Water Chemistry

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Water ChemistryAn Introduction to the Chemistry of Naturaland Engineered Aquatic Systems

Patrick L. Brezonik and William A. Arnold

3

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Copyright © 2011 by Oxford University Press

Published by Oxford University Press, Inc.198 Madison Avenue, New York, New York 10016www.oup.com

Oxford is a registered trademark of Oxford University PressAll rights reserved. No part of this publication may be reproduced,stored in a retrieval system, or transmitted, in any form or by any means,electronic, mechanical, photocopying, recording, or otherwise,without the prior permission of Oxford University Press.

Library of Congress Cataloging-in-Publication DataBrezonik, Patrick L.Water chemistry : an introduction to the chemistry of natural andengineered aquatic systems / by Patrick L. Brezonikand William A. Arnold.

p. cm.ISBN 978-0-19-973072-8 (hardcover : alk. paper) 1. Water chemistry.I. Arnold, William A. II. Title.GB855.B744 2011551.48–dc22 2010021787

1 3 5 7 9 8 6 4 2

Printed in the United States of Americaon acid-free paper

To our extended families:

Leo and Jeannette Brezonik (deceased)Carol Brezonik

Craig and LauraNicholas and Lisa

and Sarah, Joe, Billy, Niko, and Peter

Thomas and Carol ArnoldMaurice and Judith Colman; Lola Arnold (deceased)

Eric and Carly ArnoldLora Arnold

and Alex and Ben

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Contents

Preface ixAcknowledgments xiiiSymbols and Acronyms xv

Symbols xvAcronyms xviii

Units and Constants xxiiiUnits for physical quantities xxiiiImportant constants xxiii

Conversion Factors xxvEnergy-related quantities xxvPressure xxvSome useful relationships xxv

Part I Prologue 3

1 Introductory Matters 5

2 Inorganic Chemical Composition of Natural Waters:Elements of Aqueous Geochemistry 41

Part II Theory, Fundamentals, and Important Tools 77

3 The Thermodynamic Basis for Equilibrium Chemistry 79

4 Activity-Concentration Relationships 116

5 Fundamentals of Chemical Kinetics 144

viii CONTENTS

6 Fundamentals of Organic Chemistry forEnvironmental Systems 189

7 Solving Ionic Equilibria Problems 220

Part III Inorganic Chemical Equilibria and Kinetics 265

8 Acid-Base Systems 267

9 Complexation Reactions and Metal Ion Speciation 311

10 Solubility: Reactions of Solid Phases with Water 364

11 Redox Equilibria and Kinetics 406

Part IV Chemistry of Natural Waters and Engineered Systems 449

12 Dissolved Oxygen 451

13 Chemistry of Chlorine and OtherOxidants/Disinfectants in Water Treatment 482

14 An Introduction to Surface Chemistry and Sorption 518

15 Aqueous Geochemistry II: The Minor Elements:Fe, Mn, Al, Si; Minerals and Weathering 558

16 Nutrient Cycles and the Chemistry of Nitrogen andPhosphorus 601

17 Fundamentals of Photochemistry and SomeApplications in Aquatic Systems 637

18 Natural Organic Matter and Aquatic Humic Matter 672

19 Chemistry of Organic Contaminants 713

Appendix Free Energies and Enthalpies of Formation of CommonChemical Species in Water 758

Subject Index 765

Preface

In deciding whether to write a new textbook in any field, authors must answer twoquestions: (1) is there a need for another text in the field, and (2) how will their textbe different from what is already available? It is obvious from the fact that this bookexists that we answered yes to the first question. Our reasons for doing so are basedon our answers to the second question, and they are related to the broad goals we setfor coverage of topics in this book. Although previous introductory water chemistrytextbooks provide excellent coverage on inorganic equilibrium chemistry, they do notprovide much coverage on other topics that have become important aspects of the fieldas it has developed over the past few decades. These include nonequilibrium aspects(chemical kinetics) and organic chemistry—the behavior of organic contaminants andthe characteristics and behavior of natural organic matter. In addition, most waterchemistry textbooks for environmental engineering students focus their examples onengineered systems and either ignore natural waters, including nutrient chemistry andgeochemical controls on chemical composition, or treat natural waters only briefly. Thisis in spite of the fact that environmental engineering practice and research focuses at leastas much on natural systems (e.g., lakes, rivers, estuaries, and oceans) as on engineeredsystems (e.g., water and wastewater treatment systems and hazardous waste processing).Most existing textbooks also focus on solving inorganic ionic equilibria using graphicaland manual algebraic approaches, and with a few exceptions, they do not focus on theuse of computer programs to solve problems.

