3. CHAPTER CONTAMINANT PROPERTIES AFFECTING POLLUTANT
FATE AND REMEDIATION
My teaching goals for Chapter 3 are for you to:
1. Use thermodynamic relationships to determine whether a system is at
equilibrium.
2. Calculate the distribution of chemicals between different phases.
3. Use Fick's laws to calculate diffusion rates for chemicals in air and water.
4. Use boundary layer theory to calculate the rate that chemicals move from
one phase to another.
5. Appreciate how chemical equilibrium and mass transfer characteristics affect
contaminant transport and fate in the environment.
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
1
3.1 Introduction
Equilibrium Properties Control contaminant distribution between
phases
Mass Transfer Properties Control the rate that equilibrium is attained
Equilibrium Properties Affecting
the Distribution and Fate of Chemicals
in the Environment
Organic and inorganic chemicals
can exist in several phases in
soil, sediment, and groundwater.
Right is a conceptual picture of
these phases.
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
2
Understanding the distribution and fate of organic and inorganic chemicals
between and within phases is paramount to predicting pollutant transport,
fate, and remediation effectiveness.
Chemical properties/parameters that determine the distribution and fate of
chemicals in the environment that you will learn about are:
-Henrys Constant (Hcc)
-Octonal-water partition coefficient (Kow)
-Water-Solid or Air-Solid Equilibrium Distribution Coefficients (Kd)
-Water/Organic Interfacial tension (), Water/Organic Contact
Angle (), Density ()
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
3
3.2 Thermodynamics of Equilibrium
At equilibrium the amount of mass in each phase is constant.
Thermodynamics can be used to derive the phase equilibrium
relationships. The primary variable that governs equilibrium:
G = Gibbs free energy
change in G defines favorability of a system
For a change from one phase to another or from reactant A to product B
we talk about the change in the Gibbs free energy, G
- G
+ G
CEE 440
favorable
unfavorable
air
water
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
4
The change in the Gibbs free energy can be defined in terms of:
G = H - T S
(3.0)
T = temperature
H = enthalpy change
if negative heat produced during process (exothermic)
if positive heat consumed during process (endothermic)
S = entropy change
if negative system becomes more ordered
if positive system becomes less ordered (more disordered)
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
5
when we have the transfer of mass from one phase to another we talk about
the change in Gibbs free energy with respect to the change in the amount of
mass transferred:
G
n i
= i = chemical potential (J/mol)
(3.1)
T, P , n j
where ni = moles i in the system at constant T, P (pressure), and moles of j.
The chemical potential is the property governing phase equilibrium and mass
transfer.
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
6
In a system consisting of phases and m species, the conditions for
equilibrium are:
T(1) = T(2) = T()
P(1) = P(2) = P()
1(1) = 1(2) = 1()
.
.
m(1) = m(2) = m()
(3.2)
(3.3)
(3.4)
(3.5)
where P is the pressure and T is temperature
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
7
For an ideal gas, the change in chemical potential for an isothermal change
from pressure Po to P is:
i - io = RT ln (P/Po)
(3.6)
R = gas constant (8.314 j/K-mol, 0.08206 atm-L/K-mol)
P = pressure
Po= pressure at some reference value
io=chemical potential at some reference value
To generalize to real liquids, gases, and solids, G. N. Lewis defined a function
f, called fugacity, such that for an isothermal change:
i - io = RT ln (fi/fio)
(3.7)
fi = fugacity or escaping tendency (units are pressure)
fi/fio = ratio of escaping tendency to that at standard state
where for an ideal gas fi = yiP where yi is the mol fraction of i.
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
8
Considering two phases and :
i - io, = RT ln (fi /fio,)
(3.8)
i - io, = RT ln (fi/fio,)
(3.9)
If the reference state is chosen to be equal in and :
io, = io,
(3.10)
Then at equilibrium the chemical potentials are equal:
i = i
(3.11)
It then follows without any loss of generality that:
fi = fi
CEE 440
(3.12)
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
9
So at equilibrium, the fugacity of any species must be equal in all
phases.
Fugacity is the escaping tendency of a specific chemical constituent from a
particular phase (air, water, etc.)
