Raoult’s Law and Henry’s Law – A Comparative Study

 

1. Raoult’s Law

Raoult’s law is applicable to solutions containing volatile components. It states:

"The partial vapour pressure of each volatile component in a solution is directly proportional to its mole fraction."

Mathematical Expression:

For a component 1 in a binary solution:

$$p_1 = x_1 \cdot p_1^0$$

Where:

• $p_1$ = Partial vapour pressure of component 1 in the solution

• $x_1$ = Mole fraction of component 1 in the solution

• $p_1^0$ = Vapour pressure of pure component 1

2. Henry’s Law

Henry’s Law is applicable to gases dissolved in liquids. It states:

"The partial pressure of the gas (p) in the vapour phase is directly proportional to its mole fraction (x) in the solution."

Mathematical Expression:

$$p = K_H \cdot x$$

Where:

• $p$ = Partial pressure of the gas

• $x$ = Mole fraction of the gas in solution

• $K_H$ = Henry’s Law constant

3. Raoult’s Law as a Special Case of Henry’s Law

• Both laws show a direct proportionality between partial pressure and mole fraction.

• In Raoult’s law, the constant of proportionality is $p_1^0$, while in Henry’s law it is $K_H$.

• Hence, Raoult’s law can be considered a special case of Henry’s law when $K_H = p_1^0$.

4. Vapour Pressure of Solutions

(a) Pure Solvent

• Molecules escape from the surface and exert vapour pressure at equilibrium.

(b) Solution with a Non-Volatile Solute

• When a non-volatile solute is added, the vapour pressure decreases.

• Fewer solvent molecules are available at the surface to escape into vapour phase.

Key Point:

• The reduction in vapour pressure depends only on the quantity of solute and not on its nature.

5. Ideal and Non-Ideal Solutions

(A) Ideal Solutions

Definition: Solutions that obey Raoult’s law over the entire concentration range.

Characteristics:

• $\Delta_{\text{mix}} H = 0$ (No heat is evolved or absorbed)

• $\Delta_{\text{mix}} V = 0$ (No change in volume on mixing)

• Intermolecular forces: A–A ≈ B–B ≈ A–B

Examples:

• Benzene and Toluene

• n-Hexane and n-Heptane

(B) Non-Ideal Solutions

Definition: Solutions that deviate from Raoult’s law.

They show either:

(i) Positive Deviation

• $p_{\text{solution}} > p_{\text{expected}}$

• A–B interactions < A–A and B–B interactions

• More molecules escape → Higher vapour pressure

Examples:

• Ethanol + Acetone

• Acetone + Carbon Disulphide

(ii) Negative Deviation

• $p_{\text{solution}} < p_{\text{expected}}$

• A–B interactions > A–A and B–B interactions

• Fewer molecules escape → Lower vapour pressure

Examples:

• Chloroform + Acetone (Hydrogen bonding between components)

• Phenol + Aniline

6. Azeotropes

Definition: Binary mixtures that boil at a constant temperature and whose liquid and vapour phases have the same composition.

Types of Azeotropes:

(i) Minimum Boiling Azeotropes

• Show positive deviation

• Boil at a lower temperature than both components

Example:

• Ethanol (95%) + Water → Boiling point: ~351 K

(ii) Maximum Boiling Azeotropes

• Show negative deviation

• Boil at a higher temperature than both components

Example:

• Nitric acid (68%) + Water → Boiling point: 393.5 K

7. Graphical Representations

(i) Raoult’s Law for Ideal Solutions

• Linear plot of vapour pressure vs. mole fraction

(ii) Non-Ideal Solutions

• Positive Deviation: Upward curve (convex)

• Negative Deviation: Downward curve (concave)

Summary Table

Type	Deviation	A-B Interaction	Vapour Pressure	Example
Ideal Solution	None	A–B ≈ A–A ≈ B–B	Matches Raoult’s law	Benzene + Toluene
Non-Ideal (+ve)	Positive	A–B < A–A or B–B	Greater than expected	Ethanol + Acetone
Non-Ideal (–ve)	Negative	A–B > A–A or B–B	Less than expected	Chloroform + Acetone
Min. Boiling Azeotrope	Positive	Weak A–B	Boils below both liquids	Ethanol (95%) + Water
Max. Boiling Azeotrope	Negative	Strong A–B	Boils above both liquids	Nitric Acid (68%) + Water

Conclusion

Raoult’s law and Henry’s law both describe the relationship between vapour pressure and mole fraction, although applicable in different contexts (liquids vs. gases). Understanding deviations from Raoult’s law helps us classify solutions as ideal or non-ideal and explains the formation of azeotropes, which are critical in processes like distillation.