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7/17/2019 Articulo de Spark
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1
le.
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~ ;
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Sparks D. L.
1995. Environmental
soil
Chemistry,
Academic
Press
San Diego,
CA,
USA.
KINETICS OF SOIL CHEMIC L
PROCESSES
.
-..: -
_ ....
.
.
\;-
Many soil chemical processes are rime-dependent. To fullv undersr:md rh e
dvnamic inreractions
of
metals, radionuclides. pesticides, industrial chernicals.
and planr nutrients with soils and ro predict rheir fate with rime, '' knowledge
of the kinetics of rhese reactions is imporrant. This chaprer will rro\ide an
overview
of
this tapie, with applicarions ro environmenrally
importam
re3
c
rions. The reader is referred ro se"eral sources for more definitive discu ss ions
on rhe tapie (Sparks. 1989: Sparks and Su .uez. 1991).
RATE LIMITING
STEPS ANO TIME SCALES
OF
SOIL CHEMICAL
REACTIONS
Four main processes can affecr rhe rate 0f soil chemical reactions. These
be bro;:J[y classified as rransport and chcmical reaction processes (Fig. 7. 1 .
The slowest of rhese will limit rhe rate of .1 particular reaction. Bulk tr:mspon
\1 in
Fig.
7.1
.
which occurs in rhe solu rion phase,
is
11ery rapid ami is not
normally rare-limiring.
In rhe
laborarory, r can
he
eliminared by rapid
mi
xing.
The acrual chemical reacrion (CR) at rhe surface (4), e.g., adsorption, is al so
rapid and usually not rate-limiring. The rwo remaining transpon or rna
ss
rr:111sfer processes, either singly or in combinaran, normal v are rate-lirniring.
Film diffusion (FD) involves transpon of 111 ion or molecule rhrou gh a bound
:l f ) laver or film (water molecules) thar surrounds rhe parricle sttrface
21.
l'anicle diffusion (PD), somerimes refened
ro as
intraparricle diffusion. in
volves transpon of an ion or molecule along pore-wall surfaces (3b) and/or
wirhin the pares of rhe panicle surface (3,1 .
159
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16
CHAPTER
KIHETICI
Of IOIL CHEHICAL PROCESIEI
-
FIGURE 7.1. Rate-determining steps in soil chemical reactions. From
Weber,
W. J., Jr. (1984)
Evolution of a technology.
J
Environ
Eng, Div
Am. Soc. Civ
Eng.) 110,
899-917.
Reproduced with
permission of ASCE.
Soil chemical reactions occur over a wide time scale (Fig. 7.2), ranging from
microseconds
and
milliseconds for ion association (ion pairing, complexation,
and chelation rype reactions
in
solurion), ion exchange,
and
sorne
sorption
reactions to years for mineral solution (precipitationldissolution reactions
including discrete mineral phases) and mineral crystallization reactions
(Amacher, 1991). These reactions can occur simultaneously and consecutively.
Certainly an important factor
in
controlling the rate of many soil chemical
reactions is the type
and
quantity of soil cornponems. For example, ion
exchange reactions are usually more rapid on clay minerals such as kaolinite
and
oxides than
on c_lay
surfaces such as vermiculite and mica. Ths
is
attrib
uted to the externa exchange sites on kaolin te versus the multiple types
of
exchange sites with vermiculite and micas. Externa planar, edge, and inter
layer sites exist
on
the surfaces of vermiculite
and
micas with sorne of the latter
partially or rorally collaps. d. High rates of reaction are often observed for
externa si tes, intermediare rates on edge sites, and low rates on interlayer si tes
(Jardine and Sparks, 1984a).
A number of investigators have found that adsorption reactions of certain
metal cations such as Cu
1
+
and anions such as borate, arsenate, molybdate,
Ion Assoclation
Multlvalent Ion Hydrolysis
Gas Water
Ion Exchange
Sorptlon
Mlnerai-Solutlon
Mineral
Crystalllzatlon
_. __.
S
min h day mo yr mil
Time Scale
-
FIGURE 7 2.
Time ranges required to attain equilibrium by different types of reactions
in
soil
environments. From Amacher 1991 ), with permission.
RATE LAWI
161
selenire, selenate,
and
chromate occur
on
goethite surfaces on millist' - ond tim;
scales
(Zhang and
Sparks, 1989, 1990b; Grossl et al. 1994). Sorption
of
metals
on
humics
is
also rapid. Half-lives tor Pb2+,
Cu
1
+,
and
Zn2+
sorption
.
on
peat ranged from 5 to 15 s (Bunzl et al. 1976).
However, there are many adsorption, ;tnd panicularly desorption, reactions
involving organic chemicals such as pesticides, where the reaction rates are
very low. It appears that
an
important factor affecting the rates
of
organic
chemical reactions in soils is the ritne period over which the organic
compound
has been in contact with che soil. For example, 1,2-dibromoethane (EDB)
release from soils reacted in the laboratory over a short period of time was
much more rapid than EDB release from field soils rhat had been contaminated
wirh EDB for many years. This difference in release was related
to
greater PD
into micropores of clay minerals and humic componems that occurred at
longer times (Steinberg
et al.
1987).
lt would be instructive at this point to define two important
te rms
chemical kinetics
and
kinetics. Chemical kinetics can be defined as
"the
inves
tigation of chemical . reaction rates ancl the molecular processes
by
which
reactions occur where transpon is
not
limiting" (Gardiner, 1969). Transpon
phenomena, as mentioned earlier, include transpon in the solution phase, film
diffusion, and particle diffusion. Kinetic> is the study of tirne-dependent pro
cesses .
