Page 27 - Partition & Adsorption of Organic Contaminants in Environmental Systems

18 FUNDAMENTALS OF THE SOLUTION THEORY
s
s
terminates at x i = x i. If x i << 1, the P i –x i relation is expected to be largely linear
over the entire x i range; that is, g i is essentially independent of the concentra-
tion. Since at the point of saturation the activity of a solid substance at T is
the same in any system, whether its solution is ideal or not, one gets

s s
a i = x° i,id = x i g° i (2.5)
and

∞
s
s
g i = i x∞ ,id i x = i a x i s (2.6)
s
As shown later, the value of a i of a solid substance can be calculated from its
molar heat of fusion (DH fus ) and melting point (T m ), if they are known; this
s
allows the calculation of g° i (at saturation) from the measured solubility (x i ).
s
Again, if x i is very small, the g i value for the dissolved solid at any concentra-
tion below saturation is practically equal to g° i .

2.3 HENRY’S LAW

Whereas Raoult’s law applies well for a component (generally, the solvent)
when its mole fractions is close to 1, Henry’s law applies to components at
high dilution. Henry’s law can be expressed in a number of forms, such as

(2.7)
P i = k i x i or a i = k* i x i
where P i , a i , and x i are as defined before and k i and k* i are Henry’s constants.
The value of k i or k* i depends on the solvent type. By reference to Raoult’s
law with a given solvent, one finds that
• •
k i = P° i g i and k* i =g i (2.8)
•
where g i is the Raoult’s activity coefficient of substance i at infinite dilution
(i.e., x i Æ 0). The linear Henry’s law is thus limited to x i << 1 such that g i is
•
•
practically the same as g i . The P° i g i term in Eq. (2.8) may be considered as a
hypothetical vapor pressure of the pure substance according to Henry’s law,
•
which is obtained by a linear extrapolation of P i with a constant slope of g i
from infinite dilution to x i = 1.
If the activity of a substance at low concentrations is not sufficiently linear
with respect to its concentration, a Henry’s law activity coefficient (h i ) is added
to the right of Eq. (2.7), similar to the correction for deviation from the ideal
Raoult’s law:

(2.9)
P i = k i x i h i or a i = k* i x i h i