Гидрогеология Загрязнений
и их Транспорт в
Окружающей Среде
Yoram Eckstein, Ph.D.
Fulbright Professor 2013/2014
Tomsk Polytechnic University
Tomsk, Russian Federation
Fall Semester 2013
Basic
Environmental
Chemistry
Chemical concentration
Unless two substances are fully miscible there exists a
concentration at which no further solute will dissolve
in a solution. At this point, the solution is said to be
saturated. If additional solute is added to a
saturated solution, it will not dissolve (except in
certain circumstances, when supersaturation may
occur). Instead, phase separation will occur, leading
to either coexisting phases or a suspension. The
point of saturation depends on many variables such
as ambient temperature, pressure and the precise
chemical nature of the solvent and solute.
Chemical concentration
Mass versus volume
Some units of concentration — particularly the most
popular one, molarity — require knowledge of a
substance's volume, which unlike mass is variable
depending on ambient temperature and pressure.
Therefore, volumes are not necessarily completely
additive when two liquids are added and mixed.
Volume-based measures for concentration are
therefore not to be recommended for non-dilute
solutions or problems where relatively large differences
in temperature are encountered (e.g. for phase
diagrams).
Chemical concentration
Therefore, unless otherwise stated, all
the measurements of volume are
assumed to be at a standard state
temperature and pressure (for example
25 degrees Celsius at 1 atmosphere or
101.325 kPa).
The measurement of mass does not
require such restrictions.
Chemical concentration
Moles Mass
Molarity 

Volume Liter
mg/L (of the solution)
µmg/L
Chemical concentration
Moles Mass
Molality 

Mass
kg
mg/kg (of the solvent)
µmg/kg
Units of chemical
concentration
Normality (N)
Normality is equal to the gram equivalent
weight of a solute per liter of solution. A gram
equivalent weight or equivalent is a measure of
the reactive capacity of a given molecule.
Normality is the only concentration unit that is
reaction dependent.
Units of chemical
concentration
Equivalent weight
The weight of a substance that will
combine with or replace one mole of
hydrogen or one-half mole of oxygen. The
equivalent weight is equal to the atomic
weight divided by the valence.
Units of chemical
concentration
Molality
Molarity
Mass/volume
Mass/mass
Equivalents
Normality
The Second Law of
Thermodynamics
In a chemical reaction, only part
of the energy is used to do the
work. The rest of the energy is
lost as entropy.
Gibbs Free Energy
Gibbs free energy G is the amount of
energy available for work for any
chemical reaction.
G = H – TS
where: H is the enthalpy
S is the entropy
T is the absolute temperature
Gibbs Free Energy
aA + bB ↔ cC + dD
as this system proceeds toward
equilibrium, the change in Gibbs free
energy per each additional mole
reacting is:
ΔG =
o
ΔG
+ R T lnQ
Gibbs Free Energy
ΔG =
o
ΔG
+ R T lnQ
ΔGo is the standard free energy change
characteristic for a given reaction
R is the gas constant
T is the absolute temperature and
C  D

Q
 B   A where [C], [D],
[B] and [A] are molar concentrations
c
d
b
a
Gibbs Free Energy
once the reaction has reached
equilibrium
ΔG = ΔGo + R T lnQ = 0
and
o
ΔG = -R T lnKeq
Gibbs Free Energy
C   D