At equilibrium, the fugacities of a chemical compound (like TCE) are equal in all
phases as follows:
fTCE (air) = fTCE (water) = fTCE (pure org.) = fTCE (solid) = fTCE (octanol)
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
(3.13)
10
Fugacity is usually expressed in units of pressure. So the trick is figuring
out how to define the concentrations in the air, water, pure organic, and
solid phases in terms of pressure. From this, we will define the
equilibrium relationships between the different phases.
fi=Ci/Zi
(3.14)
Ci is the concentration of the chemical of interest in any phase
Zi is the fugacity capacity of that phase
So we need to define Zi for each phase and then set the fugacities for the
different phases equal to each other to define the partitioning
relationships.
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
11
Basic definitions
Saturation vapor pressure (Pisat)= The
pressure of a chemical in equilibrium with its
condensed pure phase at a specified
temperature
Gas phase
Pisat
Vinylchloride
(25C)
Pure
liquid or
solid
phase
100
F11 (Fluorotrichloromethane)
Dichloromethane
Vapor pressure kPa
R-113 (1,1,2-Trichloro-1,2,2-Trifluoroethane)
cis-Dichloroethene
Methanol
Benzene
10
C 4 H1 0
C 2H 6
S u lf u r - C o nt a i ni n g
C o mpo u nd s
P o l yc hl o r in a t e d B ip h e n yl s ( P C B s )
C4Cl
C 16 H 14
1,1,1-Trichloroethane
Cyclohexane
Trichloroethene
Toluene
Water
1
C C l 2F 2
Perchloroethene
m,p-Xylene
o-Xylene
H a l og e na t e d C 1 - C 4 C om po u nd s
C 12 H 22
P h t h al a t e s
0 ,1
Po l yc ycl i c Ar o mat i c H ydr o ca r b on s ( P AH s)
S ub s ti t u t e d B e nz e n e s
0 ,0 1
C 9H 2 0
C 3 H6
M i sc e ll a ne o us Al i ph at i c C o mp o un d s
C 18 H 38
Phenol
C 5 H 12
Naphthalene
S at u r a t e d an d U n sa t ur at e d H yd r o ca r b on s
1 ,0 0 E- 1 3
1 , 0 0 E- 1 1
1 ,0 0 E-0 9
1 , 0 0 E- 0 7
1 ,0 0 E-0 5
1 , 0 0 E- 0 3
1 , 0 0 E- 0 1
1 , 0 0 E+0 1
1 ,0 0 E+0 3
1 , 0 0 E+0 5
0
P , v a p o r p re s s u re (k P a )
CEE 440
50
100
BP (oC)
150
(modified from Schwarzenbach et al., 1993)
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
200
12
Basic definitions
Aqueous saturation concentration (Cisat)=
The concentration of a chemical in equilibrium
with its condensed pure phase at a specified
temperature
water phase
Cisat
T ( C)
40 35 30 25 20 15 10
Pure
liquid or
solid
phase
C4Cl6
CCl2F2
Haloge nate d C 1-C4 Compounds
sat
Cw
C16H22
log
Phthalates
Polycyclic Aromatic Hydrocarbons (PAHs)
(mol/L)
Polychlorinate d Biphenyls (PCBs)
-1
-2
Sa t
e
S ulfur-C ontaining Compounds
CH B r
3
CH3Br(gas, 1a tm)
CH Cl (liquid)
22
w
Log C
C2H6S
s
H
+ constant
=2.303 R T
0
C4H10
C12H14
Diethyhexyl-phthalate
( DE H P )
-3
C9H20
C3H6O
O M isce llaneous Aliphatic Compounds
-4
C5H12
Saturated and Unsaturate d Hydr ocar bons
1. 0 0 E - 0 4
1. 0 0 E - 0 2
Cw
CEE 440
sat
1. 0 0 E + 0 0
1. 0 0 E +0 2
water solub ility (mg/L)
1. 0 0 E + 0 4
(liquid)
Naphthalene
Naphthalene
C18H38
1. 0 0 E - 0 6
O
CO
CO
O
Benzene
(liquid)
Trichloroethene
CC2l = CHCl
(liquid)
(subcooled liquid)
Substitute d Be nzene s
1. 0 0 E - 0 8
0
5
1. 0 0 E + 0 6
1. 0 0 E + 0 8
(solid)
3.3 x 10 -3
3.5 x 10 -3
-1
1/T (K )
3.7 x 10 -3
(modified from Schwarzenbach et al., 1993)
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
13
3.2.1 AIR-WATER PARTITIONING RELATIONSHIP
We start with the fugacity relationship for air:
fi,air = i xi,air PT = i Pi = Ci,air/Zi,air
(3.15)
i = fugacity coefficient (accounts for nonideal behavior, set equal to 1)
xi,air = mole fraction of species i in gas phase
Ci,air = concentration of species i in the atmosphere (mol/L)
