GROUNDWATER - Water Quality Engineering in Natural Systems - page 172

the pure substances. In addition, if the nAPL mixture
is exposed to the atmosphere, the the saturation vapor
pressures of the individual substances in the surround-
ing air are less than the saturation vapor pressures of
the pure substances. The extent to which the composi-
tion of the mixture affects the solubility and saturation
vapor pressure of the individual substances can be esti-
mated using Raoult's law .

benzene resulting from a spill of gasoline that contains
a mole fraction of 1% benzene.

Solution

(a) For a spill of pure benzene, the maximum vapor
concentration of benzene is given by Equa-
tion (5.82), where x i = 1, γ i = 1 (for ideal case),
p i o =

. kPa Pa (Appendix B.2), m i =
78.1 g/mol (Appendix B.2), R = 8.31 J/K·mol, and
T = 273.15 + 18 = 291.15 K. Substituting into Equa-
tion (5.82) gives

7 0 = 7000

5.6.2.1 Effects on Saturation Vapor Pressure. Ac-
cording to Raoult's law, in cases where a nAPL consists
of a mixture of substances, the maximum vapor pres-
sure, p i , of the i ith component is related to the saturation
vapor pressure, p i o , of the pure component by

x γ p m

RT

o

( )( )( 1 1 7000 78 1

8 31 291 15

)( . )

i i i i

3

c = = = 226 g/m = 22 6 mg/L

i

( . )( . )

p = γ x p

o

(5.80)

i i i i

(b) In the case of spilled gasoline, all parameters are the
same as for pure benzene except x i = 0.01 instead of
x i = 1. Therefore, Equation (5.82) gives

where x i is the mole fraction of the i ith component in the
nAPL phase, and γ i is the activity coefficient of i th com-
ponent. The activity coefficient, γ i , in Equation (5.80)
accounts for nonidealities in gas behavior, and in many
cases, γ i can be taken as approximately equal to unity.
The concentration, c i , of a contaminant in the vapor
phase is related to the vapor pressure, p i , by the ideal
gas law

c i = ( . 0 01 226 )( ) = 2 26 mg/L .

These results demonstrate that the soil gas concen-
tration resulting from a spill of pure benzene is
considerably higher than for a spill of gasoline,
which contains only 1% benzene.

p m
RT

i i

(5.81)

c =

i

5.6.2.2 Effects on Saturation Concentration. Raoult's
law describes the partitioning of organics between the
nAPL and aqueous phases in the saturated zone.
Raoult's law states that under ideal conditions, the
aqueous phase concentration in equilibrium with the
pure constituent phase is equal to the aqueous phase
solubility multiplied by the mole fraction of the con-
stituent in the nAPL phase. Raoult's law may be written
for species i as

where m i is the molar mass of the contaminant (g/mol),
R is the universal gas constant (= 8.31 J/K·mol), and T
is the absolute temperature (K). Combining Equations
(5.80) and (5.81) gives the following relation for calcu-
lating the maximum soil gas concentration, c i , resulting
from a spill:

x γ p m

RT

o

i i i i

(5.82)

c =

i

c = γ x c (5.83)

i i i s i

Values of the saturation vapor pressure, p i o and the
molar mass, m i , for several contaminants commonly
found in groundwater are given in Appendix B.2. In
cases where the composition of the mixture is unknown,
the mole fraction, x i , in Equation (5.80) can be approxi-
mated by the mass fraction.

where x i is the mole fraction, γ i is the activity coefficient,
and c s i is the solubility of the i th component of the
nAPL. The activity coefficient, γ i is numerically set to
unity for the case of an ideal nAPL mixture. mixtures
are termed ideal if the fraction of total volume and total
surface area occupied by any one constituent is equal to
the mole fraction of that constituent in the nAPL. Typi-
cally, nAPLs composed of similar constituents behave
ideally or nearly ideally, and nAPLs composed of dis-
parate compounds are expected to exhibit nonideal
behavior. For several nAPLs of environmental concern,
such as gasoline, diesel fuel, and coal tar, experiments
have shown that the assumption of an ideal nAPL

EXAMPLE 5.15

A spill of pure benzene seeps into the ground where the
ambient temperature is 18°C. (a) Calculate the maximum
concentration of benzene in a soil gas sample. (b) Con-
trast this with the maximum soil gas concentration of