of 42 kPa is 4 kPa above ideal, so it is a positive deviation. A measured 42 kPa taken at a different temperature would not support this conclusion; the reference and measurement must share temperature.

Quick check

1. A solution has actual pressure below its ideal pressure at the same conditions. Is that positive deviation? Answer: No. Pressure below the ideal reference is a negative deviation.

Exam focus

Compute the ideal reference before labelling a deviation. State conditions, give a cautious molecular explanation and distinguish a generally raised pressure from the specific maximum needed for a minimum-boiling azeotrope.

Advanced insight

Positive deviation can be expressed through activities: ai > xi for a component with positive activity coefficient in an appropriate liquid-state convention. Because partial pressures are linked to activities, measured vapour data can reveal nonideal chemical potentials. A total-pressure curve alone is insufficient to reconstruct every activity coefficient without additional composition information.

Summary

Positive deviation means measured equilibrium vapour pressure exceeds the Raoult-law ideal prediction at the same liquid composition and temperature. Weaker average unlike interactions provide a useful qualitative picture. A sufficiently strong pressure maximum can support a minimum-boiling azeotrope, but positive deviation alone does not guarantee one.

Practice questions

1. Ideal total pressure is 35 kPa and actual is 39 kPa. Identify the deviation. Answer: Positive by 4 kPa, provided composition and temperature match. 2. Does a positive pressure deviation prove a minimum-boiling azeotrope exists? Answer: No. A suitable pressure maximum and equality of vapour and liquid composition are needed. 3. Why can warmer sample temperature mimic apparent positive deviation if ignored? Answer: Pure and mixture vapour pressures rise with temperature, so a warm measurement compared with a cooler reference is not a valid same-condition comparison.