This book was written in an effort to address these shortcomings. Our overall goalsin this textbook are to provide readers with (1) a fundamental understanding of thechemical and related processes that affect the chemistry of our water resources and (2)the ability to solve quantitative problems regarding the behavior of chemical substancesin water. In our opinion, this requires knowledge of both inorganic and organic chemistryand the perspectives and tools of both chemical equilibria and kinetics. The book thus

x PREFACE

takes a broader approach to the subject than previous introductory water chemistrytexts. It emphasizes the use of computer approaches to solve both equilibrium andkinetics problems. Algebraic and graphical techniques are developed sufficiently toenable students to understand the basis for equilibrium solutions, but the text emphasizesthe use of computer programs to solve the typically complicated problems that waterchemists must address.

An introductory chapter covers such fundamental topics as the structure of wateritself, concentration units and conversion of units, and basic aspects of chemicalreactions. Chapter 2 describes the chemical composition of natural waters. It includesdiscussions on the basic chemistry and water quality significance of major and minorinorganic solutes in water, as well as natural and human sources and geochemicalcontrols on inorganic ions. Chapters 3–7 cover important fundamentals and tools neededto solve chemical problems. The principles of thermodynamics as the foundation forchemical equilibria are covered first (Chapter 3), followed by a separate chapter onactivity-concentration relationships, and a chapter on the principles of chemical kinetics.Chapter 6 provides basic information on the structure, nomenclature, and chemicalbehavior of organic compounds. Engineers taking their first class in water chemistrymay not have had a college-level course in organic chemistry. For those that havehad such a course, the chapter serves as a review focused on the parts of organicchemistry relevant to environmental water chemistry. Chapter 7 develops the basictools—graphical techniques, algebraic methods, and computer approaches—needed tosolve and display equilibria for the four main types of inorganic reactions (acid-base,solubility, complexation, and redox). The equilibrium chemistry and kinetics of thesemajor types of inorganic reactions are presented as integrated subjects in Chapters 8–11.

Of the remaining eight chapters, six apply the principles and tools covered in the first11 chapters to specific chemicals or groups of chemicals important in water chemistry:oxygen (12), disinfectants and oxidants (13), minor metals, silica, and silicates (15),nutrients (16), natural organic matter (18), and organic contaminants (19). The other twochapters describe two important physical-chemical processes that affect and sometimescontrol the behavior or inorganic and organic substances in aquatic systems: Chapter 14describes how solutes interact with surfaces of solid particles (sorption and desorption),and Chapter 17 describes the principles of photochemistry and the role of photochemicalprocesses in the behavior of substances in water.

The book includes more material and perhaps more topics than instructors usuallycover in a single-semester course. Consequently, instructors have the opportunityto select and focus on topics of greatest interest or relevance to their course; werecognize that the “flavor” and emphasis of water chemistry courses varies dependingon the program and instructor. Those wishing to emphasize natural water chemistry,for example, may wish to focus on Chapters 12, 15, 16, and 18 after covering theessential material in Chapters 1–11; others who want to focus on engineered systemsand contaminant chemistry may want to focus more on Chapters 13, 14, and 19. Withinseveral chapters, there also are Advanced Topic sections that an instructor may or maynot use. With supplementary material from the recent literature, the book also may besuitable for a two-quarter or two-semester sequence.

A strong effort was made to write the text in a clear, didactic style withoutcompromising technical rigor and to format the material to make the book inviting andaccessible to students. We assume a fairly minimal prior knowledge of chemistry (one

PREFACE xi

year of general chemistry at the college level) and provide clear definitions of technicalterms. Numerous in-chapter examples are included to show the application of theoryand equations and demonstrate how problems are solved, and we have made an effort toprovide examples that are relevant to both natural waters and engineered systems. Theproblems included at the end of most of the chapters generally are ordered in terms ofdifficulty, with the easiest problems coming first. Finally, we encourage readers to visitthe book’s companion Web site at www.oup.com/us/WaterChemistry, which containsdownloadable copies of several tables of data, an interface for the kinetics software,Acuchem, additional problems and figures, and other useful information.