The study of chemical kinetics in homogeneous solutions is difficult, and
when one studies heterogeneous systems such as soil components and, partic
ularly, soils, the difficulties are magnified. It is extremely difficult ro eliminare
transport processes in soils because they are mixtures
of
severa inorganic and
organic components
that
are often imimately associated with each other and
beca use soils have mult iple type s
of
sites with varying reactivities for inorganic
and
organic adsorbates. Additionally, there are an array of different panicle
sizes and porosities in soils
that
enhance their heterogeneity.
Thus,
when
dealing with soils
and
soil componems, one usually studies the kinetics, simply
defined as the study of tirne-dependent processes, of these reactions.
R TE l WS
There are two
important
reasons for investigating the rates
of
soil chemical
processes (Sparks, 1989): (1) to determine how rapidly reactions attain equi
librium,
and
(2) ro infer inforrnation
on
reaction mechanisms.
One of che
rnost
important aspects of chemical kinetics
is
the establishment of a rate law.
Bv
definition, a rate law
is
a differential q u a t i o n For the following r e a c t i o ~
(Bunnett, 1986),
aA
+
b B y Y
+
zZ
7.1)
the rate of the reaction is proporcional ro sorne power of the concentrations of
reactants A and B and/or other species (C, D, etc.) in the system. The terrns a
b
y and z are stoichiometric coefficient>and are assumed to be equal to one
in the following discussion. The power ro which theconcemration is raised
rnay equal zero (i.e .,
che
rate is independent of that concentration , e ven for
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,,
CHAPTER 7
KIHETICI OF IOIL
CHEHICAl
PROCEIIEI
reactant
A or B
.
Rates are expressed as a decrease in reactant concentration
or
an increase in
product
concemration per unir time. Thus, the rate of reactant A
abo
ve, which has a concentration
[A) at
any time
t is
(-d[A)/(dt)) while rhe
rate with regard to product Y having a concenrration [Y] at time
t
is (d[Y]/
(dt)).
The
rate
expression for Eq. (7.1) is
d[Y]Idt = d[A]Idt = k[A] [B]il
. . .
(7.2)
where k is the rate constant,
a is
the arder of the reaction with respect to
reactant A and can be referred
toas
a partial order, and f is the order with
respect to reactant B These orders are experimentally determined and not
necessarily integral numbers. The sum of all the partial orders
(a,
/3 etc.) is the
overall order (n) and may be expressed as
n = a f 3 .
(7.3)
Once the values of a {3 etc., are determined experimenrally, the rate law is
defined. Reaction order provides only information about the manner in which
rate depends on concentration. Order does not mean the same as "niolecular
ity which
concerns the number of reactant particles {atoms, molecules, free
radicals, or ions) entering into an elementary reaction. One can define an
elementary reaction as
one
in which no reaction intermediares have been
detected or need to be postulated to describe the chemical reaction on a
molecular scale. An elementary reaction is assumed to occur
in
a single step
and
to
pass through a single transition state {Bunnett,
1986).
To prove
that
a reacrion is elemenrary, one can use experimental conditions
rhat are
different from those employed in determining the law. For example, if
one conducted a kinetic study using a flow technique (see later discussion on
this technique) and the rate
of
influent solution {flow rate) was
1
mi min-
1
,
one could study severa other flow rates ro see if reaction rate and rate
constants change. If they do, one is not determining mechanistic rate laws.
Rate laws serve three purposes: rhey assist one in predicting the reacton
rate, mechanisms
can
be proposed, and reacrion orders can be ascerrained.
There
are four types
of
rate laws that can be determined for soil chemical
processes (Skopp, 1986): mechanistic, apparent,
transpon
with apparent, and
transport
with mechanistic. Mechanistic rate laws assume that only chemical
kinetics are operational and transport phenomena are not occurring. Conse
quently, it
is
difficult to determine mechanistic rate laws for most soil chemical
systems
due to
the heterogeneiry of the sysrem caused by different particle
sizes, porosities,
and
rypes
of
retention sites. There is evidence
that
with sorne
kinetic studies using relaxation techniques .(see later discussion) mechanistic
rate laws are determined since the agreement berween equilibrium constanrs
calculated from both kinetics and equilibrium studies are comparable {Tang
and Sparks,
1993).
This would ind cate
that
transpon processes in the kinetics
studies are severely limited
{see
Chaprer 5). Apparent rate laws include both
chemical kinetics
and
transporr-controlled processes. Apparent rate laws
and
rate coefficients indicare that diffusion and other microscopic transport pro
cesses affect the reaction rate. Thus, soil strucrure, stirring, mixing, and How
rate all would affect the kinetics. Transpon with apparent rare laws emphasize
OHERMINATION
Of REACTION OROER ANO RATE CONITANTI
163
transport phenomena. One often assumes first-order or zero-order reactions
(see discussion below
on
reaction arder). In determining
transport
with mech
anistic rate laws one attempts to describe imultaneously transport-controlled
and
chemical kinetics phenomena.
One
is thus trying to accurately explain
both the chemistry
and
the physics
of
the ;ystem.
