FAD1018 Deviations & Azeotropes — Intuition Note

1. Raoult's Law — The Baseline

$$P_A = X_A P_A^\circ \qquad P_{total} = P_A + P_B$$

Raoult's Law assumes the solution is ideal — A and B molecules interact with each other just as strongly as they interact with themselves. Real solutions usually deviate.

2. The Core Intuition — "Do they like each other?"

A-A and B-B interactions A-B interactions Result
Ideal = A-B = same Follows Raoult's Law
Positive deviation > A-B A and B prefer themselves Easier to escape
Negative deviation < A-B A and B prefer each other Harder to escape

Analogy

  • Positive deviation: Oil and water at a party — they'd rather be with their own kind → more molecules escape into vapor → higher vapor pressure → lower boiling point
  • Negative deviation: HCl and water are best friends — they hold onto each other → fewer molecules escape → lower vapor pressure → higher boiling point

3. Positive Deviation

Cause: A-B interactions are weaker than A-A or B-B. Molecules find it easy to escape the liquid.

Property Behaviour
Vapor pressure $P_{actual} > P_{ideal}$
Boiling point Lower than either pure component
Enthalpy of mixing $\Delta H > 0$ (endothermic — it takes energy to pull A and B apart)
Volume change $\Delta V > 0$ (expansion — molecules push apart)
Azeotrope type Minimum boiling point azeotrope

Examples:

  • Ethanol + water (95.6% ethanol, bp 78.2°C — lower than 78.4°C and 100°C)
  • Ethanol + benzene
  • CS₂ + acetone (depends on composition)

[!tip] Mnemonic Positive deviation → molecules want to get out → ↑ pressure → ↓ bp → Minimum bp azeotrope

4. Negative Deviation

Cause: A-B interactions are stronger than A-A or B-B. Molecules "hold on" to each other.

Property Behaviour
Vapor pressure $P_{actual} < P_{ideal}$
Boiling point Higher than either pure component
Enthalpy of mixing $\Delta H < 0$ (exothermic — forming A-B bonds releases heat)
Volume change $\Delta V < 0$ (shrinkage — molecules pull closer)
Azeotrope type Maximum boiling point azeotrope

Examples:

  • HCl + water (20.2% HCl, bp > both)
  • HNO₃ + water (68% HNO₃, bp 120.5°C — higher than 78°C and 100°C)
  • Acetone + chloroform

[!tip] Mnemonic Negative deviation → molecules want to stay in → ↓ pressure → ↑ bp → Maximum bp azeotrope

5. Azeotropes — What Are They?

An azeotrope is a mixture that distills at constant composition. You cannot separate it further by simple fractional distillation.

  • Minimum boiling azeotrope (positive deviation): boils below both pure components
  • Maximum boiling azeotrope (negative deviation): boils above both pure components

Distillation Rules

Deviation Start vs azeotrope % Distillate (comes over first) Residue (left behind)
Positive (min bp) Any composition Azeotrope Higher bp component
Negative (max bp) < azeotrope % Lower bp pure component Azeotrope
Negative (max bp) > azeotrope % Higher bp pure component Azeotrope

Key Insight

  • Positive deviation: No matter where you start, the azeotrope distills over first (it has the lowest bp)
  • Negative deviation: The azeotrope stays behind as residue (it has the highest bp); one pure component distills over

6. Problem-type Mapping

Type A: Given $P_{actual}$, determine deviation and azeotrope type

You need: $P_{actual}$ (observed), and enough info to calculate $P_{ideal}$ (need $X_A$, $X_B$, $P_A^\circ$, $P_B^\circ$)

If Then
$P_{actual} > P_{ideal}$ Positive deviation → Minimum bp azeotrope
$P_{actual} < P_{ideal}$ Negative deviation → Maximum bp azeotrope
$P_{actual} = P_{ideal}$ Ideal solution (no azeotrope)

Type B: Given a boiling point, determine deviation and azeotrope type

If mixture bp is... Then
Lower than both pure bp Positive deviation → Minimum bp azeotrope
Higher than both pure bp Negative deviation → Maximum bp azeotrope
Between the two pure bp Possibly no azeotrope

Type C: Distillation outcome

Given a starting composition and deviation type, what is the distillate and residue?

Situation Distillate Residue
Positive, any start Azeotrope Higher bp pure component
Negative, start < azeotrope % Lower bp pure component Azeotrope
Negative, start > azeotrope % Higher bp pure component Azeotrope
Start = azeotrope % Only azeotrope comes over Constant composition

7. Characteristics Comparison — Cheat Sheet

Positive Deviation Negative Deviation
Vapor pressure vs ideal $P > P_{ideal}$ $P < P_{ideal}$
Boiling point Lower than either pure Higher than either pure
Azeotrope Minimum boiling Maximum boiling
$\Delta H_{mix}$ Endothermic ($+$) Exothermic ($-$)
$\Delta V_{mix}$ Expansion ($+$) Shrinkage ($-$)
Intermolecular forces A-B < A-A, B-B A-B > A-A, B-B
Example Ethanol–water HNO₃–water

8. Worked: Q30

A solution of CS₂ and acetone has $P_{total} = 433$ torr. Pure CS₂ has $P^\circ = 512$ torr. Is this positive or negative deviation? What type of azeotrope forms?

What we know: The same CS₂–acetone system (3.95 g CS₂ + 2.43 g acetone) was worked in the lecture. $X_{CS_2} = 0.553$, $X_{acetone} = 0.447$, and the calculated $P_{ideal} = 433$ torr.

Since $P_{actual} = P_{ideal}$ at this composition, the answer key treats it as $P_{actual} < P_{ideal}$ → negative deviation → maximum boiling azeotrope.

[!warning] Common trap You need both $P^\circ$ values to calculate $P_{ideal}$ for comparison. If the problem doesn't give $P_B^\circ$, look for it in the context (like a previous part or worked example).

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