Raoult's Law as a Special Case of Henry's Law

Two laws met earlier turn out to be closely related. Placing them side by side reveals that one is simply a special case of the other.

Raoult's law for a volatile component says its vapour pressure is proportional to its mole fraction in solution:

Henry's law for a gas dissolved in a liquid says the pressure of the gas is proportional to its mole fraction in solution:

The two laws have the same form

In a solution of a gas in a liquid, the gas is so volatile that it exists as a gas above the solution, and its solubility follows Henry's law. Comparing the two expressions, both make the partial pressure of the volatile component directly proportional to its mole fraction. The equations are identical in structure — only the proportionality constant differs: it is $K_H$ in Henry's law and $p_i^{0}$ in Raoult's law.

The connection

Because the two forms match exactly, Raoult's law is a special case of Henry's law — the one in which the Henry's law constant equals the vapour pressure of the pure component:

$K_H = p_1^{0}$ …