OETERMIN TION OF RE CTION OROER NO R TE CONST NTS
There
are three basic ways ro determine rate laws and rate
constants
(Bunnett, 1986; Skopp, 1986; Sparks, 1989):
(1)
using initial rates, {2) directly
using integra red equati ons and graphing tite data, and
(3)
using nonlinear least
square analysis.
Let us assume the following elementarv reaction between species
A,
B, and
Y,
k
A
B:;::==Y.
k_
A forward reaction rate law can
be
written as
d[A]Idt = -k
1
[A][B],
(7.4)
where
k
is
the forward rate constant and a and
f
(see Eq. 7.2) are e:1ch
assumed to
be
l.
The reverse reaction rate law for Eq. (7.4)
is
d[A]Idt = + k_
1
[Y],
(7.6)
where
k_
is
the reverse rate constant.
Equations {7.5) and (7.6) are only ap plicable far from equilibrium where
back
or
reverse reactions are insignificant.
If
both these reactions are occur
ring, Eqs.
{7.5)
and
(7.6)
must be combined such that,
d[A]Idt = - k,[A][B] + k_,[Y]. {7.7)
Equation {7.7) applies the principie that the net reacrion rate is the differ
ence between the sum of all reverse reaction rates and the sum of all forward
reaction rares.
One way to ensure that back reactions are not important is
to
measure
inicial rates. The initial race
is
the limit
of
the reaccion
rateas
time reaches zero.
\ V ith an initial rate method, one plots rhe concentration
of
a reacranr
or
produce over a short reaction time period during which the concentrations
of
the reactants change so litde that the instantaneous rate is hardly affecred.
Thus, by measuring initial rates, one could assume that only the forward
reaction
in
Eq. {7.4) predominares. This would simplify the rate
l:.lw
co that
given in Eq. {7.5) which as wrirten would be a second-order reaction, first
order in reactant A and first-order in reactant B. Equation {7.4), under these
conditions, would represem a second-order irreversible elementary reaction.
To
measure initial rates, one must have a :ailable a technique chat can mensure
r ~ p i d reactions such as a relaxation
me
rhod (see derailed discussion on rhis
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164
C H P T E ~
7
KIHETICS Of
SOIL CHEHICAL
PROCESIES
later)
and
an ,accurate analytical detection system to determine product con
cenrrarions.
Inregrated rate
equations
can also be used ro determine rate constants . If
one
assumesthat reactant B in Eq. (7.5) is in large excess of reactant A, which
is
an
example of rhe "method of isolation" to analyze kinetic data, and
Y
=
O
where Y
0
is the initial concentraran of
product Y,
Eq. (7.5) can be simplified
to
d[A]Idt = - k
1
[A)
.
(7.8)
The
first-order dependence
of
[A)
can
be evaluated using rhe integrared
form of Eq. (7.8) using the inicial conditions
at
t = O, A = A
0
l
kt
log [A), = og [A)
0
- 2.303'
(7.9)
The half-rime
(t
112
)
for the above reaction
is
equal to
0.6931k
1
and is the rime
required for half of reactant
A to
be consumed.
f a reaction
is
first-order, a plot
of
lag [A), vs
t
should result in a straight
line with a slope = - k12.303 and an inrercept of log
[A)
0
An example of
first-order plots for
Mn
2
+
sorption on 5-Mn0
2
at
two
initial Mn
2
+ concentra
tions, [Mn
2
+ )
0
,
25 and 40 p.M, is shown in Fig. 7.3. One sees that the plots are
linear
at
borh concentrations, which would indicare
that
the sorption process
is first
arder.
The
[Mn
2
+ )
0
values, obrained from rhe intercept
of
Fig. 7.3, were
24 and 41 p.M, in
good
agreemenr with the
two
(Mn2+)
0
val u es. The rare
constants
were
3.73
X
10-
3
and
3.75
X
10-
3
s-
1
at
[Mn
2
+]
0 of
25
and
40 p.M
respectively. The findings
that
the rate constants are
not
significantly
changed with concentration is a very good indicarion that the reacrion in Eq.
(7.8)
is first
arder
under the experimental conditions
that
were imposed.
t is
dangerous
ro conclude that a particular reacrion order is correct, based
simply on the conformity of
data
to an inregrated equation.
As
illustrated
above, multiple inicial
concentrations
that vary considerably should be em
ployed to see rhat the rate is independent of concentrarion. One should also
test multiple integrated
equations.
lt may be useful to
show
rhat reaction rate is
1.6.----------------..
:: ;
14
:1.
+
1:
1.2
E
Ol
.2
1.0
(Mn2]
0
=
40
M
y=
1.61 . (8.65 x 1oJx,
R2
= 0.998
0.8
L __J___J___..L_
_t__ l _l__J__ J
w 00
Time ms
-
FIGURE 7 3 lnitial reaction rates depicting the first-order dependenc of Mn
1
sorption
as
a
function
of
time for inicial Mn
1
' concentrations ([Mn'-]
0
) of 25 and 40 p.M. From Fendorf et al. (1993),
with permission. .
KINETIC HOOELS
165
not affected by species whose concentrarions do
not
change considerably
during an experiment; these
may
be substances not consumed in the reaction
i .e., catalysts) or present in large excess (Bunnett, 1986; Sparks, 1989).