K 
e
 B   A
c
eq
b
d
a
G

RT
o
Gibbs Free Energy
Some reactions are spontaneous because
they give off energy in the form of heat
(ΔH < 0). Others are spontaneous
because they lead to an increase in the
disorder of the system (ΔS > 0).
Calculations of ΔH and ΔS can be used
to probe the driving force behind a
particular reaction.
Gibbs Free Energy
Example:
Calculate ΔH and ΔS for the following
reaction and decide in which direction each
of these factors will drive the reaction.
N2(g) + 3 H2(g) ↔2 NH3(g)
Solution
Using a standard-state enthalpy of formation and
absolute entropy data table, we find the following
information:
Compound
N2(g)
H2(g)
NH3(g)
ΔHo(kJ/mol)
0
0
-46.11
So(J/mol-K)
191.61
130.68
192.45
Solution (cont’d)
The reaction is exothermic (ΔHo< 0), which means that
the enthalpy of reaction favors the products of the
reaction:
ΔHo = ΔHo (products) - ΔHo (reactants) =
= [2 mol NH3 x 46.11 kJ/mol] - [1 mol N2 x 0 kJ/mol +
+ 3 mol H2 x 0 kJ/mol] = -92.22 kJ
Solution (cont’d)
The entropy of reaction is unfavorable, however,
because there is a significant increase in the order of
the system, when N2 and H2 combine to form NH3.
ΔSo = So(products) - So(reactants) =
= [2 mol NH3 x 192.45 J/mol-K] –
- [1 mol N2 x 191.61 J/mol-K +
+ 3 mol H2 x 130.68 J/mol-K] = -198.75 J/K
Other concepts
Principle of Electroneutrality
The principle expresses the fact that all pure
substances, including natural waters carry a
net charge of zero.
Other concepts
Principle of Electroneutrality
Ci - Ai
Analytical error (%) =
Ai meq/L
0 - 3.0
3.0 - 10.0
10. – 800.
Ci + Ai
· 100
Acceptable difference
± 0.2 %
± 2%
± 5%
Other concepts
Chemical activity
In chemical thermodynamics, activity is a measure of
the “effective concentration” of a species in a mixture,
in the sense that the species' chemical potential
depends on the activity of a real solution in the same
way that it would depend on concentration for an
ideal solution.
The difference between activity and other measures of
composition arises because molecules in non-ideal
gases or solutions interact with each other, either to
attract or to repel each other. The activity of an ion is
particularly influenced by its surroundings.
Other concepts
Chemical activity
Activities should be used to define equilibrium
constants but, in practice, concentrations are
often used instead. The same is often true of
equations for reaction rates. However, there are
circumstances, e.g. in highly concentrated
brines, where the activity and the concentration
are significantly different and, as such, it is not
valid to approximate with concentrations
where activities are required.
Other concepts
Chemical activity coefficient
Deviations from ideality are accommodated by
modifying the concentration of an ion Ci by an
activity coefficient.
2
 0.51z I
log f z 
1 I
where fz is the activity coefficient; I is the ionic strength
and z is the electric charge of the ion i
1
2
I  Ci z i
2
and
aion  f z Cion
ion activity
Ionic Strength (I)
and Activity (  )
I = 0.5 Σ mi zi2
log  i 
 Azi
2
I
1  Bai I
A ~ f(t) & B ~ f(t)
zi = electric
charge of
the ion i
mi = equivalent
concentration
of the ion i
a = ionic radius
Chemical kinetics
First-order kinetics
dC
  kC
dt
C Ce
t
o
t
 kt
Error in measurements
 y
Mean
y 
n
n
i 1
i
Standard deviation
s
 ( y  y)
i
n 1
2
Chemical partition
into phases
Solubility and vapor
pressure;
The ideal gas law:
n
P

