Multicomponent Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 56

Therefore,

P i = γ i x i f w0 . (3.25)

i

Hence we have

P i

x i = γ i f w0

K H = . (3.26)

i

In the above equation, f w i is the standard state liquid fugacity. Thus, if one knows
the activity coefficient of i in the liquid phase and the standard state fugacity, then
Henry's law constant can be obtained. If the liquid phase is ideal and the more general
fugacity is used instead of partial pressure ( f i f i = ) , then we can write a general

expression for K H as follows:

f i

K H = lim

x i x i .

(3.27)

→ 0

The most general definition of Henry's law is

y i χ i P T
γ i x i

K H = . (3.28)

The above definition recognizes nonideality in both liquid and gas phases.

3.3.1.2 Raoult's Law

Raoult's law is an important relationship that describes the behavior of ideal solutions.
Its applicability is predicated on the generally similar characters of both solute and
solvents, and hence a mixture of the two behaves ideally over the entire range of mole
fractions. Let us consider a solvent i in a mixture in equilibrium with its vapor,

f vapor
i

f liquid mixture
i

= , (3.29)

P i = γ i x i P i . (3.30)

Noting that for a ideal mixture γ I = 1, we have

P i
P i

x i = . (3.31)

This is called Raoult's law.
Figure 3.1 is a description of the applicability of Henry's and Raoult's laws for
mixtures. As shown in the figure, when the mole fraction of all solutes is very small,
the solvent obeys Raoult's law while the solute obeys Henry's law. Solute obeying
both of the laws is ideal in nature. Over the range when the solvent obeys Raoult's
law, the solute will obey Henry's law.