n - PATh :.: Process and Product Applied Thermodynamics research ...

Modeling
Figure III.10 compares experimental results with the predictions given by the PR-
EOS using the average binary interaction parameter kij given in Table III.4. It can be
observed that a temperature independent kij cannot describe the oxygen solubility in
perfluoroalkanes. The average absolute deviation given in Table III.4 decreases from the
O2-C6F14 to the O2-C9F20 systems because the temperature dependence of the solubility
decreases along the perfluorocarbon series. The Peng-Robinson EoS, with one adjusted
interaction binary parameter, has limited predictive capability providing only a qualitative
description of the temperature dependence of the oxygen solubility in linear saturated
perfluoroalkanes.
2. Regular Solution Theory
According to the definition of Hildebrand and Scott (1970) a regular solution is one
involving no entropy and no volume change when a small amount of one of its components
is transferred to it. Considering this assumption, the following equation can be deduced in
order to describe the solubility of a non-polar gas in a non-polar solvent:
−
x
2
log 2 = −log
2 + δ 1 − δ 2
(
i 0.
4343V
2
x
) (III.41)
RT
where x2 is the mole fraction gas solubility, x i 2 is the ideal gas solubility, V 2 is the partial
molar volume of the gas in the solution and δ1 and δ2 are the solubility parameters for the
solvent and the solute, respectively.
When the entropic contribution is significant, the Regular Solution Theory alone
cannot describe correctly the solubility of a solute in a solvent. The entropic contribution
can be accounted for, if the Flory-Huggins combinatorial term is introduced:
−
i V ⎛ V
⎜ −
⎞
⎟
0.
4343V
2 ) (III.42)
⎝ ⎠
2
2
2
log x2
= −log
x 2 + log + 0.
4343⎜1
⎟ + δ 1 − δ 2
V1
V1
RT
where V1 is the molar volume of the solvent.
Equation III.42 requires three parameters for the solute ( x 2 , V2
, δ 2
i
) and two
parameters for the solvent (V1 and δ1). All these parameters are temperature dependent, but
- 125 -
(