PT = total pressure (atm)
Pi = partial pressure of species i (atm)
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
14
fi,air = Pi = Ci,air/Zi,air
Next we rearrange the equation, plug in the ideal gas law, and define Zi,air:
Zi,air = Ci,air / Pi
(3.16)
Pi = niRT / V
(3.17)
Zi,air = Ci,air V / (niRT) = 1/RT
(3.18)
Now we can define fi,air in terms of the concentration in the air and the
expression for Zi,air:
fi,air = xiPT = Pi = Ci,airRT
CEE 440
(3.19)
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
15
Next, we define the fugacity relationship for water:
fi,water = i,water x i,water Pisat = Ci,water / Zi,water
(3.20)
i,water = liquid-phase activity coefficient
xi,water = mole fraction of species i in liquid phase
Ci,water = concentration of species i in water (mol/L)
Pisat =
CEE 440
vapor pressure of pure i at temperature T (atm)
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
16
fi,water = i x iPisat = Ci,water / Zi,water
When xi,water=1, then i,water=1 and fi,water becomes the pure liquid state
component vapor pressure.
fi,water = Pisat
For nonionizing chemicals, the relationship between xi,water and i,water is
generally of the form (empirically determined):
ln i,water = K(1-xi,water)2
(3.21)
where: K = constant
Since xi is quite small (xi,water<<1) for nonionic or hydrophobic compounds,
ln i,water ~ K. Hence, i,water is relatively constant:
i,water = exp (K) = K
fi,water = i,waterxi,waterPisat = Kxi,waterPisat = Ci,water/Zi,water
CEE 440
(3.22)
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
17
fi,water = KxiPisat = Ci,water/Zi,water
Next we rearrange the equation to define Zi,water:
Zi,water = Ci,water / (KxiPisat)
(3.23)
xi / Ci,water = vm,water = molar volume of water (L/mol)
Zi,water = 1 / (K vm,water Pisat) = 1 / Hi
Hi = Henry's constant
Now we can define fi,water in terms of the concentration in the water and the
expression for Zi,water:
fi,water = Ci,water Hi
CEE 440
(3.24)
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
18
If the fugacities for Air and Water are set equal to each other we have the
Air-Water equilibrium relationship:
Pi=Ci,waterHi
(3.25)
or
Hi=Pi/Ci,water
(3.26)
where: Pi is in atm and Ci,water is in moles/L
Alternatively, Hi can be converted to dimensionless form to better compare
partitioning between air and water:
Hcc,i = Hi/(RT)
= Ci,air/Ci,water
CEE 440
(3.27)
(3.28)
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
19
Note the differences with units: HTCE=503 atm-L/mol, Hcc,TCE = 0.38
I prefer the dimensionless form because by observation you can immediately
tell which compartment (air or water) is more favored.
Henry's constants have been measured for many environmentally significant
organic compounds. When Henry's constants are not available, it is often a
good approximation to calculate the Henry's constant as follows:
Hi=Pisat/Cisol
(3.29)
Henry's Law is valid for predicting air-water equilibria for most nonionic
organic pollutants in the environment:
Ambient conditions: P ~ 1 atm; T = 10 -> 60C
xi < 0.001 or Ci<5 g/L if MW~100 (for most priority pollutants Csat < 5 g/L)
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
20
Temperature dependence of Hcc
As a rough approximation the Henry's constant increases by about 60% for
each 10C rise in T. This can be calculated by:
Hcc,@T = Hcc,@20C(1.048)T-20
(3.30)
where T is in C
Alternatively, Gossett measured the temperature dependence of Henry's law for
many environmentally significant pollutants and developed empirical equations
to describe this dependence[Gossett, Environ. Sci. Technol., vol. 21, pp.
202-208, 1987].
