Aquatic chemical kinetics reaction rates of processes in natural waters

Aquatic chemical kinetics reaction rates of processes in natural waters

AQUATIC CHEMICAL KINETICS

AQUATIC CHEMICAL KINETICS

Reaction Rates of Processes in Natural Waters

1"(,11 Wiley & SOilS, Illc

r ~"W York / Chil'ht'stn / Brishalll' / '1()J"oll!o / Singaporl'

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Library of Congress Cataloging-in-Publication Data

Aquatic chemical kinetics: reaction rates of processes in natural waters/edited by Werner Stumm

p cm.~~ (Environmental science and technology)

"A Wiley-Interscience publication."

Includes bibliographical references

109S76S41

CONTRIBUTORS

I' A IRICK L BREZONIK, Department of Civil and Mineral Engineering, University

of Minnesota, Minneapolis, Minnesota

lI()i.FNA COSOVH';, Rudjer Boskovic Institute, Center for Marine Research, Zagreb, Croatia, Yugoslavia

(iIRALD V GIBBS, Department of Geological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, Virginia

I'IIII.IP M GSCHWEND, Ralph M Parsons Laboratory for Water Resources and Hydrodynamics, Massachusetts Institute of Technology, Cambridge, Massachusetts

(EA WAG), Dubendorf, Switzerland; Swiss Federal Institute ofTechnology (ETH), Zurich, Switzerland

1\11(IIAEL R HOFFMANN, Department of Environmental Engineering Science, California Institute of Technology, Pasadena, California

IIII{(; HOIGNE, Institute for Water Resources and Water Pollution Control (EA WAG), Dubendorf, Switzerland; Swiss Federal Institute ofTechnology (ETH), Zurich, Switzerland

t\NI()NIO C LA SAGA, Kline Geology Laboratory, Yale University, New Haven, Connecticut

t\III{AIlAM LERMAN, Department of Geological Sciences, Northwestern ity, Evanston, Illinois

Univers-( ;1 ClI{W: W LUTHER, III, College of Marine Studies, University of Delaware, Lewes, Delaware

IIIAN(.OIS M M MOREL, Ralph M Parsons Laboratory for Water Resources and Hydrodynamics, Massachusetts Institute of Technology, Cambridge,

Engin-VI Contributors

NEIL M PRICE, Ralph M Parsons Laboratory for Water Resources and Hydrodynamics, Massachusetts Institute of Technology, Cambridge, Massachusetts

JERALD L SCHNOOR, Department of Civil and Environmental Engineering, The University of Iowa, Iowa City, Iowa

JACQUES SCHOTT, Laboratoire de Geochimie, Universite Paul-Sabatier, louse, France

Tou-RENE P SCHWARZENBACH, Swiss Federal Institute for Water Resources and Water Pollution Control (EA WAG), Dubendorf, Switzerland; Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

ALAN T STONE, Department of Geography and Environmental Engineering, The Johns Hopkins University, Baltimore, Maryland

WERNER STUMM, Institute for Water Resources and Water Pollution Control (EA WAG), Dubendorf, Switzerland; Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

BARBARA SULZBERGER, Institute for Water Resources and Water Pollution Control (EA WAG), Dubendorf, Switzerland; Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

BERNHARD WEHRLI, Lake Research Laboratory, Institute for Water Resources and Water Pollution Control (EA WAG), Kastanienbaum, Switzerland; Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

ERICH WIELAND, Institute for Water Resources and Water Pollution Control (EA WAG), Dubendorf, Switzerland; Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

ROLAND WOLLAST, Laboratoire d'Oceanographie, Universite Libre de BruxelJes, Brussels, Belgium

SERIES PREFACE

Environmental Science and Technology

The Environmental Science and Technology Series of Monographs, Textbooks, alld Advances is devoted to the study ofthe quality of the environment and to the technology of its conservation Environmental science therefore relates to the dlcmical, physical, and biological changes in the environment through contamin.ation or modification, to the physical nature and biological behavior of air, water, soil, food, and waste as they are affected by man's agricultural, IIIdustrial, and social activities, and to the application of science and technology

10 the control and improvement of environmental quality

The deterioration of environmental quality, which began when man first

<,ollccted into villages and utilized fire, has existed as a serious problem under the rvcr-increasing impacts of exponentially increasing population and of Illdustrializing society Environmental contamination of air, water, soil, and food has become a threat to the continued existence of many plant and animal

<llll1munities of the ecosystem and may ultimately threaten the very survival of Ihc human race

I t seems clear that if we are to preserve for future generations some semblance

of the biological order of the world of the past and hope to improve on the ddcriorating standards of urban public health, environmental science and Irchnology must quickly come to playa dominant role in designing our social Il1d industrial structure for tomorrow Scientifically rigorous criteria of environ-IIll'lItal quality must be developed Based in part on these criteria, realistic ,t:lndards must be established and our technological progress must be tailored to IIICe( them It is obvious that civilization will continue to require increasing

;1I11ounts of fuel, transportation, industrial chemicals, fertilizers, pesticides, and (ountless other products; and that it will continue to produce waste products of ,III dcscriptions What is urgently needed is a total systems approach to modern 'lvilization through which the pooled talents of scientists and engineers, in , "opcration with social scientists and the medical profession, can be focused on

I hr dcvelopment of order and equilibrium in the presently disparate segments of Ihr human cnvironment Most of the skills and tools that are needed are already III existcncc Wc surely havc a right to hope a technology that has created such IIlallifold cnvironl\lcnt prohlems is also capahlc of solving them It is our hopc

VII

viii Series Preface

that this Series in Environmental Sciences and Technology will not only serve to make this challenge more explicit to the established professionals, but that it also will help to stimulate the student toward the career opportunities in this vital area