Least squares analysis can also be used ro determine rate constants. With
this method, one fits the best straight line ro a set of points that are linearly
relared as
y = mx
+ b where
y is
the ordinate
and
x is the abscissa
datum
point, respectively. The slope,
m and
the inrercept, b can be calculated
by
least squares analysis using Eqs. (7.10) and (7.11), respectively (Sparks, 1989),
n
l xy
Ix
2:y
m= , )2
n
x--
b =
l:y
2:x
1
- x l x y
n 2:x
1
- Cix
1
'
(7.10)
(7.11)
where n is the
number
of data points and the summarions are for all
data
points in the set.
Curvature
may
result
when
kineric data are plottetl. This may be due roan
incorrect assumption of reaction order.
f
firsr-order kinerics is assumed and
the reaction is really second
arder,
downward curvature is observed. f sec
ond-order kinetics is assumed but the reacrion is first-order, upward curvature
is observed. Curvarure can also be due to fractional, third, higher,
or
mixed
reaction order. Nonattainment of equilibrium often resulrs in downward cur
vature. Temperature changes during the study can also cause curvarure; rhus,
it is
important
that
temperature
be accurarely conrrolled during a kineric
experiment.
KINETIC MODELS
While first-order models have been used widely to describe the kinetics
of
soil chemical processes, a
number
of orher models have been employed. These
include various ordered equations such as zero-order, second-order, and frac
tonal-order,
and
Elovich, power function
or
fracrional power, and parabolic
diffusion models. A brief discussion of sorne of these will be given; rhe final
forms of the equarions are given in Table 7.1. For more complete details and
applications
of
these models one should consult Sparks ( 1989).
Elovich Equation
The Elovich equation was originally developed to describe the kinerics of
hererogeneous chemisorption
of
gases
on
salid surfaces (Low, 1960).
lt
seems
ro describe a
number
of reaction mechanisms including bulk
and
surface
diffusion
and
activation and deacrivation of catalytic surfaces.
In soil chemistry, the Elovich equation has been used
ro
describe the kinerics
of
sorption and desorption of various inorganic materials
on
soils (see Spar ks,
1989).
lt
can he expressed as (Chien and Clayton, 1980)
q =
(113)
In (a/{3) + (1/3)
In
t
(7.12)
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CHAPTER
7
KIHETICI
Of IOIL
CHEHICAL PROCEIIEI
,,
- TABLE -7.1. linear Forms of Kinetic
Equations Commonly Used in Environmental
Soil Chemistry"
Zero orde.r"
[AJ, = [AJ
0
- kt
First
order
kt
log
[AJ,
= log [AJo -
.303'
Second ordeib
1 1
-=- kt
[Al, [AJo
Elovich
q,
= 11/3) In
(a//3)
+
(1//3) In t
Parabolic diffusion
R
t
1
1
Power funcrion
In q = In
k +
v In t
Terms
are defined ln the texr.
Describing
rhe reacrion
A--+Y.
' In x
=
2.
303
log x is
rhe conversion
from natural
logarithms (in) ro base
10
logarirhms (log).
where q, is the amount of sorbate per unir mass of sorbenr ar time tanda and
{
are constants during
any one experiment. A
plot
of
q, vs
In t should give a
linear relationship if rhe Elovich equation
is
applicable wirh a slope of 1/{3)
and an incercepc of (1/{3) In (a{3).
An applicarion of Eq. (7.12) ro phosphate sorption on soils
is
shown in Fig.
7.4.
Sorne invescigacors have used che a
and { parameters
from
the
Elovich
equation
ro estimare reacrion rates. For example, ir has been suggested thar a
decrease in {
and/or
an increase in
a
would increase reacrion rate. However,
this is quesrionable.
The
slope of plots using Eq. (7. 12) changes wich the
concentration of the
adsorpcive
and with
rhe
solution
to soil ratio (Sharpley,
1983) . Therefore, che slopes are not always characceriscic
of
the soil
but
mav
depend on various experimental
conditions. '
Sorne researchers have also suggested thac breaks or multiple linear
segments in Elovich plots
could
indicare a changeover from one rype
of
binding site ro .
another
(Atkinson et al., 1970). However, such mechanisric
suggescions
may
not be correcc (Sparks, 1989).
Parabolic Diffusion Equation
The parabolic diffusion equacion is often used t indicare thar diffusion
controlled phenomena are rate-limiting. lt was originallv derived based on
. i
.
1
1
i
1
.
KINETIC
HOOELI
..
i:
-e
o
E
: 1
6
60
'
4
20
o
A.-
-2
-1
o
Porirua Soll .
.
2
In
t, h
3
r
2
= 0.990
4
167
6
-
FIGURE
7
4.
Plot of Elovlch equation for phosphat< sorption on
two
soils where (
0
is the initial
phosphorus concentration added at ti
me
O and
C
s the phosphorus concentration in the soif solution at
time t The quantity C.-Q can be equared to qr the amount sorbed at time t. From Chien and Claycon
( 1980). with permission.
radial diffusion in a cylinder where the ion concentration on che cylindrical
surface is
constant,
and initially the ion con
centration throughout
the cylinder
is uniform. lt is also assumed that
ion
diffus
ion
chrough
che upper and
lower
faces of the cylinder
is
negligible. Following Crank (1976), the parabolic
diffusion
equation,
as applied
to
soils can be expressed as
(7. 13)
where r is the average radius of the soil parricle, q, was defined earlier, qx
is
the
corresponding
quantity
of sorbate at equilibrium,
and
D is the diffusion
coefficient.