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
21
Example Problem:
Pore gas samples are taken from the unsaturated zone (20C) and the
concentration of trichloroethene (TCE) in the vapor phase is measured to be
200 g/L. The water loading on the soil is determined to be 0.04 ml of water
per gram of soil. Assuming the soil water and the soil vapor are in
equilibrium, how much TCE (Hcc=0.35) is dissolved in an REV (representative
elementary volume) containing 3 kilograms of soil.
CTCE,water = Cair / Hcc,TCE = 200 g/L / 0.350 = 571 g/L
MTCE,water = 571 g/L * 0.04 ml/g * 3 kg *
1000 g/kg * 1e-3 L/ml)
= 68.5 ug
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
22
Dimensionless Henry's constants for some organic chemicals at 20C
(Adapted from Howe et al., USAFESC Report No. ESL-86-66, 86pp., 1986)
Compound
nonane
n-hexane
2-methylpentane
cyclohexane
chlorobenzene
1,2-dichlorobenzene
1,3-dichlorobenzene
1,4-dichlorobenzene
o-xylene
p-xylene
m-xylene
propylbenzene
ethylbenzene
toluene
benzene
methyl ethylbenzene
1,1-dichloroethane
1,2-dichloroethane
1,1,1-trichloroethane
1,1,2-trichloroethane
cis-1,2-dichloroethylene
trans-1,2-dichloroethylene
CEE 440
Hcc,@20C
13.80119
36.70619
26.31372
5.81978
0.14175
0.06984
0.12222
0.10767
0.19704
0.26813
0.24859
0.36623
0.24983
0.23071
0.1879
0.2091
0.23404
0.06111
0.60692
0.03076
0.14965
0.35625
Compound
tetrachloroethylene
trichloroethylene
decalin
vinyl chloride
chloroethane
hexachloroethane
carbon tetrachloride
1,3,5-trimethylbenzene
ethylene dibromide
1,1-dichloroethylene
methylene chloride
chloroform
1,1,2,2-tetrachloroethane
1,2-dichloropropane
dibromochloromethane
1,2,4-trichlorobenzene
2,4-dimethylphenol
1,1,2-trichlorotrifluoroethane
methyl ethyl ketone
methyl isobutyl ketone
trichlorofluoromethane
Hcc,@20C
0.58614
0.35002
4.40641
0.90207
0.45727
0.24568
0.96442
0.23736
0.02536
0.90622
0.10143
0.13801
0.03035
0.07898
0.04282
0.07607
0.41986
10.18462
0.0079
0.01206
3.34222
Charles 2011 J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
23
Rough classification of volatility for CEE440
Hcc @20C
Classification
>1
0.1 to 1
0.01 to 0.1
< 0.01
extremely volatile
volatile
slightly volatile
not volatile
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
24
3.2.2 OCTANOL-WATER PARTITIONING RELATIONSHIP
We start by deriving the fugacity relationship for octanol. Octanol can be
thought of as a partitioning medium just as water. Thus, it follows that
the fugacity relationship is similar:
fi,oct = i,oct xi Pisat = Ci,oct / Zi,oct
(3.31)
i,oct = octanol activity coefficient
xi
= mole fraction of species i
Ci,oct = concentration of species i in octanol (mol/L)
Pisat
= vapor pressure of pure i at temperature T (atm)
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
25
fi,oct = i,oct xi Pisat = Ci,oct / Zi,oct
i,oct is relatively constant so:
xi Pisat = Ci,oct / Zi,oct
(3.32)
Zi,oct = Ci,oct / ( xi Pisat )
(3.33)
vm,oct = xi / Ci,oct = molar volume of octanol (L/mol)
(3.34)
Zi,oct = 1 / ( vm,oct Pisat) = 1 / Ki,oct
(3.35)
Now we can define fi,oct in terms of the concentration in the octanol and the
expression for Zi,oct:
fi,oct = Ci,oct / Zi,oct = Ci,oct Ki,oct
CEE 440
(3.36)
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
26
If the fugacities for Water and Octanol are set equal to each other we have
the Octanol-Water equilibrium relationship:
Ci,octKi,oct=Ci,waterHi
(3.37)
Ki,ow = Hi / Ki,oct = Ci,oct / Ci,water
(3.38)
Kow = octanol-water partition coefficient (dimensionless units)
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
27
Kow is an indicator of the hydrophobicity of a compound.