ROBERT L METCALF WERNER STUMM

PREFACE

Thc objectives of this book are (1) to treat features of chemical kinetics in IIqucous solutions and in the context of aquatic systems (oceans, fresh water, atmospheric water, and soil), (2) to strengthen our understanding of reaction Il1cchanisms and of specific reaction rates in natural waters and in water technology, and (3) to stimulate innovative research in aquatic chemical kinetics The authors-physical and inorganic chemists, surface and colloid chemists,

environmental engineers-have attempted to write their chapters in such a way

liS to provide a teaching book and to assist the readers (students; geochemists; physical chemists; air, water, and soil scientists; and environmental engineers) in IIlldcrstanding general principles; emphasis is on explanation and intellectual

\till1ulation rather than on extensive documentation The information given should also be helpful in guiding research in aquatic chemistry and in applying

k IIlef ics to the exploration of naturally occurring processes and in developing

1l,·W cngineering practices

III this volume we progress from simple concepts and laboratory studies to IIpplications in natural water, soil, and geochemical systems We start by lilt IOducing kinetics as a discipline and giving a set of basic principles emphas-

IIlIlg the elementary reaction as a basic unit of chemical processes Then we

t Ilscuss the environmental factors that are of importance in cont~olling the rate of ,hcmical transformations and illustrate from a mechanistic point of view the

k Illet ics of chemical catalysis in the areas of cloud chemistry, groundwater , hCllIistry, and water treatment processes We show how to use linear free-energy It"latiollships-to bridge the gap between kinetics and equilibria especially for

I r;ll"l ions of homologous series of compounds in order to procure kinetic lltiollllation on reactions that have not been determined in the laboratory Such Iltiolll1ation is especially useful in the chemical transformation of chemical polllltants and in redox processes We address the question of whether in some Illstallccs the rates of biogeochemical reactions may be influenced, or even

I IIl1t IOlIcd, hy the rates of metal coordination reactions

All apprcciation of the role of solid-water interfaces and surface-controlled ,,·actiolls is a prerequisite for understanding many important processes in 1I;lllIral systcms, and especially thc cOlltrihutions of physicochemical and

x Preface

biological reactions Thus, special attention is paid to the kinetics of surface reactions The discussion spans the range from ab initio quantum mechanical calculations and frontier-molecular-orbital theories to extracellular enzymatic reactions and includes the adsorption of organic solutes and redox processes occurring at these surfaces It is shown that the geochemical cycling of electrons

is not only mediated by microorganisms but is of importance at particle-water interfaces, especially at the sediment-water interface due to strong redox gradients and in surface waters due to heterogeneous photoredox processes This volume also reflects the great progress achieved in recent years in the study of kinetics of the dissolution of oxide and carbonate minerals and the weathering of minerals

Finally, we demonstrate in discussions on weathering rates in the field, on the kinetics of colloid chemical processes, and on the role of surficial transport processes in geochemical and biogeochemical processes that spatial and tem-poral heterogeneities and chemical versus transport time scales need to be assessed in order to treat the dynamics of real systems

Most of the authors met in March 1989 in Switzerland for a workshop Background papers formed the basis for the discussions However, this book is not the "proceedings of a conference", instead, it is the offspring of the workshop and its stimulating discourses

I am most grateful to many colleagues who have reviewed individual chapters and have given useful advice Credit for the creation of this volume is, of course, primarily due to its authors

Zurich, Switzerland

January 1990

WERNER STUMM

CONTENTS

I Kinetics of Chemical Transformation in the Environment 1

Alan T Stone and James J Morgan

2 Formulation and Calibration of Environmental Reaction Kinetics;

Oxidations by Aqueous Photooxidants as an Example 43

Jurg Hoigne

;1 ('atalysis in Aquatic Environments

Michael R Hoffmann

Principles of Linear Free-Energy and Structure-Activity

Relationships and their Applications to the Fate of

('hemicals in Aquatic Systems

Patrick L Brezonik

~, The Kinetics of Trace Metal Complexation: Implications for Metal

71

113

Janet G Hering and Franfois M M Morel

fl TIll' Frontier-Molecular-Orbital Theory Approach in Geochemical

I>rocesses

(,'('orge W Luther, III

7, ('hl'micltl Transformations of Organic Pollutants in the Aquatic

Environment

R('ne P Schwarzenbach and Philip M Gschwend

173

199

H Ruh' of ":xtracellular Enzymatic Reactions in Natural Waters 235

Nt'il M Price and Fram;ois M M Morel

II All Initio Quantum-Mechanical Calculations of Surface

Antonio C I_a.~axa anti (;('rtlttl V (iihh.~

~I

XII Contents

to Adsorption Kinetics of the Complex Mixture of Organic Solutes at

Bozena Cosovii:

It Redox Reactions of Metal Ions at Mineral Surfaces 311

Bernhard Wehrli

12 Modeling of the Dissolution of Strained and Unstrained Multiple

Jacques Schott

13 Dissolution of Oxide and Silicate Minerals: Rates Depend on Surface

Werner Stumm and Erich Wieland

14 Photoredox Reactions at Hydrous Metal Oxide Surfaces: A Surface

17 Kinetics of Chemical Weathering: A Comparison of Laboratory and

Jerald L Schnoor

18 Transport and Kinetics in Surficial Processes 505

Abraham Lerman

AQUATIC CHEMICAL KINETICS

1

KINETICS OF CHEMICAL

TRANSFORMATIONS IN THE ENVIRONMENT

Alan T Stone

Department of Geography and Environmental Engineering,

The fohns Hopkins University, Baltimore, Maryland

hlvironmental chemists are most often concerned with the response of an

\'lIvironmental system to change, This change may be natural (such as the dllllnal cycle of solar irradiation) or caused by human intervention (such as the dispersion of a pesticide), Since change is such a major concern, it should not be Nlilprising that chemical kinetics is an integral component of models 0" natural Nystellls, Intrinsically "kinetic" questions concerning the nature and behavior of IIlIt IIlal systems include:

W hen will the maximum concent1'ation of a pollutant appear in a system, and how high will it be?

When will the minimum concentration of an important nutrient occur, and how low will it be?

What is the residence time of a particular element or species?

Will a given compound be accumulated or exported from an open system? Ilow is the ability of various physical processes to transport a compound depelldent on its chemical form?

