Page 34 - Partition & Adsorption of Organic Contaminants in Environmental Systems

MOLAR HEAT OF SOLUTION 25
o
ln x i =-D H i(sol ) RT + constant (2.38)

Equation (2.37) or (2.38) is often referred to as the van’t Hoff equation and
is used extensively to obtain the molar heat of solution of a solute in a par-
tially miscible solvent from a plot of lnx° i versus 1/T, which gives a slope of
-DH i(sol) /R. In dilute systems, the overall heat of solution results mainly from
the solute heat of solution. If the x° i term in Eq. (2.37) is small, it can be
replaced by more convenient alternative forms (e.g., by molar concentration
or weight percent). Although Eq. (2.38) is derived with the application of
Raoult’s law for solute activity in solution, in which the Flory–Huggins model
provides a more accurate account of the solute activity with certain solvents
as mentioned, the equation remains valid as long as the solute of interest
exhibits a limited solubility in mass or volume fraction in the solvent.
As noted with Eq. (2.3) for a liquid solute with a small solubility, where
x° i 1/g i, the DH i(sol) term represents the “excess heat” required to disperse a
mole of the liquid solute into solution. For a solid solute with a small solubil-
s
s
ity [see Eq. (2.5) with x° i = x i ], where x° i a i /g i, the DH i(sol) term is the sum of
the molar excess heat of solution of the supercooled-liquid solute and the
molar heat of fusion (DH i(fus)) of the solid. This accounts for the fact that
the molar heat of solution for a solid solute is generally greater than that for
a liquid solute if they have comparable structures and sizes (e.g., solid
p-dichlorobenzene versus liquid o-dichlorobenzene at room tempera-
ture). Although the molar heat of solution of a solute depends strongly on
solute–solvent polarities, it is generally less than the corresponding heat of
vaporization because the van der Waals forces of attraction between solute
and solvent offset part of the energy needed to break apart solute molecules.
The heat of solution of a solute with a solvent serves as a useful reference to
be compared with the heat effects associated with the transfer of the solute
from that solvent into other phases of the system where the solute may be
taken up by either surface adsorption or phase partition.
Since water is probably the most important medium for contaminant trans-
fer to other natural phases, it is of considerable interest to determine the heats
of solution in water of contaminants from their water solubility–temperature
relations. For example, by Eq. (2.38), Friesen and Webster (1990) determined
the heats of solution in water (DH w) of 1,2,3,7-tetrachlorodibenzo-p-dioxin
(T 4 CDD), 1,2,3,4,7-pentachlorodibenzo-p-dioxin (P 5 CDD), 1,2,3,4,7,8-
hexachlorodibenzo-p-dioxin (H 6 CDD), and 1,2,3,4,6,7,8-heptachlorodibenzo-
p-dioxin (H 7CDD) from their measured water solubilities in the temperature
range 7 to 41°C, where all the compounds exist as solids. The water solubility
data are presented in Table 2.1, and a plot of lnx° versus 1/T is shown in Figure
2.3. The van’t Hoff plot yields virtually straight lines, meaning that the DH w
values of the four solid compounds are relatively temperature independent
over this temperature range. The DH w values calculated for T 4CDD, P 5CDD,
H 6CDD, and H 7CDD are 39.8, 47.5, 45.5, and 42.2kJ/mol, respectively. If
the van’t Hoff plot does not produce a straight line, the DH w value at a