It is an indicator of the extent that an organic compound will partition to
natural organic matter in sediments and to fatty tissue (i.e. compounds with
a higher Kow bio-accumulate more in human tissue).
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
28
Kow varies over many orders of magnitude. Shown below is a table of Kow
values where Kow varies over 6 orders of magnitude.
Compound
Log Kow
Kow
Polar
Water
H20
-1.38
0.0417
Polar & completely
miscible
Methanol propanol
CH3OH
C3H7OH
-0.77
0.3
0.17
2
Slightly miscible
Chloromethane
MTBE
Chloroform
TCE
Dichlorobenzenes
CH3Cl
C5H12O
CHCl3
C2HCl3
C6H4Cl2
0.91
1.1
1.95
2.29
3.3
8.1
12
89.1
195
1900
Very slightly
miscible
DDT, PCBs
>5
>100,000
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
29
Rough classification of hydrophobicity (polarity) for CEE440
log Kow
<0
Classification
Strongly hydrophilic
0 to 1
Mildly hydrophilic
1 to 3
Mildly hydrophobic
>3
Strongly hydrophobic
Do the values of Kow affect the choice or operation of
remediation technologies
e.g.,
Soil (soil washing, in situ bioremediation)
Groundwater (pump and treat, in situ bioremediation)
Surface water sediments (reactive caps, sediment washing)
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
30
3.2.2 MORE GENERAL ORGANIC-WATER AND ORGANIC-AIR
PARTITIONING RELATIONSHIP FOR ORGANIC LIQUID MIXTURES
For organic-water, we start with the same relationship used for octanol fugacity,
and set this equal to the fugacity relationship for water:
fi,orgmix = i,orgmix xi,orgmix Pisat = Ci,orgmix / Zi,orgmix
(3.39)
i,orgmix = organic activity coefficient
xi,orgmix
= mole fraction of species i in organic phase
Pisat
= vapor pressure of pure i at temperature T (atm)
fi,orgmix = fi,water
(3.40)
i,orgmix xi,orgmix Pisat = Ci,water Hi
(3.41)
Ci,water = i,orgmix xi,orgmix (Pisat/Hi)
(3.42)
Ci,water = i,orgmix xi,orgmix Ci,sol
(3.43)
For ideal solutions (i.e., structurally similar chemicals) we get the liquid phase form
of Raoults Law:
Ci,water = xi,orgmix Ci,sol
CEE 440
(3.44)
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
31
For organic-air, we start with the same relationship used for organic-water, and set
this equal to the fugacity relationship for air:
fi,orgmix = i,orgmix xi,orgmix Pisat = Ci,orgmix / Zi,orgmix
(3.45)
fi,orgmix = fi,air
(3.46)
i,orgmix xi,orgmix Pisat = Pi
(3.47)
For ideal solutions (i.e., structurally similar chemicals) we get the gas phase form of
Raoults Law:
Pi = xi,orgmix Pisat
CEE 440
(3.48)
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
32
3.2.3 SOLID-WATER OR SOLID VAPOR PARTITIONING
RELATIONSHIPS
The solid or sorbed phase refers to metals or organic chemicals sorbed to
a solid such as soil or granular activated carbon. We start with the basic
fugacity relationship below:
fi,solid = Ci,solid/Zi,solid = qi,solid / Z*i,solid
(3.49)
Ci,solid = concentration of species i on solid surface
(mass i/volume solid)
qi,solid = concentration of species i on solid surface
(mass i/mass solid)
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
33
The relationship between fi,solid and Ci,solid is not usually linear over large
concentration ranges. Hence, this is usually as far as we get with the solid
equation alone. We can use an empirical relationships for Z*i,solid based on
an equilibrium relationship between the sorbed phase and another phase
such as water or air. This allows us to relate the fugacity of the solid in
terms of either the aqueous phase concentration or the vapor pressure.
