Question

The vapour pressure of the solute in dilute solutions is proportional to the mole fraction of the solute in the liquid. This relationship is known as ______

• A. Gas law
• B. Dalton's law
• C. Henry's law
• D. Amagat's law

Hint:

In any dilute binary solution, always remember that the solvent obeys Raoult's Law (ideal behavior), while the solute obeys Henry's Law.
This is a standard concept tested frequently in thermodynamics and mass transfer.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks us to identify the name of the physical law that describes a relationship where the vapour pressure of a solute in a dilute solution is directly proportional to its mole fraction in the liquid phase.
This belongs to the core area of phase equilibria in chemical engineering thermodynamics, which deals with how components distribute between liquid and vapour phases.

Step 2: Key Formula or Approach:
For a dilute solution, the concentration of the solute approaches zero (\( x_i \rightarrow 0 \)).
Under these conditions, the partial pressure (or vapour pressure) of the solute in the gas phase is related to its mole fraction in the liquid phase by:
\[ p_i = x_i \cdot H_i \]
where \( H_i \) represents the Henry's law constant of the solute in that solvent.

Step 3: Detailed Explanation:

• Henry's Law: In a highly dilute solution, solute molecules are separated by a vast number of solvent molecules.
Because solute-solute interactions are negligible, the escaping tendency of solute molecules is independent of other solute molecules and varies linearly with concentration.
Thus, the vapour pressure of the solute is directly proportional to its mole fraction, which is the definition of Henry's Law.

• Raoult's Law: For the solvent in a dilute solution, the solvent mole fraction approaches unity (\( x_j \rightarrow 1 \)).
It obeys Raoult's law: \( p_j = x_j \cdot P^*_j \), where \( P^*_j \) is the vapour pressure of the pure solvent.

• Dalton's Law: Dalton's law of partial pressures states that the total pressure of a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases.
It does not describe liquid-phase solution behaviour.

• Amagat's Law: Amagat's law states that the total volume of a non-reacting gas mixture is equal to the sum of the partial volumes of the individual components at the same temperature and pressure.


Step 4: Final Answer:
Based on the definition of solute behaviour in dilute solutions, the correct option is Henry's law.