Why is Raoult's law called a special case of Henry's law?

Raoult's law is considered a special case of Henry's law because it represents a specific scenario where the proportionality constant in Henry's law becomes equal to the vapor pressure of the pure solvent.

Understanding Raoult's and Henry's Laws

To understand why Raoult's law is a special case of Henry's law, let's first define both laws:

• Raoult's Law: This law states that the partial vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent in the solution. Mathematically, it is expressed as:

  • p = x * p^o

  where:

  • p is the partial pressure of the solvent above the solution
  • x is the mole fraction of the solvent in the solution
  • p^o is the vapor pressure of the pure solvent

• Henry's Law: This law states that the partial pressure of a gas above a solution is directly proportional to the mole fraction of the gas dissolved in the solution. Mathematically, it is expressed as:

  • p = K_H * x

  where:

  • p is the partial pressure of the gas above the solution
  • x is the mole fraction of the gas dissolved in the solution
  • K_H is Henry's law constant

Raoult's Law as a Special Case

By comparing the two equations, we can see the similarity. Both laws state that the partial pressure of a volatile component (either a solvent or a gas) is directly proportional to its mole fraction in the solution.

The key difference lies in the proportionality constant:

• In Raoult's law, the proportionality constant is the vapor pressure of the pure solvent (p^o).
• In Henry's law, the proportionality constant is Henry's law constant (K_H), which depends on the specific gas and solvent.

According to the provided reference, since p^o = K_H , Raoult's law is a special case of Henry's law. In other words, Raoult's law applies when Henry's law constant is equal to the vapor pressure of the pure solvent. This typically occurs when the solute and solvent are chemically similar, and the solute follows ideal solution behavior across the entire concentration range, behaving as if it were the solvent.

Feature	Raoult's Law	Henry's Law
Applies to	Solvent in a solution	Gas dissolved in a liquid
Equation	p = x * po	p = KH * x
Constant	Vapor pressure of the pure solvent (po)	Henry's law constant (KH)
Special Case	When KH = po	General case for gases dissolved in liquids