So, lets set the fugacities for solid and water equal:
fi,solid = fi,water = qi,solid/Z*i,solid = Ci,water/Zi,water = Ci,water * Hi,
(3.50)
Z*i,solid = qi,solid / (Hi * Ci,water )
(3.51)
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
34
To relate qi,solid and Ci,water we need an isotherm. Lets use the most
common empirical relationship the Freundlich isotherm:
qi,solid = KFCi,waternF
(3.52)
It follows that:
Z*i,solid = (KF Ci,waternF) / (HiCi,water)
Z*i,solid = (KF Ci,waternF-1) / Hi
(3.53)
(3.54)
KF = Freundlich capacity parameter (mol/g)/(mol/L)nF
nF = Freundlich exponent parameters (-)
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
35
Note:
-KF is a measure of the distribution of a chemical between the
sorbent and the pore water
-nF is a measure of the favorability of a chemical for the sorbent
-when nF>1 the isotherm is said to be
unfavorable and the ratio of the amount
adsorbed to the amount in the pore water
increases with increasing concentration
nF<1
nF = 1
q
nF > 1
C
-when nF<1 the isotherm is said to be
favorable and the ratio of the amount
adsorbed to the amount in the pore
water decreases with increasing
concentration
The values of KF and nF are a function of both the chemical properties and
the sorbent (soils, sediments, activated carbon) properties. We will
examine the sorbent properties that control sorption later when we look at
relevant site properties.
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
36
Often times it is advantageous to linearize the Freundlich expression:
log (qi,solid) = nF log Ci,water + log KF
(3.55)
We can plot log (qi,solid) versus log Ci,water and the slope of the
plotted line will be nF. Therefore, if the line slope is >1 the isotherm is
unfavorable and if the line slope <1 the isotherm is favorable
nF > 1
nF = 1
Log q
nF<1
Log C
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
37
If nF=1 we get another commonly used isotherm expression called the linear
isotherm:
qi,solid = Kd Ci,water
(3.56)
Kd = equilibrium distribution coefficient (mol/g) / (mol/L)
Note that for this case:
Z*i,solid = qi,solid/(HiCi,water) = KdCi,water/(HiCi,water) = Kd/Hi
(3.57)
Freundlich parameters (KF and nF) and Kd values are available for a variety of
sorbates (organic chemicals) on a variety of adsorbents (soil and activated
carbon). Usually, the greater a compounds Kow, the greater the compounds KF
or Kd value on a given solid. Hence, the Kd value for a PCB should be much
greater than the Kd value for TCE.
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
38
Compound Kow
(-)
TCE
200
PCB
1x106
Kd (measured in aquifer sediments)
(mol/g) / (mol/m3)
1.3x10-6
6.3x10-3
Units
The general form of the units for the KF values are:
KF =
CEE 440
(
(
q i, solid
n
C i ,F
water
)
)
massof chemcial sorbed
massdry solid
massof chemical inwater nF
volumeof water
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
39
Converting between units can at first be confusing. For example:
g g
moles Mol .Wt. g g g
g g
moles
moles Mol .WtWt.g g
moles
Mol Wtmole
gg
Mol. . mole ole
Mol ..Wt.. mole
g g
mole
m
g g = K
KK n = K g gn *
*
* *
F
F
KK F g n Fn = = K F moles n Fn
KFF
nn
F
F g F F
moles F F Mol.Wt. g g g n FnF F
n
moles
FF
g g n F
gg
moles n F
L L
Mol.WtWt.
Mol Wtmole
L L
Mol. . mole ole
L L
Mol..Wt.. mole
mole
L L
m
(())
(( ))
()
()
( ( ) ) {{
(())
()
{
()
(( )) = K (( )) *
(
)
( )
moles
moles
moles
moles
gg
gg
KK
F
KK F
F
F moles n Fn F
moles
moles n F F
moles n
3
m m 3
3
mm 3
moles
moles
moles
moles
gg
gg
F
= K
KF
= = F F moles n Fn
K
moles n F F
moles n F
moles
L L
LL
(( ))
()
((( )))
()
((( )))
}}
( )}
1
11
11
nF
*
**
n
n
1000L L3n FF
nF F
1000 LL
1000 L3
m
1000 3
1000 m m3
mm 3
The units of Kd can be manipulated in a similar but simpler fashion.
Consequences of Solid-Water Partitioning: Partitioning onto stationary solids
(soils and sediments) greatly reduces the mobility and bioavailability of chemicals
in the subsurface (i.e. the stuff on the solids is immobile and not available for
microbial degradation). This very phenomenon is used to remove chemicals
from water during the granular activated carbon treatment of water.