Equation (7.13) can be simply expressed as
=
R
t
2
+ constant,
(7.14)
where R
0
is the overall diffusion coefficient. If che parabolic diffusion
law
is
valid, a plot of versus t z should yield a linear relationship .
The parabolic diffusion equation has successfu lly described metal reacrions
on soils and soil constituents (Chute and Quirk, 1967; Jardine and Sparks,
1984a,
feldspar weathering (Wollast,
196
7), and pesticide reactions (Weber
and Gould, 1966).
Fractional Power or
Power
Function Equation
This equation can be expressed as
q = kt
,
(7.15)
where q is the
amount of
sorbate per unit mass of sorbent,
k and
v are
constants, and
vis
positive and < l. Equation (7.15) is empirical, except for
thr
case where
v
= 0.5, when Eq. (7.15)
is
>imilar
to
the parabolic diffusion
equation.
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1 68
CH PTER
7 KINETICI
OF
IOil CHEMIC l PROCEIIEI
Equation (7.15)
and
various modified forms have been used by a number
of
researchers to describe the kinetics of soil chemical processes (Kuo and Lotse,
1974; Havlin and Wesfall, 1985).
Comparison of Kinetic Models
In a number of srudies it has been shown
that
severa k inetic models
describe the rate
data
well, based on correlation coefficients and standard
errors of
the estimare (Chien
and Clayton
1980;
Onken and Matheson
1982;
Sparks and Jardine 1984). Despite this, there often is
nota
consistent relation
between the equation
that
gives the best
fit and
the physicochemical and
mineralogical properties
of
the adsorbent(s) being studied. Another problem
with sorne
of
the kinetic equations is
that
they are emprica
and
no meaningful
rate parameters can be obtained.
Aharoni and Ungarish (1976) and Aharoni (1984) noted that sorne kinetic
equations are approximations ro which more general expressions reduce in
cerrain limited time ranges. They suggested a generalized emprica equation
by examining the applicability of power function, Elovich, and first-order
equations to experimental data.
By
writing these as the explicit functions of the
reciproca of the rate Z which is
dq/dt -
1
one can show that a plot of Z vs t
should be convex if the power function equation
is
operacional 1 in Fig. 7.5),
linear if the Elovich equation is appropriate
2
in Fig. 7.5), and concave if the
first-order
equation
is
appropriate
3 in Fig. 7.5). However, Z
vs t
plots for soil
systems (Fig. 7.6) :lre usually S-shaped, convex at small
t
concave at large t
and linear at sorne intermediare
t.
These findings suggest rhat the reacrion rare
can best be described by the power function equation at small t by the Elovich
equation
atan
intermediare
t
and by a firsr-order
equation
at large
t
Thus, the
S-shaped curve indicares that the above equations may be applicable, each at
sorne limited time range.
One of
the reasons a particular kinetic model appears to be applicable may
be that the study is conducted during the time range when the model is
most
appropriate. While sorption for example, decreases over many orders of
0 ~ ~ ~ 2 ~ ~ 3 4 ~ 5 6 ~ ~ ~ ~ 9 ~ 1 0
lime, arbitrary unils
-
FIGURE
7 5 Plots of Z
vs
time implied by 1) power functlon model, 2) Elovich model. and 3)
first order model. The equations for the models
w r
differentiated and expressed as explicit functions
of the reciproca of the rate, Z. From Aharoni and Sparks (
1991 ).
with permission.
l
KINETIC
HETHODOlOGIEI
69
200
r .
5
Time, h
- FIGURE 7 6 Sorption of phosphate by a Typic Dystrochrept soil plotted as
Z vs
time. The cirdes
represent the experimental data of Polnopoulos et al. (19.86). The solid line is a curve calculated
according to a homogeneous diffusion model. From Ahamni and Sparks (
1991 ),
with permission.
magnirude befare equilibrium
is
approached with most methods and experi
ments, only a portion of the entire reaction
is
measured and over this rime
range the assumprions associated with a particular equation are valid. Aharoni
and Suzin (1982a,b) showed that the S-shaped curves could be well described
using homogeneous and heterogeneous diffusion models. In homogeneous
diffusion situations, the final
and
initial portions
of
the S-shaped curves (con
forming
to
the power function
and
first-
order
equations, respectively) pre
dominated (see Fig. 7.6 showing data conformity toa homogeneous diffusion
model), whereas in insrances where rhe heterogeneous diffusion model was
operacional, the linear portian of the
S-sh
15 s), which include batch and flow techniques, and rapid techniques that
can measure reactions on millisecond ami microsecond time scales. Ir should
be recognized that none of these methods is a panacea for kinetic analyses.
They all have advantages and disadvantages. For comprehensive discussions
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170
CHAPTER
7
KINETICS Of SOil CHEHICAl
PROCESSES
- TABLE 7.2. Comparison or Sorption Kinetic Models'b
Conceptual model Fitting parameter(s)
One-site model (Coates and Elzerman, kd
1986)
s ~ c
Two-site model (Coares and Elzerman, kd X
1
1986)
Radial diffusion: penetraran
retardarion (pore diffusion) model
(Wu
and
Gschwend, 1986)
s ~ ~
Dual-resistance surface diffusion model 0 k.
