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Table 4.2. Examples of correlations for the sorption of vapors at the water–gas interface
Equation Nomenclature Reference Ong
=−( p/RT)(dγ/dp) – surface excess (mol cm −2 ) Gibbs equation (as
γ – surface tension presented in Chattoraj
p – partial pressure and Birdi, 1984)
R – universal gas constant
T – temperature
log K IW =−5.53 + 0.2735I x K IW – water–gas partition coefficient, Valsaraj (1988)
I x – first order molecular connectivity
index
log K IW =−8.58−0.769 log C s K IW – water–gas partition coefficient Hoff et al. (1993b)
W
(m)
C s – saturated solubility of the VOC
W
∗
ln K IW = A − ( H s /R)(1/T − K IW – water–gas partition coefficient Goss (1994)
1/323.15) − C(100 − (m), vp – vapor pressure (pascal), β –
RH)(3) where hydrogen bond acceptor, mR – molar
∗ refraction, µ – dipole momentum,
A =
−0.615 ln vp + 7.86ß − 5.80 H s – heat of adsorption (kJ mol −1 ) R
C =−0.054β − 0.00070 mR − – universal gas constant (kJ
K
0.0041µ + 0.00061 H s = mol −1 −1 )
3.20 ln vp − 50.2β − 55.0.

be a dominant retention mechanism depending on the moisture content (Costanza and
Brusseau, 2000). Obviously as the moisture content approaches saturation the water–
gas interface (A) available will be reduced resulting in insignificant sorption at the
water–gas interface. It must be pointed out that VOCs with high aqueous solubility
would prefer to be in the aqueous phase rather than at the water–gas interface. TCE
has an aqueous solubility of 1100 mg/L which is higher than the solubility of p-xylene
(198 mg/L). Therefore it is probable that because of the physical characteristic of the
TCE used by Ong and Lion (1991c), sorption at the water–gas interface was found to
be negligible.
Several researchers have proposed correlations for the estimation of mass sorbed
at the water–gas interface (see Table 4.2). Sorption at the water–gas interface can
be modeled using the Gibbs equation where the surface excess is determined by the
change in the surface tension with varying vapor pressure. The equations proposed
by Goss (1994) imply that for a VOC with high saturated solubility and high vapor
pressure vapors such as TCE, the air–water partition coefficients would be low and
that the VOC that are most likely to be sorbed at water–gas interface are those with
a high β, hydrogen bond acceptor, value.
MostvaporsorptionstudieswereconductedusingasingleVOCincompetitionwith
water for sorption sites. There are only a few studies investigating sorption of multiple
vapors under unsaturated zone conditions even though many different VOCs may be
found at a typical contaminated site. For simplicity sake, it is assumed that each VOC