III Ihls chapter, we will discuss (\) the basic "unit" of chemical kinetics, the ,l"lIl\'/llalY reaction; (2) collections of elementary reactions that represent entire

2 Kinetics of chemical transformations in the environment

chemical processes; (3) dynamic models that represent complete natural and engineered systems; (4) unique characteristics of surface chemical reactions; and (5) kinds of kinetic information and how they can be used to answer questions such as the ones listed above

Chemical kinetics can be examined on several levels of sophistication diner, 1969; Denbigh and Turner, 1984) The first level is qualitative and based solely on prior practical experience; if a certain set of chemical conditions exists,

(Gar-a p(Gar-articul(Gar-ar outcome is observed Experiments c(Gar-an be performed th(Gar-at tematically catalog factors influencing rates of chemical reactions The next level attempts to capture the chemical dynamics of a system in a quantitative description; a set of equations is developed using experimentally derived rate constants allowing reaction rates to be predicted over a range of chemical conditions Whether or not extrapolations accurately predict chemical reactions under unexplored chemical conditions depends on how well the set of kinetic equations and rate constants captures the true dynamics of the system On the most fundamental level, chemical kinetics is a molecular description of chemical reactions A series of encounters between chemical species is hypothesized, and the level of agreement between the proposed mechanism and experimental findings is critically examined In special circumstances, the molecular descrip-tion of chemical reactions allows generalizations to be made concerning the reaction behavior of an entire class of compounds These generalizations provide the basis for structure-reactivity relationships, which yield quantitative predic-tions concerning rates of unexplored chemical reactions

sys-A mechanism is a set of postulated molecular events that results in the observed conversion of reactants to products (Gardiner, 1969) Proposed mech-anisms are important statements about the dynamics of a chemical process As

we shall see, mechanisms imply certain relationships between physical and chemical properties of a system (species concentrations, temperature, ionic strength, etc.) and rates of chemical transformations As long as these relation-ships are consistent with experimental evidence, proposed mechanisms are considered useful The provisional nature of all chemical mechanisms is import-ant to recognize; as new experimental evidence is acquired, proposed mech-anisms are tested with greater scrutiny At some point, all mechanisms may have

to be discarded in favor of new proposed mechanisms that agree more favorably with experimental evidence

2 THE BASIC "UNIT" OF CHEMICAL PROCESSES:

THE ELEMENTARY REACTION

2.1 Reaction Mechanisms

ASSUllH:, for thc moment, that a proposed mechanism has heen provided What docs this mechanism tcllus ahout the course and rate of a chcmical process, and about thc inllucnce of variolls physical and chcmical factors"

The elementary reaction 3

We begin by considering an important environmental reaction, the l'atalyzed hydrolysis of carboxylic acid esters (Tinsley, 1979):

I

OH

0-I RC-OR'

0

II RC-OH

O-I R-T-OR'

OH

0

/I RC-O-

tIll' l'llnccntration of each species participating in the molecular event: 1III'Il'IIsing participant concentrations yields a proportional increase in encounter

""'IIIl"I1CY, This observation, called the principle of mass action (Gardiner, 1969)

I~ till' hasis for quantitative treatment of reaction kinetics, Reaction 7, which II'Pll'Sl'I1ts the overall reaction stoichiomctry, is also balanced for mass and

4 Kinetics of chemical transformations in the environment

charge Reaction 7 is a composite of several molecular events; it cannot be used

to make fundamental statements concerning reaction mechanism and rate Rates of each reaction step can be calculated by use of the principle of mass action and values of pertinent rate constants The rate of the hydroxide ion addition to the ester is given by

2.2 Concentration versus Time

We are often concerned with changes in concentration as a function of time, requiring that rate equations be integrated This requires that boundary conditions be taken into account, such as the concentrations of species at the

onset of reaction (t = 0) Equation 9 cannot be integrated without some tional work, since changes in [RCOOR'] and [RC(O-)(OH)(OR')] are inter-connected with changes in concentrations of other reaction species We will leave the discussion of processes involving two or more elementary reactions for a later section

addi-Most elementary reactions involve either one or two reactants Elementary reactions involving three species are infrequent, because the likelihood of simultaneous three-body encounter is small In closed, well-mixed chemical systems, the integration of rate equations is straightforward Results of integra-tion for some important rate laws are listed in Table 1, which gives the concentration of reactant A as a function of time First-order reactions are particularly simple; the rate constant k has units of s - \ and its reciprocal value

speak in terms of the half-life (t l/Z ) for reaction, the time required for 50% of the reactant to be consumed When

[A]=HA]a, 0.693

t l / Z = k

-(10) (11)

For first-order reactions in closed vessels, the half-life is independent of the initial reactant concentration Defining characteristic times for second- and third-order reactions is somewhat complicated in that concentration units appear in the reaction rate constant k Integrated expressions arc availahle in a numher 01

The elementary reaction 5

1:\ BLE l Analytical Solutions to Differential Equations Describing

It'ill IlIlIl must be elaborated accordingly In a later section, we will discuss how

I " II chemical reaction and mass transport can be accounted for in calculating

I h,III}'l'S in species concentrations as a function of time

1 I, Tht'ory of Elementary Reactions, ACT

I 1I'IIII'IlIary reactions are distinguished from one another by the chemical

I 11.11 a 1'1 nisI ics of the participating reactants and their modes of interaction with

"110 ;11101 her Fundamental distinctions are made between unimolecular 11"11', (l',g" A -4 products), bimolecular reactions (e,g" A + B ->products), and 111"',1' o<'cllrring in homogeneous solution and those occurring at an interface

reac-1110 it'1' "',clleous reaclion) All elementary reactions are, however, representations ,01 ',lIl1'k Illolecular events, and therefore rate constants should respond in

"llIti.lI Jllnliclable ways 10 changes in the physical characteristics of the system 111.1i ,I 1\ l'<' I illolecular molion: lemperature, pressure, and ionic strength Activ- ,I," ""IIJl"',\ Iheory (;\( "1'), also referred 10 as transitioll-state Iheory(TST), was

