Pollutants and environmental
compartments
1(ii)
Physico-chemical properties of pollutants
and their influence on their behaviour in
the environment
Aims
• To provide overview of molecular properties of pollutants in the
environment:
– Vapour pressure – theoretical background, molecular
interactions governing vapour pressure, availability of
experimental vapour pressure data and estimation methods
– Activity coefficient and solubility in water – thermodynamic
consideration, effect of temperature and solution composition on
aqueous solubility and activity coefficients, availability of
experimental data and estimation methods
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their
influence on their behaviour in the environment
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Outcomes
• Students will be able to:
– estimate relevant physico-chemical properties of pollutants from
their structure
– predict reactivity of pollutants and possible environmental
behavior of pollutants
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Vapour pressure
• Definition:
– Pressure of a substance in equilibrium with its pure condensed
(liquid or solid) phase – pº
• Why is it important?
– Air/water partitioning
– Air/solid partitioning
• When is it important?
– Spills
– Pesticide application
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Ranges of pº (atm)
– PCBs – 10-5 to 10-9
– n-alkanes – 100.2 to 10-16
• n-C10H22 ~ 10-2.5
• n-C20H42 ~ 10-9
– benzene ~ 10-0.9
– toluene ~10-1.42
– ethylbenzene ~ 10-1.90
– propylbenzene ~ 10-2.35
– carbon tetrachloride ~ 10-0.85
– methane 102.44
• Even though VP is “low”, gas phase may still be important.
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Phase diagram and aggregate state
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Thermodynamic considerations
(deriving the van’t Hoff equation)
– In equilibrium the change in chemical potential in the two
systems is equal :
G12  1  2  0
d1  d 2
d1   S1dT  V1dp
where S = molar entropy
d 2   S 2 dT  V2 dp
and V = molar volume
dp ( S1  S 2 ) S12


dT (V1  V2 ) V12
dp H 12

dT TV12
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Liquid-vapor equlibrium
• For a liquid vaporizing, the volume change can be assumed to be
equal to the volume of gas produced, since the volume of the solid or
liquid is negligible:
V12  Vgas
dp H12

dT TVg
RT
 0
p
dp 0 p 0 (H12 )

dT
RT 2
where H12 = Hvap (gas) or Hsub (solid) =
energy required to convert one mole of liquid
(or solid) to gas without an increase in T
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
d ln p 0 H12

dT
RT 2
The van’t Hoff
equation
8
• Integration assuming Hvap is constant over a given temperature range
leads to:
A
ln p    B
T
0
0
ln p  
 vap H
RT
a
• If the temperature range is enlarged Hvap is not constant:
A
ln p  
B
T C
0
Antoine equation
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Solid-vapor equilibrium
• For sublimation:
Hsub = Hmelt (~25%) + Hvap (~75%)
• Still use liquid phase as reference:
– Hypothetical subcooled liquid = liquid cooled below melting
point without crystallizing
-log p
compound
pºs
<
Pºl
1,4-dichlorobenzene
3.04
2.76
phenol
3.59
3.41
22’55’ PCB
7.60
6.64
22’455’ PCB
8.02
7.40
Important for solubility
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Molecular interactions affecting vapor pressure
• Molecule:molecule interactions in condensed phase (l or s) have
greatest affect on VP:
– strong interactions lead to large Hvap, low VP
– weak interactions lead to small Hvap, high VP
• Intermolecular interactions can be classified into three types:
– van der Waals forces (nonpolar)
– Polar forces
– Hydrogen bonding
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Vapor Pressure Estimation Technique
based on regression of lots of VP data, best fit gives:

ln piL*  4.49 V iL

 
2/3
 n 1  

   15.1( i )(  i )  14.5
 n  2  
2
Di
2
Di
2
size
polarizability
H-bonding
ability
pressure in Pa, where:
V iL  molar volu me (MW/densit y)
nDi  refractive index
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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H-bonding ability
compound (class)
alkanes
1-alkenes
aliphatic ethers
aliphatic aldehydes
aliphatic alcohols
carboxylic acids
benzene
phenol
naphthalane
fluorene
pyrene
DCM
Water
 (H-donor)
0
0
0
0
0.37
0.60
0
0.6
0
0
0
0.1
0.82
 (H-acceptor)
0
0.07
0.45
0.45
0.48
0.45
0.14
0.31
0.2
0.2
0.29
0.05
0.35
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Refractive index
• Refractive index
(response to light) is a
function of
polarizability
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Trouton’s rule
• At their boiling points, most organic compounds have a similar
entropy of vaporization:
S vap Tb   85  90 J / molK
– exception: strongly polar or H-bonding compounds
• Kistiakowsky’s expression gives slightly more accurate predictions:
S vap Tb   K F 36.6  8.31ln Tb 
– KF = 1 for apolar and many monopolar compounds
– For weakly bipolar compounds (e.g., esters, ketones, nitriles), KF = 1.04
– Primary amines KF = 1.10, phenols KF = 1.15, aliphatic alcohols KF = 1.30
• At Tb:
G  0  H vap  Tb S vap
– So, if we know Tb, we can estimate Hvap (at the boiling point)
fairly accurately.
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Estimating vapor pressure at other T
H vap  1 1 
  