Patrick L. Brezonik and William A. ArnoldUniversity of Minnesota

February 2010

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Acknowledgments

We owe a great debt of gratitude to the individuals whose reviews of individual chaptersprovided many comments and suggestions that improved the content of the book, and weappreciate their efforts in finding errors. We list them here alphabetically with chaptersreviewed in parentheses: Larry Baker (1, 2, 16), Paul Bloom (18), Steve Cabaniss (18),Paul Capel (4, 6, 19), Yu-Ping Chin (18, 19), Joe Delfino (1, 2), Baolin Deng (10, 11),Mike Dodd (13), Dan Giammar (7, 8), Ray Hozalski (13), Tim Kratz (12), Doug Latch(17), Alison McKay (4, 6), Kris McNeill (17), Paige Novak (6, 15), Jerry Schnoor (15),Timm Strathmann (3, 5), Brandy Toner (14), Rich Valentine (9, 11), and Tom Voice (8,9). Any remaining errors are the authors’ responsibility, but we sincerely hope that thereaders will find few or no errors. We especially thank Mike Dodd for his extensivereview and suggestions for Chapter 13 and Paul Bloom and Yo Chin for their detailedreviews and input to Chapter 18.

The senior author is happy to acknowledge the role that his previous book, ChemicalKinetics and Process Dynamics in Aquatic Systems (CRC Press, 1994), played ininforming the writing of Chapters 5 and 17 and parts of Chapters 13 and 15. He alsoexpresses his thanks to the students in his 2008 and 2009 water chemistry classes, inwhich drafts of various chapters were used as the textbook, for their helpful commentsand for finding many errors. Special thanks go to Mike Gracz, Ph.D. student in Geologyand Geophysics, for his detailed reviews of the chapters. The junior author hopes thatstudents in his future water chemistry classes do not find any mistakes.

Several individuals were helpful in supplying data used in this book.We are pleased toacknowledge Larry Baker, Joe Delfino, Paul Chadik, Charles Goldman, PatriciaArneson,and Ed Lowe for chemistry data used in Chapter 2; Tim Kratz and Jerry Schnoor fordissolved oxygen data used in Chapter 12; Rose Cory for fluorescence spectra andAbdulKhwaja for NMR spectra in Chapter 18; and Dan Giammar and Mike Dodd for someof the problems at the ends of several chapters. Several of the in-chapter examples

xiv ACKNOWLEDGMENTS

were inspired by lecture notes of Alan Stone. Thanks also to Kevin Drees and BethanyBrinkman for helping the authors collect additional data used in Chapters 2 and 18.We thank Mike Evans, graduate student in Computer Science and Engineering at theUniversity of Minnesota, for developing a user-friendly interface to the kinetic programAcuchem, and Randal Barnes for advice on solving problems using spreadsheets.

We happily acknowledge the excellent library system of the University of Minnesotaand the inventors of Internet search engines, which greatly facilitated our library researchand hunts for references, enabling us to continue this work wherever we could find anInternet connection.

The senior author thanks the Department of Civil Engineering and his environmentalengineering colleagues at the University of Minnesota for a light teaching load over thepast few years, which enabled him to focus his time and efforts on writing the book.The junior author wishes he had the same luxury, but he still managed to squeeze ina fair bit of writing. Both authors thank their colleagues and especially their familiesfor their understanding and patience when the writing absorbed their time. We alsoappreciate the great work and helpful attitudes of the following staff at OUP and theirassociates in moving our manuscript through the publication stage: Jeremy Lewis, editor;Hallie Stebbins, editorial assistant; Patricia Watson, copy editor; Kavitha Ashok, ProjectManager; and Theresa Stockton and Lisa Stallings, Production Editors.

Finally, we acknowledge with gratitude our predecessors in writing water chemistrybooks, starting with Werner Stumm and James J. Morgan and extending to morerecent authors: Mark Benjamin, Philip Gschwend, Janet Hering, Dieter Imboden, DavidJenkins, James Jensen, Francois Morel, James Pankow, Rene Schwarzenbach, VernonSnoeyink, and others, on whose scholarly efforts our own writing has relied, and thecountless researchers, only some of whom are cited in the following pages, responsiblefor developing the knowledge base that now enriches the field of environmental waterchemistry.