01, \, l"l)('d 10 explore Ihese relatiollships,

6 Kinetics of chemical transformations in the environment

The ACT begins by postulating an activated complex for each elementary reaction, the high-energy ground-state species formed from the encounter of reactant molecules An elementary bimolecular reaction

where A, B, and (AB)'" are in local equilibrium with one another, and K '" is a

kind of equilibrium constant Decay of the activated complex to form products is simply related to the vibrational frequency of the species imparted by thermal energy (Gardiner, 1969):

The rate of product formation (e.g., in moles per liter per second) is related to the concentration (in moles per liter) of the activated complex (AB)"' Because

K '" is a thermodynamic quantity, it is related to the activity of the species involved in reaction 13

The elementary reaction 7

(in liters per mole per second) Equations 17 and 18 indicate the connection hetween the ACT rate for an elementary bimolecular reaction and the second-(lrder rate constant k

Ionic Strength The effect of ionic strength on rates of elementary reactions readily follows Using Eq 18, we can let ko be the value of the second-order rate l"onstant in the reference state, such as an infinitely dilute solution (where all the

IIctivity coefficients are unity); k is the rate constant at any specified ionic

strength:

(19)

"rom the ionic strength, values of YA' YB, and l' * can be calculated using the

I >avies equation (Stumm and Morgan, 1981, p 135) (The charge of the activated complex is known; it is simply the sum of the charge of the two reactants.) Activity coefficients for anions and cations typically decrease as the ionic

Ht rength is increased According to Eq 19, increasing the ionic strength (1) lowers the reaction rate between a cation and anion, (2) raises the reaction rate between like-charged species, and (3) has little effect on reaction rate when one or both of the reactants is uncharged

Temperature The effect of temperature on rate constants for elementary

1"l~lIctions will now be examined To assist in the interpretation of experimental illlimnation, Arrhenius (1889) postulated the following relationship:

(20) _-t /1 ( T) and Ea are referred to as the Arrhenius parameters The logarithmic 1'01111 of Eq 20

E

In k=ln A

-RT

MII/1.J.\ests plotting logarithms of experimental rate constants versus reciprocal

IIl'tlvation energies Ea We can relate the Arrhenius parameters to ACT by

IltI~tlllating a Gibbs free energy of activation, llGo*, related to K* in the rollowing manner:

(22) hlllHtion IX can now be rewritten in terms of llGo*, llHo*, and IlSo*:

k= kllTYAYII e /lG"'/RI'-; kllTYAYII e/lS"'/Re /l1I"'/RT (23)

II 1'* II i'l

8 Kinetics of chemical transformations in the environment

For an elementary reaction, comparison of the Arrhenius equation (Eq 20) with the corresponding ACT equation (Eq 23) (and with)' A =)'B =)' '" = 1.0) yields the following values for the Arrhenius parameters:

(24)

Thus, the Arrhenius equation, predicting a linear relationship between In k and

I

Mechanisms for most chemical processes involve two or more elementary I

reactions Our goal is to determine concentrations of reactants, intermediates, : and products as a function of time In order to do this, we must know the rate: constants for all pertinent elementary reactions The principle of mass action is used to write differential equations expressing rates of change for each chemical involved in the process These differential equations are then integrated with the help of stoichiometric relationships and an appropriate set of boundary condi-tions (initial concentrations, for example) For simple cases, analytical solutions are readily obtained Complex sets of elementary reactions may require numeri-cal solutions

3.1 Reactions in Series

Two first-order elementary reactions in series are

P5) From the principle of mass action, rates of the first and second steps are given by

(28) Two processes act on R; it is produl.:cd hy thc first e1cmcntary rca\.:lion, hut

Simple collections of elementary reactions 9

consumed by the second:

As expected, the dynamic behavior of [BJ depends on the relative magnitudes of

Ii I and kz When k t '?> kz, the maximum value of [B] will be high; when kl 4, kz,

lhe maximum value of [B] will be low

Only one process acts on C; it is produced by the second elementary reaction The concentration of C as a function of time is found by inserting Eq 31 into

hj 27, or by taking advantage of the mass-balance equation:

[AJo + [BJo + [C]o = [AJ + [BJ + [CJ [C] = [C]o + ([A]o - [A]) + ([BJo - [B])

(37)

(38) (39)

I lie equations are considerably more complex than in the preceding case, but an lInalytical solution can still be found [Szabo (1969) and Capellos and Bielski

j 1 "XO) provide useful compilations of analytical solutions] The mass balance

!'qllalion, and its derivative with respect to time, are useful in solving these

"'I lIa lions

[A]o + [Hlo + [e]o + rl)10 = [AJ + [B] + [C] + [DJ (40) () d[AlIdt+d[B]/dt+d[C]!dt+drDl/dt (41)

10 Kinetics of chemical transformations in the environment

Species constants and rates of the three contributing elementary reactions are shown in Figures la for the case when kl = k2 = k3 = 0.1 day-l and [BJo = [C]o

= [DJo = O As the reaction progresses, the predominant species shifts from A to

B to C, eventually forming D Reaction rates, proportional to reactant trations, are continually changing as the reaction progresses Rate r 1 decreases

concen-exponentially, as the original pool of A is consumed; r2 and r3 first grow, as

intermediates Band C are produced, but eventually diminish as significant amounts of D are formed

For comparison, similar calculations are shown in Figures Ib but using a different set of rate constants (k 1 =0.02 day-I, k2=k3=0.lOday-I) The characteristic time for the first reaction step is now five times longer than characteristic times for the second and third steps:

tl = l/kl =50.0 days

t2 = 1/ k2 = t3 = 1/ k3 = 10.0 days

(42) (43)

As a consequence, the rates of the second and third elementary reactions are

0.08 0.06

[ i 1

mM

1.0 0.8 0.6 0.4 0.2 0.0 0.10 0.08 -

0.06 I- 0.04 I-

Simpl~ collections of elementary reactions 11

I

(b)

