Raoult's law — ideal vs non-ideal solutions with examples

Question

State Raoult’s law. Distinguish between ideal and non-ideal solutions, giving one example of each and explaining why non-ideal behaviour occurs.

Solution — Step by Step

Raoult’s law: For a solution containing a volatile solute, the partial vapour pressure of each component is proportional to its mole fraction in the liquid phase.

p_A = x_A \cdot p_A^*

where $p_A$ is the partial vapour pressure of component A, $x_A$ is its mole fraction, and $p_A^*$ is the vapour pressure of pure A.

For a binary solution, the total pressure is:

P_{total} = p_A + p_B = x_A p_A^* + x_B p_B^*

An ideal solution obeys Raoult’s law over the entire composition range. This requires:

A–B interactions ≈ A–A and B–B interactions (similar molecules)
$\Delta H_{mix} = 0$ (no heat released or absorbed on mixing)
$\Delta V_{mix} = 0$ (total volume = sum of individual volumes)

Example: Benzene + toluene. Both are non-polar aromatic hydrocarbons; A–B forces are essentially the same as A–A and B–B forces.

The $p$ vs $x$ plot is a straight line from $p_B^*$ to $p_A^*$ .

When A–B interactions are weaker than A–A or B–B, molecules escape more easily from the liquid phase. Vapour pressure is higher than predicted by Raoult’s law — positive deviation.

Example: Ethanol + water. Ethanol breaks some of the strong hydrogen bonding network of water; the intermolecular forces weaken. Result: $p_{total} > x_A p_A^* + x_B p_B^*$ .

$\Delta H_{mix} > 0$ (endothermic mixing), $\Delta V_{mix} > 0$ (volume increases).

Acetone + carbon disulfide is another classic example in JEE.

When A–B interactions are stronger than A–A or B–B, molecules are held more tightly in the liquid. Vapour pressure is lower than predicted — negative deviation.

Example: Acetone + chloroform. Chloroform (H-bond donor) forms hydrogen bonds with the carbonyl oxygen of acetone (H-bond acceptor). The mixture has stronger forces than either pure component.

$\Delta H_{mix} < 0$ (exothermic mixing), $\Delta V_{mix} < 0$ (volume decreases).

HCl + water and HNO₃ + water also show large negative deviations.

Large positive or negative deviations lead to azeotropes — mixtures that boil at a constant temperature without change in composition.

Positive deviation azeotrope: ethanol–water (95.5% ethanol, bp 78.1°C) — minimum boiling
Negative deviation azeotrope: HCl–water (20.2% HCl, bp 108.6°C) — maximum boiling

Why This Works

Raoult’s law is essentially a thermodynamic consequence of ideal mixing: if all molecules experience the same intermolecular environment regardless of neighbours, the probability of a molecule escaping to the vapour phase is simply proportional to its mole fraction.

Non-ideality arises when this assumption fails — when A and B molecules interact differently than A–A or B–B pairs. The direction of deviation directly tells you whether mixing strengthens or weakens the intermolecular forces.

Alternative Method

A quick way to remember which deviation is which: think about what happens to vapour pressure. If mixing is endothermic (you had to input energy to mix), molecules are less “happy” in the liquid → they escape more → positive deviation. If mixing is exothermic, molecules prefer to stay in the liquid → negative deviation.

Common Mistake

Students often confuse the sign of deviation with the sign of $\Delta H_{mix}$ . Remember: positive deviation goes with positive $\Delta H_{mix}$ (endothermic) — more vapour, higher pressure. Negative deviation goes with negative $\Delta H_{mix}$ (exothermic) — less vapour, lower pressure. Getting these mixed up in NEET or JEE MCQs is one of the most common errors in the Solutions chapter.

In JEE Main, the solutions chapter typically contributes 2–3 marks. The most common question type gives you a pair of liquids and asks whether the vapour pressure of the mixture is greater than, less than, or equal to $x_A p_A^* + x_B p_B^*$ . The answer requires you to predict A–B vs A–A/B–B interaction strength.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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