Symbols and Acronyms

Symbols

[ ] mass or molar concentration{ } activity≡M metal center attached to a solid surface≡S surface site‰ parts per thousand�i fraction of XT present as species i�� beam attenuation coefficient of light at wavelength �

� cumulative stability (formation) constant� buffering capacity (Chapter 8)� Bunsen coefficient (Chapter 12)� activity coefficient�± mean ionic activity coefficient of a salt� interfacial energy or surface tension (Chapters 3, 14)�O ligand field splitting parameter� temperature coefficient in kinetics�A macroscopic binding parameter for sorbate A (Chapter 14)� transmission coefficient (Chapter 5 only)�−1 radius of ionic atmosphere (Debye parameter), and characteristic thickness

of the electrical double layer� wavelength chemical potential stoichiometric coefficient kinematic viscosity (m2 s−1) (Chapter 12)

xvi SYMBOLS AND ACRONYMS

f fundamental frequency factor Scatchard equation variable (= [ML/LT])� extent of reaction� density� susceptibility factor (Chapter 19)�w flushing coefficient for water in a reactor (= Q/V) Hammett constant� characteristic time� quantum yield�0 electrostatic surface potentialω electrostatic interaction factora� light absorption coefficient at wavelength �

ai activity of iai size parameter for ion i in Debye-Hückel equationA preexponential or frequency factor in Arrhenius equationat. wt. atomic weightat. no. atomic numberb.p. boiling pointc, C concentrationc correction factor (Chapter 19)Cp heat capacity�Cp change in heat capacity for a reactionD� wavelength-dependent distribution function for scattered light (Chapter 17)D diffusion coefficientD distribution coefficient (Chapter 19)D dielectric constant (relative static permittivity)Do permittivity in a vacuumDobs observed distribution coefficient (Chapter 4)Dtheor thermodynamic distribution coefficient (Chapter 4)Da daltons (molecular weight units)�E change in internal energyeg type of molecular orbitale−

aq a hydrated electronE◦ electrical (reduction) potential under standard conditionsEact energy of activationEbg band gap energyE0(�,0) scalar irradiance just below the water surfaceesu electrostatic unitsf fraction of a substance in a specific phase (Chapter 19)fi fugacity of substance ifi fragment constants for fragment i (Chapter 19)foc fraction of organic carbonF Helmholtz free energyF Faraday, unit of capacitance (Chapter 14)F1 Gran function (used in alkalinity titrations)F Faraday’s constant

SYMBOLS AND ACRONYMS xvii

G Gibbs free energyG(�) total irradiance (sun + sky) at the Earth’s surfaceG◦

f free energy of formation under standard conditions�G◦ change in free energy (or free energy of reaction under standard conditions)�G �= free energy of activationh Planck’s constantH enthalpyH Henry’s law constant (= K−1

H )i currenti0 exchange currentI ionic strengthIa(�) (wavelength-dependent) number of photons absorbed per unit timeJ joulekPa kilopascals (unit of pressure)k Boltzmann constant (gas constant per molecule)k◦

i molar compressibility of ik rate constantK� diffuse attenuation coefficient of light at wavelength �

K thermodynamic equilibrium constant (products and reactants expressed interms of activity)

cK equilibrium constant expressed in terms of concentrations of products andreactants

Kd solid-water partition coefficientKH Henry’s law coefficient (= H−1)KL gas transfer coefficient (units of length time−1)KL Langmuir sorption constantKoc organic carbon-water coefficientKow octanol-water partition coefficientKw ion product of waterl (light path) lengthL0 ultimate (first-stage) biochemical oxygen demandm molal concentrationM molar concentrationMT total massm/z mass-to-charge ration number (of molecules, atoms, or molecular fragments)n nuclophilicity constant (Chapter 19)N normality (equivalents/L)N(K) probability function for equilibrium constant KNA Avogadro’s numberpε negative logarithm of relative electron activity; a measure of the free energy

of electron transfer, pronounced “pea epsilon”pH negative logarithm of hydrogen ion activitypHPZC pH of point of zero charge on surfacespHZNPC pH of zero net proton chargepX negative logarithm of XP pressure

xviii SYMBOLS AND ACRONYMS

P primary production (Chapter 12)q heatq charge density in diffuse layer (Chapter 14)Q hydraulic flow rater ratio of peak areas determined via gas chromatographyR gas constantR respiration (Chapter 12)R rates substrate constant (Chapter 19)s� wavelength-dependent light-scattering coefficientS entropyS saturation ratioSc dimensionless Schmidt number (kinematic viscosity/diffusion coefficient)t2g type of molecular orbitalt½ half-lifetc critical time (time to achieve maximum DO deficit in Streeter-Phelps

model)T temperatureTOTX total concentration of X in all phases of a systemU10 wind velocity 10 m above the surfaceV volumeV◦

i standard molar volume for iw, W workXT total concentration of all species of X in solutionXmax maximum sorption capacityy amount of O2 consumed at any time in biochemical oxygen demand testz depth (Chapter 17)z, Z charge (on an ion)ZAB collision frequency between A and B