,,.jal ive to the other three (k[ =0.02 day- [, k2 = k3 =0.1 day- [) The "bottleneck" caused by the

rate-Irlllll,ng step restrains reaction rates for subsequent steps in the reaction,

lllilstrained by the supply of intermediate B coming from the first reaction step Illlder these conditions, the first step can be termed the rate-controlling step, l'Xl'rling the strongest influence on the rate of final product formation

t\ generality can be made about all reactions in series The rate of final product

I, "Illation is influenced by the rate constants of all prior reactions steps Overall

, Ii" lacteristic time This step constrains the rates of subsequent steps, despite llil'il larger rate constants

12 Kinetics of chemical transformations in the environment

Rates of the two competing reactions are proportional to the concentration of the common substrate A and the concentrations of the two competing reactants Band C:

r1 =kl [A][B]=d[P1]/dt

r2 =k2[A] [C] =d[P 2]/dt d[A]/dt= - r1- r2= -(kl[B]+k2[C])[A]

(46) (47)

(48)

A first example of parallel reactions is presented in Figure 2; reactants Band C are present in equal concentrations at the start of reaction, but C is five times more reactive Concentrations and rates for the two contributing reactions have

mM

Rate

mM day-I

k A+B -1 P1

k2

A+C - P2

k1 2.0x102 M- 1 day-1 k2 1.0 x 103 M-1 day-1 1.0 r - - - , - - - T " " - - - ,

0.08 0.06 0.04 0.02

[A]o 1.0x10-3M [6]0 5.0 x 10-4 M

[C]o 5.0 x 10-4 M

0.00 o L _ _ _ -' -=======c:==_ J

Time (days) Figure 2 Two second-order parallel irreversible reactions Rates of the two elementary reactions in parallel are dependent on the concentration of t he common suhstrate (I AJ) and the concentrations 01 the competing reactants ([B1 and [( '1) For the condil ions given ( reae!., more" uick ly I han B hut i.1 quickly depicted hy reaction Once this has ,aken place read ion of A wilh B hecomes Ihe dominanl reaction

Simple collections of elementary reactions 13

heen calculated numerically At the onset, reaction of A with C predominates, :Iud production of P 2 exceeds the production of P j • As the reaction progresses, however, C is depleted more quickly than B, causing the production of P 2 to decline relative to the production of P j Reaction of A with B grows in importance as the reaction progresses, eventually becoming the predominant pathway For this particular case, [A]o is high enough for complete conversion

I)f B to P j and of C to P 2 to occur as the reaction reaches completion

1ft he supply of A is limiting [A]o < ([B]o + [c]o), the final product tion is determined by the relative magnitude of rate constants kj and k 2 • If the competitive reactants Band C are initially present at equimolar concentrations, ( will consume a disproportionate share of limiting substrate A It should be remarked that the rates and time scales in this example depend on two reactant concentrations, so that it is not possible to identify characteristic times from rate constants alone

distribu-Pseudo-First-Order Treatment A convenient simplification is possible when the concentrations of reactants Band C are much greater than the substrate A

As the reaction progresses, changes in [B] and [C] are small relative to changes

in r A], and the former can be considered effectively constant Each elementary reaction can then be considered "pseudo-first-order" with respect to A Let

k'j=kj[B]o and k~=k2[C]O

'j =k'j [A] =d[Pj]/dt

r 2 = k~ [A] =d[P 2 ]/dt

(49) (50) (51 )

I J nder these conditions, , j and, 2 decrease in proportion to one another as the Il'action progresses, and products PI and P 2 are produced at a constant ratio to one another An example illustrating this situation is presented in Figure 3 Equation 48 is easily integrated under pseudo-first-order conditions, since (/\ 118] +k 2 [C]) can be considered constant Then [A], [Pj], and [P2 ] as a function of time are

14 Kinetics of chemical transformations in the environment

1.0 O.b

[ i J 0.6 fLM 0.4 0.2

[C]o 5.0 x 10-_5 _M_ I

20 25 30 35 Time (days)

Figure 3 Pseudo-first-order parallel irreversible reactions [B]o and [C]o are large relative to [A]o, and can be considered constant As a consequence, reactions are pseudo-first-order with respect to A, and products PI and P2 are generated at a constant ratio to one another

Product yields under pseudo-first-order conditions can also be calculated using Eqs 53 and 54:

Fractional yield of PI:

Simple collections of elementary reactions 15

II pproached, however, the rate of the back reaction becomes significant, and can

k z [B]o = 0.0 M

k, K' k ' 3.0

Figure 4 Single reversible reaction In going from case 1 to case 2, the ratio of the two rate constants

(k, / k 2) is varied while keeping their sum (k, +k2) the same As a consequence, the characteristic time for attaining equilibrium [(k t +k 2 ) - ' ] is unchanged, but the position of the final equilibrium is different

Figure 5 Consecutive reversible reactions The individual rate constants, k I k2 kh' are all set equal

to 0.1 day - , The initial concentration of A is 0.10 111M ('01J(;cnt rations of all species approach their final equilibrium values In this case, the cquilibrium wnccntration ratios arc unity

Simple collections of elementary reactions 17

,'onstants is the same but relative values are different In case 1, the final ('quilibrium position favors product B over reactant A In case 2, equilibrium lies Illore in favor of reactant A Because the sum of rate constants is the same, progress toward the final equilibrium position occurs at the same rate in both rases Thus, the ratio of rate constants (K = k1 / k 2 ) determines the final equilib-rium position, while the sum of rate constants (k1 + k 2 ) determines how quickly

I hat position is approached

Three reversible reactions in series are presented in Figure 5 In contrast to the ease of consecutive irreversible reactions presented earlier (Fig 1), all four species coexist at the final equilibrium position The product concentrations [B], [C],

lind [0] grow as the reaction progresses without overshooting their final equilibrium position

\.4 Combined Chemical Kinetics and Mass Transport: A CSTR Model Lake

In order to explore the dynamics of open systems, it is necessary to formulate a material balance equation that accounts for all processes that work to elevate or depress the concentrations of chemical species of interest Physical and chemical processes have been included in Eq 65 (biological processes have not been considered) (Imboden and Schwarzenbach, 1985):