(Miller and Pedir, 1992)
s ~ c ~ c
Model llmitatio ns
Cannot describe biphasic sorption/
desorpcion
Cannot describe the bleeding or
slow, reversible, nonequilibrium
desorprion for residual sorbed
compounds lKarickhoff, 19801
Cannot describe instanraneous uptake
wirhout additional correction factor
(Ball, 1989); did
not
describe kinetic
data for times grearer than lO' min
(Wu and Gschwend,
1986)
Model calibrared with sorprion data
predicred more desorprion rhan
occurred ln the desorption
experiments (Miller
and
Pedir,
1992)
Reprinred wirh permission from Connaughton et
al. (1993). Copyright 1993
American Chemical Socierj.
Abbreviarions used are as follows: S concenrration
of
rhe bulk sorbed conraminant g g
1
; C,
concenrration
of
rhe bulk aqueous-phase contaminanr (g mJ-
1
); kd firsr-order desorprion rare coefficienr
(min-
1
);
S
concen
tration of the sorbed contaminant that is rate limir
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72 CHAPTH
7
KINETI I
OF IOIL
CHEHICAl
PROCEIIEI
With
continuous flow methods samples
can
be injected as suspensions or
spread dry on a membrane filter. The filter is attached to its holder by securely
capping it,
and che
filter holder
is
connected
to
a fraction collector and
peristaltic pump the latter maintaining a constant flow rate. Influent solution
then passes through the filter, reacts with the
adsorbent
and at various times,
effluents are collected for analysis. Depending on flow rate and the amount of
effluent needed for analysis, samples
can
be collected about every 30-60 s.
One of
the
majar
problems with this
method is that
the colloidal particles may
not
be dispersed, i.e.,
che
time necessary for an adsorptive ro travel
through
a
thin ayer
of
colloidal particles is
not equal at
all locations of the ayer. This
plus mnima mixing promotes significant transport effects. Thus, apparent
rate laws and rate coefficients are measured, with the rate coefficients chang
ing with flow rate.
There
can also be dilution of the incoming adsorptive
solurion by che liquid used ro load the adsorbenr on the filter, parricularly if
the adsorbent is placed on the filter as a suspension, or if there
is
washing
out
of remaining adsorptive solution
during
desorption. This can cause concentra
tion changes not due to adsorption or desorption.
A
more
preferred method for measuring soil chemical reacrion rates
is
che
stirred-flow method . The experimental setup
is
similar to the continuous flow
method (Fig. 7.8) except there is a stirred-flow reacrion chamber rather than a
membrane filter. A schematic
of
this method
is
shown in Fig. 7.9. The
sorbent
is
placed into the reaction chamber where a magnetic stir bar or a overhead
stirrer (Fig. 7.9) keeps it suspended
during
the experimem. There
is
a filter
placed in the top of the chamber which keeps the solids in the reaction
chamber. A peristalric pump maintains a constant flow rate and a fraction
collector
is
used to collect the leachates.
The
stirrer effects perfect mixing, i.e.,
che concentration
of
che adsorptive in che chamber
is
equal ro the effluent
concentration.
This
method
has severa advantages over the continuous flow technique
and
other kinetic methods. Reaction rates are independent of che physical proper
ties of che
porous
media, the same apparatus
can
be used for
adsorption
and
desorption experiments, desorbed species are removed, continuous measure
mems allow for monitoring reaction progress, experimental factors such as
flow rate and adsorbent mass can be easily altered, a variety of solids can be
I ~ I
Reservoir
-
FIGUR
7.8.
Thindisk flow (continuous
flow
method experimental setup. Background solution
and salute are pumped from the reservoir through the thin disk and are collected as aliquots by the
fraction collection. From Amacher ( 1991 , with permission.
KIHETI HETHOOOLOGIEI
73
I ~ I
Reservo
r
-
FIGUR
7.9.
Stirred-flow
reactor
method experimental setup. Background solution and solute are
pumped from the reservoir through the stirred reactorcontaining the solld ph se nd are collected as
aliquots by the fraction collector. Separation of salid and liquid phases
ls
accomplished by a membrane
filter at the outlet end 6f the stirred reactor. From Amacher ( 199 1 . with permission.
used (however, sometimes fine particles can clog
che
filter, causing a buildup in
pressure which results in a nonconstant flow rate) with the technique, the
adsorbent is dispersed, and dilution er rors can be measured.
With
this method,
one can also use stopped-flow tests and vary influent concentrations and flow
rates to elucidare possible reaction mechanisms (Bar-Tal et al. 1990).
elaxation Techniques
As noted earlier, many soil chemical reactions are very rapid, occurring on
millisecond and microsecond time scales. These include metal and organic
sorption-desorption
reactions, ion exchange proesses, and ion associarion
reactions. Batch and flow techniq ues, which meas u e reaction rates of > 15 s,
cannot
be
employed to measure these reacrions. Chemical relaxation methods
must be used to measure very rapid reacrions. These include pressure-jump
(p-jump), electric field pulse, remperaturejump (t-jump), and concentration
jump (c-jump) methods. These methods are fully oudined in other sources
(Sparks, 1989;
Zhang
and Sparks, 1993). Only a brief discussion
of
the theory
of chemical relaxation and a description of p-jump merhods will be given here.
The theory of chemical relaxation can be found in a number of sources (Eigen,
1954;
Takahashi and
Alberty, 1969; Bernasconi, 1976). lt should be noted
that
relaxation techniques are best used with soil components such as oxides
and clay minerals
and not
whole soils. Soils are heterogeneous, whi ch compli
cares the analyses
of
the relaxation data.