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
40
Example Problem:
Consider an activated carbon treatment system used to remove o-Xylene
from water. If the concentration of o-Xylene in the water is 0.20 mg/L and
the water and the activated carbon are in equilibrium, what is the mass
concentration (g/g) of o-Xylene on the activated carbon?
Given: KF=9,760 (g/g)/(g/L)nF, nF=0.474 (-)
q (g/g) = 9760 * 2000.474
q (g/g) = 120,264 (g/g) of o-Xylene on the soil
If there is 1 kg of activated carbon in the treatment system and the entire
system is at equilibrium with the water (i.e. the activated carbon is
exhausted), then there is how much o-Xylene on the carbon?
Mass (o-Xylene) = 120,264 (g/g) * 1000g =120 g o-Xylene
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
41
Example:
You are given the Freundlich parameters on three different soils and asked
to evaluate on which soil trichloroethylene partitioning will be more
favorable. You are told to examine the entire concentration range over
which the Freundlich parameters were measured.
Given:
soil#1 KF = 10 (g/g) / (g/mL)nF, nF = 0.27 (-)
soil#2 KF = 3.1 (g/g) / (g/mL)nF, nF = 0.70 (-)
soil#3 KF = 15 (g/g) / (g/mL)nF, nF = 0.59 (-)
All Freundlich coefficients were calculated from data measured over
CTCE,water= 0.1 to 100 g/ml
We can use Excel to calculate the values of qTCE,sorbed for all three solids at
different CTCE,water values between 0.1 and 100 g/ml. Then we can plot
these values on a log-log and a linear plot to see on which soil partitioning is
more favorable.
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
42
The linear plot on the left only shows which isotherm is more favorable for
high concentrations. However, it is impossible to discern which chemical is
more favorably sorbed at Cwater<1 g/ml.
The log-log plot on the right provides a much better visualization of the
isotherms when data extends for greater than 2 orders of magnitude.
Sorption to soil #3 is always more favorable than sorption to soil #2,
sorption to soil #1 is more favorable than to soil #2 at Ci,water <10 g/ml,
and more favorable than to soil #3 at Ci,water <0.2 g/ml.
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
43
Example Problem:
Now we can combine all of the equilibrium equations that we derived from
the fugacity relationships. Consider an REV in the unsaturated zone at 15C
containing: 100g of dry soil, 10g of water, and 100ml of vapor.
Approximately 10g of TCE were released into this system. How is the TCE
distributed between the phases (i.e. what is the concentration of TCE in each
phase)
Given:
CEE 440
Hcc,TCE=0.227,
KF=0.20 (g/g)/(g/ml)nF
nF=0.65
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
44
Solution:
First we must do a mass balance on the entire system:
MTCE,total = MTCE,soil + MTCE,water + MTCE,vapor
Now we can express each of these quantities in terms of Cwater and other
known parameters obtained above in our equilibrium equations:
MTCE,soil = KF(CTCE,water)nFMsoil
MTCE,water = CTCE,waterVwater
MTCE,vapor = HTCECTCE,water * Vvapor (HTCE = Henry's constant)
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
45
Solution:
We can substitute these expressions back into the expression for MTCE,total:
MTCE,total = KF(CTCE,water)nFMsoil + CTCE,waterVwater + HTCECTCE,water Vvapor
1x107 ug = 0.20(CTCE,water)0.65100g + CTCE,water10ml + 0.227CTCE,water 100ml
Now we can iteratively solve for CTCE,water.
CTCE,water = 303,571 g/ml
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
46
Solution:
From this we can solve for the concentrations in the individual phases
MTCE,soil = KF(CTCE,water)nF Msoil
MTCE,soil = 0.20*(303,571)0.65100 = 73,198 g
MTCE,vapor = HTCECTCE,waterVvapor
MTCE,vapor = 0.227* 303,571 * 100 =6,891,083 g
MTCE,water = CTCE,water * Vwater
MTCE,water = 282 * 10 = 3,035,719 g
fTCE,water ~ 30%
fTCE,soil ~ 0.7%
fTCE,air ~ 70%
CEE 440
2011 Charles J. Werth, University of Illinois at Urbana-Champaign. All rights reserved.
47