ln

pT1
R  T1 T2 
pT2
• Important: Hvap is not constant.
• Especially if Tb is high (> 100ºC), the estimate of Hvap from
Trouton/Kistiakowsky may not be valid.
• Empirically, Hvap is a function of the vapor pressure:
H vap (T1 )  a log piL* (T1 )  b
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• From a data set of many compounds, Goss and Schwarzenbach
(1999) get:
H (298K )  8.80 log p* (298K )  70.0
vap
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
iL
18
• Less empirically, assume Hvap is linearly proportional to T (i.e.
assume that the heat capacity, vapCp is constant):
H vap (T )  H vap (Tb )   vapC p (Tb )  (Tb  T )
• Substitution into the Clausius-Clapeyron equation and integration
from Tb to T gives:
H vap (Tb )  1 1   vapC p (Tb )  Tb   vapC p (Tb )  Tb 
   
ln p 
 1   
ln  
R
R
R
 T
T 
 Tb T 
0
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Substitution H vap (Tb )  Tb S vap (Tb ) in previous equation gives:
 Svap (Tb )  vapC p (Tb )   Tb   vapC p (Tb )  Tb 
  1   
ln p  

ln  
R
R
R
T 

  T
0
• Generally:
 vapC p (Tb )  0.8  S vap (Tb )
S vap Tb   88 J / molK
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Inserting Kistiakowsky’s expression, the following equation is
obtained:
  Tb 
 Tb  (bar)
ln p   K F (4.4  ln Tb ) 1.8  1  0.8 ln  

 T 
 T
0
– KF is the Fishtine factor, usually 1, but sometimes as high as 1.3
• OK for liquids with Tb < 100 ºC
• High MW compounds, need correction for intermolecular forces
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Aqueous Solubility
• Equilibrium partitioning of a compound between its pure phase and
water
• Will lead us to Kow and Kaw
Air
A gas is a gas is a gas
T, P
KH = PoL/Csatw
Kow = Csato/Csatw
Koa = Csato/PoL
Koa
KH
Octanol
PoL
Water
Fresh, salt, ground, pore
T, salinity, cosolvents
Csatw
Kow
Pure Phase
(l) or (s)
Ideal behavior
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on their behaviour in the environment
NOM, biological lipids, other
solvents
T, chemical composition
Csato
22
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Relationship between solubility and
activity coefficient
• Organic liquid dissolving in water:
 iL  
*
iL
 RT ln  iL  xiL
for the organic
liquid phase
 iw   *iL  RT ln  iw  xiw
for the organic
chemical in the
aqueous phase
• At equilibrium:
iw  iL  0  RT ln  iw  xiw  RT ln  iL  xiL
sat
xiw
RT ln  iL  RT ln  iwsat
ln

xiL
RT
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
At saturation!
24
• If we assume: xiL = 1 and iL = 1
sat
ln xiw
RT ln  iwsat
GiwE , sat


RT
RT
• The relationship between solubility and activity coefficient is:
sat
iw
x

1
 iwsat
or
sat
iw
C

1
V w iwsat
for liquids
– The activity coefficient is the inverse of the mole fraction
solubility
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Solids
– additional energy is needed to melt the solid before it can be
solubilized:
C ( L)  C (s)  e
sat
iw
sat
iw
  fusGi / RT
piL*
 fusGi  RT ln
pis
*
p
Ciwsat ( L)  Ciwsat ( s)  iL
pis
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Gases:
– solubility commonly reported at 1 bar or 1 atm (1 atm = 1.013 bar)
– O2 is an exception
– the solubility of the hypothetical superheated liquid (which you
might get from an estimation technique) may be calculated as:
*
iL
p
C ( L)  C 
pi
sat
iw
pi
iw
theoretical “partial” pressure
of the gas at that T (i.e. > 1
atm)
Actual partial pressure of the
gas in the system
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Concentration
dependence of 
–  at saturation   at
infinite dilution
– However, for
compounds with  >
100 assume:
•  at saturation = 
at infinite
dilution, i.e.
solute molecules
do not interact,
even at saturation
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Molecular picture of the
dissolution process
• The two most important driving forces in determining the
extent of dissolution of a substance in any liquid solvent are:
– an increase in entropy of the system
– compatibility of intermolecular forces.
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Ideal liquids:
– For ideal liquids in dilute solution in water, the intermolecular attractive
forces are identical, and Hmix = 0. The molar free energy of solution
is:
GS  Gmix  TS mix  RT ln
xf
x
= Gibbs molar free energy of solution, mixing i(kJ/mol)
Gs ,Gmix
TSmix = Temperature  Entropy of mixing (kJ/mol)
R = gas law constant (8.414 J/mol-K)
T = temperature (K)
Xf, Xi = solute mole fraction concentration final, initial
– for dilute solutions mole fraction of solvent  1
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Nonideal liquids:
– The intermolecular attractive forces are not normally equal in magnitude
between organics and water:
GS  Gmix  Ge
GS  H S  TS S  H e  T (S mix  Se )
Ge = Excess Gibbs free energy (kJ/mol)
He, Se = Excess enthalpy and excess entropy (kJ/mol)
He = intermolecular attractive forces; cavity formation (solvation)
Se = cavity formation (size); solvent restructuring; mixing
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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•
For small molecules, enthalpy
term is small (± 10 kJ/mol)
– Only for large molecules is
enthalpy significant
(positive)
•
Entropy term is generally
unfavorable
– Water forms a “flickering
crystal” around the
compound, which fixes
both the orientation of the
water and of the organic
molecule
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Solubility estimation techniques
• Activity coefficients and water solubilities can be estimated a priori using
molecular size, through molar volume (V, cm3/mol). Molar volumes can be
approximated:
Vi   ( Nij )(aij )   (nij )(6.56)
Ni = number of atoms of type i in j-th molecule
ai = atomic volume of i-th atom in jth molecule (cm3/mol)
nj = number of bonds in j-th molecule (all types)
• Solubility can approximated using a LFER of the type:
ln  iw ( L)  a  ( size )  b
ln Ciwsat ( L)  c  ( size )  d
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• This type of LFER is only
applicable within a group of similar
compounds:
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Another estimation technique – universal – valid for all
compounds/classes/types:
Vapour
pressure
molar volume
describes
vdW forces
refractive index
describes
polarity
2