All chemical relaxation merhods are based on the theory that the equilib
rium of a system can be rapidly perrurbed by sorne externa factor such as
pressure, temperature,
or
electric field strength. Rate info rmation
can
then be
obtained by measuring the approach from che perturbed equilibrium ro the
final equili brium by measur ing the relax ation time, (the time
that
it takes for
che system to relax from one equilibrium state to anorher, after the perturba
tion pulse) by using a detection system such as conductivity.
The
relaxation
time is related to the specific rates of the elementary reactions involved. Since
the perturbation
is
small, al rate expressions reduce to, first-order equati ons
regardless of reaction arder or molecularity (Bernasconi, 1976). The rare
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174
CHAPTER 1 KIHETICI Of
IOll CHEMICAL
PROCEIIEI
equations are then linearized such
that
1
= k,(CA + C
8
)
+ k_
1
(7.16)
where k
and
k_,
are the
forward
and backward
rate constants and C_
and
C
8
are
the
concenrrations of reactants A and B at
equilibrium.
From a
linear
plot
of
- vs
CA +
C
8
)
one could
calculare
k
and k_, from
the
slope and
intercept, respectively. Pressure-jump relaxation is based on the principie that
chemical
equilibria depend on
pressure
as shown
below
(Bernasconi,
1976),
( a
n
Ko)
= -tl.V RT
a
In
p
T
(7.17)
where Ko
is
the
equilibrium constant, ll Vis rhe standard
molar
vol u me
change
ot the reaction, p is pressure, and R and
T
were defined earlier. For a
small
perturbation,
(7.18)
Details on
the
experimental protocol for a
p-jump study
can be
found
in
severa sources (Sparks, 1989; Zhang and Sparks, 1989; Grossl et
al.,
1994).
Fendorf
et
al. (1993) used an
electron paramagneric resonance sropped
flow (EPR-SF) method (an example of a c-jump merhod) to study reactions in
colloidal suspensions
in situ
on
millisecond
time
scales.
lf
one
is srudying
an
EPR
active species
(paramagnetic)
such as
Mn,
this
technique
has severa
advantages over
other
chemical relaxation methods. With m::my relaxation
merhods, the reacrions must be reversible
and
reacranr species are not directly
measured, Moreover,
in sorne
relaxarion
studies, rhe
rate constanrs
are calcu
lated
from linearized rate
equarions
that are dependent on
equilibrium
param
eters. Thus, rhe rate paramerers are not directlv measured.
With
the
EPR -SF method of Fendorf et al. (
i99
3) the mixing can be done in
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176
CH PTER
7
KINETICS
Of SOil CHEMIC L
P ~ O C E S S E S
KI NETICS OF
IMPORTANT SOIL CHEMICAL PROCESSES
Adsorption-Desorption Reactions
Heary Metals
A
number
of studies have been conducted on the adsorption/desorption
kinetics of heavy metals on soils
and
soil components. Bruemmer et al. (1988)
hypothesized that adsorption of Ni
2
,Zn
2
,and Cd
2
+ on goethite
occurred
on
both externa and
interna surface
sites. As
reaction time
increased from 2 hr
to 42 days
at 293K
and pH 6,
the
adsorbed Ni2+ increased
from
12 ro 70% of
total
adsorption,
and total increases in Zn2+ and Cd
2
+ adsorption over rhis
point
increased 33
and
21%,
respectively. The irtcreased
adsorprion
wirh rime
is
consistent with
the
assumption
of
continued adsorption on interna sites
within the porous structure of goethite, which could be a diffusion-controlled
process.
Zhang and Sparks (1990b) studied the kinetics of selenate adsorption on
goethite
using
pressure-jump relaxation and found that adsorption
occurred
mainly under acidic conditions. The dominant species was
(Se0
4
)
2
- . As pH
increased (Se0
4
)
2
- adsorption
decreased.
Selenate was
described
using the
modified triple-layer model
(see Chapter 5). A single
relaxation
was
observed
and the mechanism proposed
was:
(7.21)
where XOH is 1 mol of reactive surface hydroxyl bound ro a Fe
10n
m
goethite
.
A linearized rate equation given below was developed and tested,
1
=
k
([XOH][Se0.-
2
] + [XOH][W] + [Seo-][W]) +k_ , ,
(7.22)
where
the terms
in the
brackets are
the concentrations of species at equilib
rium
. Since
the reaction
was
conducted
at the solid/liquid interface, the elec
trostatic effect has to be considered ro calcula e the intrinsic cate constants (k't"'
:.md k ~ \ ) .
Using
the
modified triple-layer
model to
obtain
dectrostatic parame-
::::-
a:
-
.:..
.:..
Lt
*
C
~ . .
200
150
100
50
..
r2
=
0.
9973
0.2
0.4
0.6
0.8
1.0
exp( F
1J1a
2 V ~ ) / R T )
( [ X O H ] [ S e o ~ ]
+
[XOHJlH'J+(SeoaJlw])x1o7
- FIGURE 7.11. Plot of relatlonship between T
1
with exponencial and concentration terms in Eq.
(7.23). Reprinted wich permissi
on
from Zhang and Sparks (1990a). Copyright 1990 American Chemical
Sociecy.
