Page 36 - Partition & Adsorption of Organic Contaminants in Environmental Systems

COHESIVE ENERGY DENSITY AND SOLUBILITY PARAMETER 27

temperature of interest is obtained from the derivative of lnx° with 1/T at that
particular temperature. Heats of solution are discussed in more detail in
Chapter 3.
Let us consider the associated molar entropies of solution in water (DS w)
of the chlorinated dibenzo-p-dioxins in the example above. It is important to
note that whereas the DH w, or DH i(sol) in general, for a liquid or solid substance
that exhibits a limited solubility in water (or a solvent) is practically inde-
pendent of the solute concentration (x), the DS w, or DS i(sol), varies with x on
its path toward saturation (x°) [see Eq. (2.36)]. However, at x = x°, DG w is zero
s
according to Eq. (2.33) (where x°g° = P /P°), and one obtains under this con-
dition DS w =DH w/T over the temperature range studied (Chiou and Manes,
1990). For example, the DS w values calculated at T = 299K for solid T 4CDD,
P 5CDD, H 6CDD, and H 7CDD at the points of solid–water equilibria are 113,
159, 152, and 141J/K◊mol, respectively; the DS w values at other temperatures
can be calculated similarly. The finding that both DH w and DS w values are pos-
itive is much expected, since the solubilization of nonionic organic solutes in
water or a solvent is favored by the entropic effect and commonly disfavored
by the enthalpic effect.

2.7 COHESIVE ENERGY DENSITY AND
SOLUBILITY PARAMETER

The sum of the various attractive forces that hold the molecules of a substance
in a liquid or solid state is called the cohesive energy. The magnitude of this
energy is not only a function of the molecular makeup but also of the molec-
ular size. Types of cohesive forces that operate in uncharged liquids and solids
include the induced dipole–induced dipole force (also called the London force),
the dipole–dipole force (the Debye force), the dipole–induced dipole force (the
Keesom force), and the H-bonding force. With the possible exception of the H-
bonding force, these molecular forces are frequently lumped together as the
van der Waals forces.The London force,also referred to as the dispersion force,
originates from the momentary distortion of electrons around nuclei and is thus
operative in all molecules. This molecular force is temperature independent
and is the sole attractive force for nonpolar substances. On the other hand, the
involvement of dipolar and H-bonding forces for a substance requires the pres-
ence of polar and H-bonding groups in its molecular structure. The energy of
evaporation per unit volume of a liquid or a supercooled liquid,called the cohe-
sive energy density, is a critical parameter in determining its compatibility with
other liquid species. The cohesive energy density (CED) is defined as

V (2.39)
CED =DE int
where DE int is the internal energy per mole of the liquid and V is the molar
volume of the liquid at a given system temperature. Thus CED has units of