n
2/3
*
Di  1
  5.78( i )
ln  iw   ln piL  0.572 Vix   2
 nDi  2 

additional
 8.77( i )  11.1(  i )  0.0472Vix  9.49
polarizability
term
H-bonding
cavity term
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their
influence on their behaviour in the environment
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Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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Factors Influencing Solubility in
Water
•
•
•
•
•
Temperature
Salinity
pH
Dissolved organic matter (DOM)
Co-solvents
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Temperature effects on solubility
– Generally:
• as T , solubility  for solids.
• as T , solubility can  or  for liquids and gases.
– BUT For some organic compounds, the sign of Hs changes;
therefore, opposite temperature effects exist for the same
compound!
• The influence of temperature on water solubility can be
quantitatively described by the van't Hoff equation as:
1 H
ln Csat  
C
R T
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Solids:
• Liquids:
• Gases:
ln Ciwsat ( s )  
 fus H i  H iwE
RT
C
E
H
ln Ciwsat ( L)   iw  C
RT
ln Ciwsat ( g )  
  vap H i  H iwE
RT
C
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• The effect of salinity
– As salinity increases, the solubility of neutral organic compounds
decreases (activity coefficient increases)
 iw, salt   iw 10
 K is [ salt]tot
typical seawater
[salt] = 0.5M
– Ks = Setschenow salt constant (depends on the compound and the salt)
K is, seawater   K is, saltk  xk
k
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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on their behaviour in the environment
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on their behaviour in the environment
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• The effect of pH
– pH effect depends on the structure of the solute.
– If the solute is subject to acid/base reactions then pH is vital
in determining water solubility.
– The ionized form has much higher solubility than the
neutral form.
– The apparent solubility is higher because it comprises both
the ionized and neutral forms.
– The intrinsic solubility of the neutral form is not affected.
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on their behaviour in the environment
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• The effect of DOM
– DOM increases the apparent water solubility for hydrophobic
compounds.
– DOM serves as a site where organic compounds can partition, thereby
enhancing water solubility.
– Solubility in water in the presence of DOM is given by the relation:
Csat, DOM  Csat (1  DOM K DOM )
• [DOM] = concentration of DOM in water, kg/L
• KDOM = DOM/water partition coefficient
– Again, the intrinsic solubility of the compound is not affected.
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on their behaviour in the environment
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• The effect of cosolvents
– the presence of a co-solvent can increase the solubility of
hydrophobic organic chemicals
– co-solvents can completely change the solvation properties
of “water”
– examples:
• industrial wastewaters
• “gasohol”
• engineered systems for soil or groundwater remediation
• HPLC
Environmental Processes / 1(ii) / Physico-chemical properties of pollutants and their influence
on their behaviour in the environment
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• Solubility increases exponentially as cosolvent fraction
increases.
• Need 5-10 volume % of cosolvent to see an effect.
• Extent of solubility enhancement depends on type of cosolvent
and solute:
– effect is greatest for large, nonpolar solutes
– more “organic” cosolvents have greater effect
propanol>ethanol>methanol
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on their behaviour in the environment
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• Bigger, more non-polar
compounds are more
affected by co-solvents
• Different co-solvents
behave differently,
behavior is not always
linear
• We can develop linear
relationships to describe
the affect of co-solvents on
solubility. These
relationships depend on
the type and size of the
solute
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on their behaviour in the environment
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