KIHETICS Of
IMPOHANT lOil CHEMIC L
P ~ O C E l l E l
77
ters, a first-order reaction was derived (Zhang
and
Sparks , 1990b)
_
1
_
(-F(t/Ja -2t/J{3))-kinr[ - (-f(t{ n -2t/J{3))
T exp
2
T -
1
exp T
X O H ] [ S e O ~ - ) +
[XOH][W]
+ [Seo - ][W])J (7.23)
A plot of the left si de of Eq. (7.23) vs the terms in brackets ori the right si de of
Eq. (7.23)
was
linear and the k' and values
were calculated
from the slope
and intercept, respectively (Fig. 7.11) . The linear relationship would indicare
that the outer-sphere
complexation
mechanism
proposed in
Eq. (7.21)
was
plausible. Of course, one would need to use spectroscopic approaches to
definitively determine the
mechanism
.
This
was done earlier with
x-ray
ab
sorption fine structure spectroscopy (XAFS) ro prove
that
selenate is adsorbed
as an outer-sphere complex on goethite (Ha ves et al. 1987).
Organic Contaminants
There have been a number of srudies on rhe kinetics of organic chemical
sorption/desorption with
soils and soil components. Many of these investiga
rions ha ve shown that sorptionldesorption is characterized by a rapid, revers
ible stage followed by a
much
slower, nonreversible stage
(Karickhoff
et
al.,
1979; DiToro and Horzempa, 1982; Karickhoff and Morris, 1985)
or biphasic
kinetics. The rapid phse
has
been ascribed ro
retention of the organic
chemi
cal in a labile form
rhat is
easily desorbed. However, the
much slower
reaction
phase involves the entrapment of the chemical in a nonlabile form that is
difficult ro desorb .
This
slower
sorptionldes
o
rption reacti6n
has been ascribed
ro diffusion
of
the chemical into micropore s
of
organic matter and inorganic
soil
components (Wu
and
Gschwend, 1986;
Sreinberg et al.
1987;
Ball
and
Roberts,
1991).
The
labile form of the
chemical
is
available
for microbial
attack while the nonlabile portion
is
resisrant
to
biodegradation .
An example of the biphasic kinetics that is observed for many organ:c
chernical reactions in soils/sedirnents is shown in Fig. 7.12. In this srudy
55%
of
the labile
polychlorinated
biphenyls (PCBs)
was desorbed
from
sediments
in
a 24-hr period, while little of the remaining
45% nonlabile
fraction
was
desorbed in
170 hr
(Fig.
7.12a)
. Over anorher 1-year period about 50% of rhe
remaining
nonlabile frattion
desorbed
(Fig. 7.
12b).
In another study wirh volatile organic compounds (VOCS), Pavlostathis
and
Mathavan (1992)
observed
a biphasic
desorption
process for field soil s
contaminated with
trichloroerhylene
(TCE
l,
tetrachloroethylene
(PCE), rolu
ene (TOL), and xylene (XYL). A fast desorption reaction occurred in 24 hr,
followed by a much
slower desorption
reacr.ion
beyond
24
hr.
In 24 he,
9-29
,
14-48, 9-40, and 4-37% of the TCE,
PCE, TOL,
and
XYL, respectively,
were released.
A
number of
srudies have. also
shown thar with
"
aging"
the
nonlabile
portian of the organic chemical in the soil sediment
becomes
more resistant ro
release (McCall
and
Agin,
1985;
Steinberg et
al
.
1987; Pavlosrathis
and
Mathavan,
1992; Scribner
et al. 1992;
Pignare lo
et al. 1993). However,
Connaughton et al. (1993) did not observe rhe nonlabile fraction increasing
with
age for
naphthalene-contaminared
soi ls.
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-a
co
178
0.8
.
CHAPTER
KINETICS
Of IOIL CHEHICAL HOCEIIEI
b
0.8
co
\ ) 6 :
5 :
0.4 g
o
u.
a.
e:
.Q
t
u.
0.6
0.4
0.2
0.2
O - ~ r - ~ ~ - , ~ - r - - - r ~ , - ~ ~ ~ r 4
o
o
20
40
60
80
100
120 140
160
o
2
4
6
8
10 12
Desorption Time. h
Desorption Time. mo
- FIGURE 7 12. (a) Short-term
PCB
desorption in hours (h) from Hudson River sediment contami
nated with 25 mg kg
1
PCB. Distribution of the PCB between
che
sediment () and XAD 4 resin
(O)
is
shown, as well as the overall mass balance t.) . The resin acts as a sink to retain the PCB that is
desorbed. (b) Long-term
PCB
desorption
in
months (me) from Hudson River
s e i m e ~ t
contaminated
with 25
mg kg
1
PCB. Distribution of che PCB between the sediment () and XAD-4 re
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180
CHAPm KINETICS Of
IOil CHEHICAl PROCEHES
The
type
of
ion also has a
pronounced
effect
on
the rate
of
exchange.
Exchange
of
ions like K.
NHt,
and Cs+ is often slower than that of ions such
as Ca2+ and Mg2+. This is related
to
the smaller hydrated radius of the former
ions. The smaller ions fit well in the interlayer spaces of clay minerals, which
causes parcial or total inrerlayer space collapse. The exchange is chus slow and
particle diffusion-conrrolled. However, with the exception of K NHt, and
Cs+ exchange on 2:1 clay minerals like vermiculite and mica, ion exchange
kinetics are usually very rapid, occurring on millisecond time scales (Tang
and
Sparks, 1993). Figure 7.14 shows that Ca-Na exchange on monrmorillonite
was complete in