Articulo de Spark

7/17/2019 Articulo de Spark

1/14

1

le.

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+

~ ;

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J ::

-\

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

--

-

----- -


2/14

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


3/14

l 62

,,

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


4/14

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)


5/14

166

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.


6/14

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


7/14

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


8/14

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


9/14

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


10/14

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.


11/14

-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


12/14

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

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