Page 30 - Partition & Adsorption of Organic Contaminants in Environmental Systems

VARIATION OF ACTIVITY COEFFICIENT WITH CONCENTRATION 21
2
lna 1 = lnf 1 +f 2 +c 1 f 2 (2.12)

If the pure component 1 is a liquid at temperature T and has a limited
solubility in a high-molecular-weight polymeric or macromolecular sub-
stance (component 2), at the point of saturation Eqs. (2.10) and (2.12)
become
o
lnf 1 +( 1- 1 VV 2 ) f 2 + c f 2 = 0 (2.13)
2
1
and
o 2
lnf 1 + f 2 + c f 2 = 0 if VV 2 0 (2.14)
1
1
where f° 1 = 1 -f 2 is the volume fraction solubility of the liquid at temperature
T.
If the pure component 1 is a solid at T, the corresponding equations are

o
2
lnf 1 +( 1- 1 VV 2 ) f 2 + c f 2 = lna 1 s (2.15)
1
and
o 2 s
lnf 1 + f 2 + c f 2 = lna 1 if 1 V V 0 (2.16)
2
1
s
where a 1 is the activity of pure component 1 as a solid at temperature T,as
defined before. We shall later make use of Eqs. (2.10) to (2.16) to account for
the solubility and partition behaviors of organic compounds with some macro-
molecular natural organic substances, including biological lipids that are only
moderately large in molecular size.

2.5 VARIATION OF ACTIVITY COEFFICIENT
WITH CONCENTRATION

For a nonideal solution, as noted, the activity coefficient of a substance (g i) is
a function of its concentration (x i). The relation between g i and x i for a binary-
component solution was derived by van Laar (1910, 1913) and extended by
Carlson and Colburn (1942):
log g 1 = A ( 1 + Ax 1 Bx 2 ) 2 (2.17)

and

log g 2 = B ( 1 + Bx 2 Ax 1 ) 2 (2.18)

where g 1 and g 2 are the activity coefficients of components 1 and 2 at mole
fractions x 1 and x 2 and A and B are defined as