( 'hange of moles

wllhin volume

('klllent

moles entering moles leaving

= volume element - volume element ± or consumed by moles prol'luced

chemical reaction

(65) ( )verall changes in concentration depend on the relative magnitude of produc-

right-ha nd side are equal to zero, and the material balance equation exhibits the simple It'l'IllS used in earlier sections

To illustrate the combined effects of chemical reaction and mass transport, a

hl' examined The inflow and outflow rates are constant and equal to one

111101 her:

Instantaneous contaminant input

~

lJin -I~~ L I _ _ _ _ _ _ _ _ 'I -i~ qout

lJin = qout = 7.5 X 106 m3/day

I It I he lirst example, an instantaneous input of two pollutants is made to the IIIIItlel lake Pollutant t\ decays to chemical B according to first order kinetics,

18 Kinetics of chemical transformations in the environment

while pollutant C is a conservative tracer (no reaction):

A~B (k=2.5 X 10-3 days-I)

C (conservative) Three material balance equations can be written:

Integration yields:

Vd[A]/dt=O-q[A]- Vk[A]

Vd[B]/dt=O-q[B] + Vk[A]

Vd[C]/dt=O-q[C]

[A] = [A]o e-(q/V+k)'

[B] = [A]o (e-(qjV)' - e-(qjV +k)')

[B] = [A]oe-(qjV)'(1-e- k')

[C] = [C]oe-(qjV)'

(66) (67)

(68) (69)

and has a value of 400 days In the CSTR model lake, both [A] and the sum ([A] + [B]) decrease exponentially, relating to the following characteristic times:

"II/llfe 6 Combined effect of chemical reaction and mass transport Single instantaneous inputs of A

IItlll (' are made to: (a) a welt-mixed closed system and (b) a continuously stirred tank reactor (CSTR)

!' lIl1lant C is conservative tracer; its concentration is constant in the closed system, and decreases in

til<' ( 'STR because of the outward flux of water Chemical A is transformed into product B according

I litsl-order kinetics The sum ([A] + [B]) is constant in the closed system, but decreases in the ( 'SIR Loss of A from the CSTR arises from both chemical reaction and mass transport

Ilist relative to physical removal and becomes the dominant removal mechanism

"or exceedingly slow chemical reactions (k ~ q/ V), physical removal is

domi-1111111

As illustrated in Figure 6, the concentration of reaction product B in the CSTR lilt ldellake increases initially, reaches a maximum value, and then decreases In a luttural water, a reaction product may be more toxic to biota than its precursor

I hilS, the height of the concentration maximum for a product, such as B, is Itllportant Fast chemical reaction relative to physical removal (k ~ q/ V) is Ilivorahle for temporary buildup of B in the lake

The foregoing examples have examined the dynamics of a CSTR model lake Inllowing a single addition of pollutant We will now examine results from a '''l'lIdy continuous input of pollutants A and C, reactive and conservative, It'~pcctivcly The pollutants are added to the inlet water, commencing at t=O As

·.hnwn in Figure 7a, concentrations of reactive pollutant A, reaction product B,

, nnccnt rations arc reached At steady state, inflow and chemical production of a

"I'l'l'leS is matched hy outflow and chemical consumption In Figure 7h, the

If the steady /low rate is increllsed the fluid residence tillle of the (,STR VIII decrellses (e) The residence time of rellctllllt A is therehy decrellsed 111111 the yield of product H is lowered

Complex environmental kinetics 21

IIlflow rate to the CSTR model lake is increased, while keeping the

concentra-I ions of pollutants A and C in the inflow constant As the inflow is increased, the

I csidence time in the lake decreases As a consequence (Fig 7c), the steady-state nll1centration of A increases while that ofB decreases; less time is available in the lake for chemical reaction to occur

4 COMPLEX ENVIRONMENTAL KINETICS

The examples presented in the previous section are exceedingly simple Vastly lIIore detailed models have been formulated and used to investigate the dynamics

of real systems It is important to justify the level of complexity required in a lIlodel As part of the modeling effort, issues such as the following must be IIddressed:

To what extent have important physical, chemical, and biological processes been identified and quantified?

Is the available information about a particular natural system sufficient to support a detailed spatial and temporal model?

What assumptions or simplifications can be made to streamline the modeling activity without introducing unnecessary error?

Several excellent reviews discuss the development and implementation of kinetic lIIodels of lakes (Imboden and Lerman, 1978; Fischer et aI., 1979; Schwarzen-hach and Imboden, 1984; Imboden and Schwarzenbach, 1985) and sediments (Berner, 1980) More recently, models have been developed for examining IlIelllical reaction and mass transport in soils (Furrer et aI., 1989) and aquifers (I .i II and Narashiman, 1989; Jennings, 1987) Our goal here is to highlight central

I~Slles relating to the role of chemical kinetics in environmental processes

4.1 Characteristic Time Scales

Illihoden and Schwarzenbach (1985) have illustrated how the mass-balance I'qllation is a means of accounting for chemical and biological reactions that

1111 Id lice or consume a chemical within a test volume, and for transport processes

Ilia I import or export the chemical across the boundaries Each process acting on

/I IlIcmical can be characterized by an environmental first-order rate constant,

n pressed in units of time -1 Transport mechanisms include water renewal by Ilvns, horizontal and vertical turbulent diffusion, advection by lake particles,

"lid settling of particles (Imboden and Schwarzenbach, 1985) Chemical reaction

I a Il'S and reaction half-lives for a wide variety of reactions have been summarized

hv Iloll'mann (1981), Pankow and Morgan (1981), Morgan and Stone (1985), and Salilschi (1988)

22 Kinetics of chemical transformations in the environment

Comparison of characteristic times for chemical and biological processes (T,.xn)

with those of transport processes (Tphys ) is critical to explaining the dynamic behavior of chemical species in the environment Fast chemical and biological

processes have short characteristic times (Tnn ~ Tphys ) and will proceed to products or to equilibrium in natural systems Transformation processes with

long characteristic times (Trxn ~ Tphys ) are appropriately characterized as slow: chemicals are removed from the test volume before reaction takes place to any significant extent Reactions for which T,.xn and Tphys are within an order of magnitude of one another (with T,.xn in the range of 103 to 109 s) require a kinetic description to account for element and chemical species distributions For species involved in coupled chemical reactions with both short (T,.xn ~ Tphys ) and longer (T,.xn ~ Tphys ) time scales, quasi-equilibrium descriptions of fast reactions may be combined with kinetic descriptions of slow reactions to yield "con-strained equilibrium" or "pseudoequilibrium" models (Morel, 1983; Keck, 1978)