V
RT
Chemical partition
into phases
C
H 
C
A
B
Chemical partition
into phases
Henry’s Law Constants
C
H 
C
A
B
Chemical partition
into phases
Ranges of Henry’s law
constants for some
classes of organic
pollutants
Chemical partition
into phases
Polarity, sorption and
solubility;
Kow=[n]octanol/[n]water
Chemical partition
into phases
Kow – octanol/water partition coefficient
octanol – CH3(CH2)7OH
Has both hydrophobic and hydrophilic
character ("amphiphilic")
Therefore a broad range of compounds will have
measurable Kow values
Chemical partition
into phases
The Kow, or Octanol - Water partition
coefficient, is simply a measure of the
hydrophobicity (water repulsing) of an
organic compound. The more
hydrophobic a compound, the less soluble
it is, therefore the more likely it will
adsorb to soil particles.
Chemical partition
into phases
Kow can be determined by adding a known
amount of contaminant to a bottle
consisting of equal volumes of octanol and
water. The coefficient is determined by
calculating the concentration in the
octanol phase compared to the
concentration in the water phase.
Chemical partition
into phases
The Kow of a compound can also be used to find the
Koc of a particular contaminant. Koc is the
partition coefficient of the contaminant in the
organic fraction of the soil. Koc depends on the
physico-chemical properties of the contaminant,
not the percent of organic matter in the soil. One
such relationship between Kow of aromatic
compounds and Koc is:
Log Koc = 1.00 (Log Kow) - 0.21
Chemical partition
into phases
A separate equation is used for every class of
compound to determine the organic partitioning
coefficient from the octanol-water partitioning
coefficient of the compound.
Chemical partition
into phases
Kow – octanol/water partition coefficient
Importance:
 Method of quantifying the hydrophobic character of a
compound
 Can be used to estimate aqueous solubility
 Huge database of Kow values available
 Can be used to predict partitioning of a compound into
other nonpolar organic phases:
 other solvents
 natural organic material (NOM)
 biota (like fish, cells, lipids, etc.)
Chemical partition
into phases
Ranges of Kow
constants for some
classes of organic
pollutants
Chemical partition
into phases
Sorption
is the common term used for both absorption and adsorption.
These terms are often confused. Absorption is the
incorporation of a substance in one state into another of a
different state (e.g., liquids being absorbed by a solid or gases
being absorbed by water). Adsorption is the physical
adherence or bonding of ions and molecules onto the surface
of another molecule. It is the most common form of sorption
used in cleanup. Unless it is clear which process is operative,
sorption is the preferred term.
Adsorption and
absorbtion
Adsorption
As3+ sorbing to the negative charges
on the surface of clay minerals
Absorbtion
As3+ replacing idiomorphically Fe3+ in
iron-oxides
d
Adsorbate = material
being adsorbed
Adsorbent = adsorbing
material
Types of adsorption
Exchange adsorption (ion exchange)– electrostatic due to
charged sites on the surface. Adsorption goes up as ionic
charge goes up and as hydrated radius goes down.
Physical adsorption: Van der Waals attraction between
adsorbate and adsorbent. The attraction is not fixed to a
specific site and the adsorbate is relatively free to move on
the surface. This is relatively weak, reversible, adsorption
capable of multilayer adsorption.
Types of adsorption
Chemical adsorption: Some degree of chemical bonding
between adsorbate and adsorbent characterized by strong
attractiveness. Adsorbed molecules are not free to move
on the surface. There is a high degree of specificity and
typically a monolayer is formed. The process is seldom
reversible.
Generally some combination of physical and chemical
adsorption is responsible for activated carbon adsorption
in water and wastewater.
ADSORPTION EQUILIBRIA
If the adsorbent and adsorbate are contacted
long enough an equilibrium will be
established between the amount of adsorbate
adsorbed and the amount of adsorbate in
solution. The equilibrium relationship is
described by isotherms.
ADSORPTION EQUILIBRIA
qe = mass of material adsorbed (at equilibrium)
per mass of adsorbent.
Ce = equilibrium concentration in solution when
amount adsorbed equals qe.
qe/Ce relationships depend on the type of
adsorption that occurs, multi-layer, chemical,
physical adsorption, etc.
Sorption column
experimental setup
ADSORPTION EQUILIBRIA
Four
possible
models for
isotherms
ADSORPTION EQUILIBRIA
Four
common
models for
isotherms
Langmuir Isotherm
This model assumes monomolecular layer coverage and
constant binding energy between surface and adsorbate.
The model is:
Qao is the maximum adsorption
capacity (monolayer coverage)
(g solute/g adsorbent).
Ce has units of mg/L
K has units of L/mg
BET isotherm
(Brunauer, Emmett and Teller)
This is a more general, multi-layer model. It assumes that a
Langmuir isotherm applies to each layer and that no
transmigration occurs between layers. It also assumes that
there is equal energy of adsorption for each layer except for
the first layer.
BET isotherm
(Brunauer, Emmett and Teller)
CS =saturation (solubility limit)
concentration of the solute.
(mg/liter)
KB = a parameter related to the binding intensity for all layers.
Note: when Ce << CS and KB >> 1 and K = KB/Cs BET isotherm
approaches Langmuir isotherm.
Freundlich isotherm
For the special case of heterogeneous surface
energies (particularly good for mixed wastes) in
which the energy term, “KF”, varies as a function of
surface coverage we use the Freundlich model.
n and KF are system
specific constants.
Determination of
appropriate model
To determine which model to use to describe the
adsorption for a particular adsorbent/adsorbate
isotherms experiments are usually run. Data from these
isotherm experiments are then analyzed using the
following methods that are based on linearization of the
models
For the Langmuir model linearization gives:
Determination of
appropriate model
A plot of Ce/qe versus Ce
should give a straight
line with intercept :
and slope:
or:
Determination of
appropriate model
Here a plot of 1/qe versus 1/Ce should give a
straight line with intercept 1/Qao and slope:
Determination of
appropriate model
For the Freundlich isotherm use the log-log
version :
A log-log plot should yield an intercept of log KF
and a slope of 1/n.
Determination of
appropriate model
For the BET isotherm we can arrange the isotherm
equation to get:
Intercept =
Slope =
Factors which affect adsorption
extent (and therefore affect
isotherm)
Adsorbate:
Solubility
In general, as solubility of solute increases the extent of
adsorption decreases. This is known as the “Lundelius’
Rule”. Solute-solid surface binding competes with
solute-solvent attraction as discussed earlier. Factors
which affect solubility include molecular size (high
MW- low solubility), ionization (solubility is minimum
when compounds are uncharged), polarity (as polarity
increases get higher solubility because water is a polar
solvent).
Factors which affect adsorption
extent (and therefore affect
isotherm)
Adsorbate:
pH
pH often affects the surface charge on the adsorbent
as well as the charge on the solute. Generally, for
organic material as pH goes down adsorption goes up.
Temperature
Adsorption reactions are typically exothermic i.e.,
Hrxn is generally negative. Here heat is given off by
the reaction therefore as T increases extent of
adsorption decreases.
Factors which affect adsorption
extent (and therefore affect
isotherm)
Adsorbent:
Virtually every solid surface has the capacity to
adsorb solutes. From the wastewater/water
treatment point of view activated carbon (AC) is the
adsorbent of choice. AC can be prepared from many
sources:
Wood, Lignite, Coal, Nutshells, Bone
Factors which affect adsorption
extent (and therefore affect
isotherm)
Adsorbent:
Preparation of Activated Carbon
These raw materials are pyrolyzed at high temperature
under low oxygen conditions (so we don’t get complete
combustion). This forms a “char”. The char is then
activated by heating to 300 – 1000 oC in the presence
of steam, oxygen or CO2.
Result: “Activated carbon” which is highly porous,
micro-crystalline material which resembles graphite
plates with some specific functional groups (e.g.
COOH, OH)
Porosity of activated carbon
From Macroscopic to Scanning Electron Microscope
micropores:
<2nm diameter
Surface area of the AC is huge. Most of the surface
area is interior in micro- and macropores. Typical
surface area is in the range of 300-1500 m2/gram.