4.2 Import and Export of Chemicals

We are often concerned with the dispersion of pollutants and other chemicals in the environment Advection and mass flux are indiscriminate transport pro-cesses In the water column of a lake, for example, these processes transport dissolved and particle-bound chemicals equally across the boundaries of the test volume Settling of particles, in contrast, causes a downward flux of particle-bound chemicals while leaving dissolved chemicals in place Similarly, sur-factants or gases that join rising air bubbles are carried to the surface These

discriminate transport processes are very important in a variety of environmental situations:

i Discriminate transport processes can deplete chemicalsfrom one environmental compartment, causing them to accumulate in another Heavy metals, hydro-phobic organic compounds, and other pollutants that have an appreciable affinity for settling particles can be removed from the water column and transported into sediment Although the water column is cleansed by this process, the sediments become a repository for pollutants

When sorption-<iesorption processes are fast relative to particle settling, the effectiveness of the downward transport is related to the particle concentration, downward particle flux, and the particle-water partition coefficient for the pollutant in question Rates of sorption-desorption may be limiting in some instances; characteristic times for sorption-desorption then become important, along with the contact time available for interaction with particles

ll Discriminate transport processes can spatially separate potential reactants In the photic zone oflakes, photosynthesis generates a strong oxidant (02 ) and

a strong reductant (natural organic matter) Natural organic matter is largely particle-bound, and a small proportion ofthc total production is transported

Kinetics at interfaces 23

10 the sediments (The remaining portion is oxidized in complex reactions with O 2 in the water column.) The oxidant O 2, in contrast, is not particle-hound; its downward flux is brought about by advection, turbulent mass flux, and molecular diffusion, but not by downward particle settling The larger flux of reductant into bottom waters and sediments provides an impetus for lhe development of anoxic conditions

III Discriminate transport processes can remove reaction products from an onmental compartment, promoting forward reaction Products of chemical and biological reactions seldom have the same volatility, solubility, and sorptive characteristics of the reactants Groundwater inflow may bring dissolved Mn 2 + and Fe2 + into the water column of a lake Reaction with O 2 generates insoluble hydrous oxide particles, which then settle downward into sediments Despite a potentially high inward flux of Mp2 + and Fe2 +, the total concentration of iron and manganese in the water column may be low, a result of an efficient removal process

envir-I n soils, sediments, and aquifers, the transport situation is the reverse of what has heen discussed above; solids-bound chemicals (apart from colloidal frac-lions) are immobile, while dissolved chemicals are mobile As a consequence, Norplion and precipitation retard or prevent dispersion, while desorption and dissolution encourage dispersion Again, it is important to consider time scales tor chemical and biological processes (T,.xn) relative to time scales for aqueous-phase transport (Tphys )' When T,.xn ~ T phy" quasi-equilibrium can be used to rh-scribe chemical reactions in an environmental compartment In this case, pllrtition coefficients and solubility product constants are used to calculate the I"' 'portion of each chemical bound to solids at successive steps in time When

I'Il'l'ipitation, and dissolution must be accounted for, along with rates of flow

ill KINETICS AT INTERFACES

( '''('mical reactions at interfaces are of great importance in many areas of aquatic

I ""llIislry Adsorption and partitioning phenomena are responsible for

III rising air bubbles move relative to the aqueous medium Through such drlkrcntial transport, adsorption and partitioning are able to influence the

III Intcrfaccs because participating reactants do not share a common phase For nillllplc, manganese dioxide [Mn02(s)] is sparingly soluble in neutral aqueous ',IIhltion, hut ahle to oxidize many highly soluble species such as oxalate, I'Vlllvate, and ascorhate (Stone and Morgan, 1984b; Stone, 1987) through IIllnf'acial reaction Some chcmical reactions may occur slowly in the aqueous

24 Kinetics of chemical transformations in the environment

phase, but experience acceleration within the chemical microenvironment of an interface Many biological processes, for example, take advantage of the unique qualities of interfacial reactions; reactive biological molecules are often embed-ded within a membrane in order to improve the efficiency and yield of biochemical reactions

The following physical and chemical steps are involved in interfacial reactions:

1 Movement of reactant molecules into the interfacial region by convection, diffusion, or electrical migration

2 Diffusion of reactant molecules within the interfacial region

3 Surface chemical reaction: ligand replacement, electron and group transfer reactions: addition or elimination reactions

4 Outward movement of product molecules from the interfacial region to bulk solution

Overall rates of reaction may depend on rates of one or more of these steps Many of the important and unique qualities of interfacial reactions arise from strong interconnections between surface chemical reactions and mass transport

5.1 Transport Terms: Movement in One, Two, and Three Dimensions

Transport is an integral component of all reaction systems In well-mixed homogeneous solutions, the concentrations of all reactants and products are the same throughout the system, and there is no net movement of chemicals in space The role of mass transport becomes evident only when chemical reactions are extremely fast Diffusion determines the encounter frequency of reacting mole-cules and sets an upward limit on overall rates of reaction (For example, for a diffusion-controlled bimolecular reaction in water the reaction rate constant is

on the order of 1010 to 1011 M-1s-1.) Mass transport plays a pronounced role in surface chemical reactions, since net movement of reactants (from solution to the surface) and products (from the surface to solution) often takes place

The flux of chemicals to and from surfaces depends on the magnitude of forces causing molecular movement and on the dimensionality of the system Mole-cules in solution are transported by the mean motion of water, the advection process (Fischer et aI., 1979) Molecules also move relative to the water by diffusion, in response to concentration gradients For ions, electrostatic forces that contribute to movement are also experienced in regions of changing electrical potential These three forces are incorporated in the following equation for flux (in one dimension) of a migrating chemical species (Newman, 1973,

p 301):

Overall flux = (advection) + (Fickian diffusion)

Kinetics at interfaces 25

where Fj(x) = flux of species i (mol cm - 2 S -1)

v=fluid velocity (cm S-1)

[i]x = species concentration (mol cm - 3)

D j = diffusion coefficient of species i (cm2 s - 1)

Zj = charge number of species i (equiv mol-1)

Uj = electrical mobility of species i (cm2 mol J - 1 S -1)

ff = Faraday's constant (96,487 C equiv - 1 )

!/I x = electrical potential (V)

The subscript x denotes the value of a parameter at a particular distance from the

Nil r!;\ce

III the ensuing discussion of surface chemical reactions, the contribution of

"" vection to transport will not be explicitly included Advection is readily Ill'" ted on a physical basis without consideration of individual molecular dtaracteristics In many laboratory situations, bulk solution can be considered

"wl'lI-mixed" and molecular transport visualized as a migration across a

"11I~nant layer near surfaces where advective transport is negligible

Surface chemical reactions provide the impetus for molecular movement IInoss interfaces The acquisition of charge through adsorption of protons, hV"lOxide ions, and other ions creates electrical potential gradients which bring IIhout electrical migration Depletion of reactants and accumulation of products

hy surface chemical reactions create concentration gradients that bring about

""fusion Mass transport rates near an interface are not fixed, however, since l'1l1ll'Clltration gradients and electrical potential gradients can change as a Mil lace chemical reaction progresses

('onsider, for the moment, cations near a negative surface that are not NllI'rilically adsorbed or chemically transformed The cations migrate in response III l'Iectrostatic forces, which favor inward movement and accumulation at the

~\lIlace and in response to a growing concentration gradient, which favors IIlItward movement Eventually, an equilibrium distribution is reached where Inward electrical migration and outward diffusion exactly cancel one another At

IIII~ point, Eq 77 can be solved by setting the net flux (and the advective flux) of Ihl' ration Mn+ equal to zero, providing the following relationship:

(78)

III hi 7X,::j is the species charge and !/Ix is the electrical potential experienced at a dl'.tllnce x from the surface Thus, the equilibrium concentration of cations near a '''''ililve surface is lower than in bulk solution Near a negative surface, the

"'Jlllhhrillm cation concentration is higher than in bulk solution The reverse is

II Ill' It Ir anions

When adsorption and chemical reaction are taking place, additional terms

1I111~1 he added to Fl) 77 to account for these processes Figure 8 illustrates

26 Kinetics of chemical transformations in the environment

boundary

boundary region

concentration profiles for a chemical reactant consumed by surface chemical reaction When surface chemical reaction is fast relative to mass transport, the species is depleted at the oxide surface (Fig 8a) When mass transport is fast relative to surface chemical reaction, no depletion is observed (Fig 8c) Situ-ations also exist where characteristic times for chemical reaction and for mass transport are close to one another; then the concentration of reactant drops near the surface, but it is not fully depleted (Fig 8h)

Molecules or ions from homogeneous solution approaching a surface arc diffusing in three-dimensional space Once on a surface, latcral or two-dimen-

Kinetics at interfaces 27

,jonal diffusion may take place, which can be characterized by a ,jonal diffusion coefficient Similarly, molecules migrating within pores essen-Iially travel in one-dimensional space This one- and two-dimensional diffusion

two-dimen-IS important for many kinds of surface chemical reactions (Hardt, 1979)

( 'onsider, for example, two reactants A and B that can react either in the free or III the adsorbed state In order to calculate the impact of adsorption on reaction late, we must know the values ofthe diffusion coefficient in the free and adsorbed state; when diffusion coefficients are of comparable values, the mean time rl'quired for encounter is substantially shortened on adsorption (Adam and

I klbruck, 1968) This increases overall reaction rate, provided that other factors that influence rate (molecular conformation, local medium characteristics) have lIot been significantly altered by adsorption In a different situation, reactant A is present in a fluid streaming past a surface to which the second reactant B is imillobilized Adsorption removes one dimension from the direction of diffusion

of A This, in turn, improves the "catch" of reactant A by B immobilized on the Nurl:lce (Adam and Delbruck, 1968) In terms of the Arrhenius expression,

A ;I exp ( - Ea/ RT), we may view the "dimensionality" or geometric features of

" chemical reaction as reflected in the preexponential terms of the Arrhenius expression, whereas E reflects the intrinsic molecular energetics, for instance, of forilling the activated complex The A term has been predicted from ACT (see

"hove) and from collision theory For details, see Wehrli (Chapter 11, this volume) and Astumian and Schelly (1984)

I{eaction of solutes with mineral surface sites is analogous to the immobilized Il'adant model discussed by Adam and Delbruck (1968) A difference is that lIIallY sites line the surface, and lateral movement may bring the adsorbed solute III contact with sites exhibiting higher reaction free energies

~.2 Adsorption and Surface Chemical Speciation

Whenever two phases come in contact with one another, an interfacial region 1IIIIIlS within which physical and chemical characteristics of each phase are III\t urhed relative to interior (bulk) regions of each phase At the air-water III tl'I'face, for example, the directional orientation of water molecules is more 1'1 OIlOU nced than in bulk solution, in order to compensate for the lack of

h vdlOgen-bonding partners on the gas-phase side of the interface As a 'I11t'IICe, the dielectric constant and other solvent characteristics that influence 111I'IIIical reactions are perturbed to some degree Solute molecules added to nil water or solvent-water systems may reside predominately in one phase or 1111' ot her, or may concentrate in the interfacial region Whether or not solute Illoll-rules arc surface-active depends on the relative energies of possible

conse-".oIl1ll' solute, solute-solvent, and solvent-solvent interactions (Tanford, 1980)

1111' wnformation of molecules at interfaces is of great importance: reactive 11111I'llollal groups may he aligned towards or away from each bulk phase,

,dl"IIIII~ ease of encounter with other reactants Gas liquid and liquid liquid