Acronyms

2,4-D 2,4-dichlorophenoxyacetic acidAAS atomic absorption spectrophotometryACD Ahrland-Chatt-Davies classification systemACP actual concentration productACT activated complex theoryAHM aquatic humic matterANC acid-neutralizing capacity (= alkalinity)AOP advanced oxidation processAPase alkaline phosphataseBCF bioconcentration factorBET Brunauer-Emmet-Teller sorption equation

SYMBOLS AND ACRONYMS xix

BNC base neutralizing capacityBOD biochemical oxygen demandBTEX benzene, toluene, ethylbenzene, and xyleneCAS Chemical Abstract ServiceCB conduction bandCCM constant capacitance modelCD-MUSIC charge distribution multisite complexation (model)CFSTR continuous-flow stirred tank reactorcgs centimeter-gram-second, system of measureCDOM colored (or chromophoric) dissolved organic matterCH carbonate hardnessCOD chemical oxygen demandCP-MAS NMR cross-polarization-magic angle spinning nuclear magnetic

resonance (spectroscopy)CUAHSI Consortium of Universities for the Advancement of Hydrologic

Science, Inc.DBP disinfection by-productDCE dichloroethyleneDDT dichlorodiphenyltrichloroethaneDEAE diethylaminoethyl (functional group)DFAA dissolved free amino acidDHLL Debye-Hückel limiting lawDIC dissolved inorganic carbonDLM double-layer modelDMF 2,5-dimethylfuranDMG dimethylglyoximeDO dissolved oxygenDOC dissolved organic carbonDOM dissolved organic matterDON dissolved organic nitrogenDOP dissolved organic phosphorusEAWAG German acronym for Swiss Institute for Water Supply, Pollution

Control, and Water ProtectionEDHE extended Debye-Hückel equationEDTA ethylenediaminetetraacetic acidEfOM effluent organic matterEPC equilibrium phosphorus concentrationEPICS equilibrium partitioning in closed systemsEPI Suite Estimation Programs Interface SuiteEXAFS extended x-ray absorption fine structure spectroscopyFA fulvic acidFFA furfuryl alcoholFITEQL nonlinear data fitting programFMO frontier molecular orbital (theory)FT-ICR MS Fourier transform ion cyclotron resonance mass spectrometryGC-MS gas chromatography-mass spectrometry

xx SYMBOLS AND ACRONYMS

GCSOLAR public domain computer program to calculate light intensity andrates of direct photolysis

HA humic acidHAA haloacetic acidHAc acetic acidHMB heteropoly-molybdenum blueHMWDON high-molecular-weight dissolved organic nitrogenHOMO highest occupied molecular orbitalHPLC high-performance liquid chromatographyHRT hydraulic residence timeHSAB (Pearson) hard-soft acid-base (system)IAP ion activity productIC ion chromatographyICP inductively coupled plasmaIHSS International Humic Substances SocietyIMDA imidodiacetic acidIP inositol phosphateIR infraredis inner sphere (complex)IUPAC International Union of Pure and Applied ChemistryLC-MS liquid chromatography-mass spectrometryLED light-emitting diodeLFER linear free energy relationshipLFSE ligand-field stabilization energyLMCT ligand-to-metal charge transfer (process)LUMO lowest unoccupied molecular orbitalMCL maximum contaminant levelMEMS microelectromechanical systemMINEQL computer program to calculate mineral equilibriaMINEQL+ commercially available equilibrium computer program based on

MINEQLMINTEQA2 public domain computer program based on MINEQLMW molecular weightNADP National Atmospheric Deposition ProgramNCH noncarbonate hardnessNDMA N-nitrosodimethylamineNMR nuclear magnetic resonance (spectroscopy)NOM natural organic matterNTA nitrilotriacetic acidNTU nephelometric turbidity unitos outer sphere (complex)PAH polycyclic aromatic hydrocarbonPBDE polybrominated diphenyletherPCB polychlorinated biphenylPCDD/Fs polychlorinated dibenzodioxins/furansPCE perchloroethylene or tetrachloroethylenePCU platinum-cobalt color unit (Hazen unit)

SYMBOLS AND ACRONYMS xxi

PES potential energy surfacePFOA perfluorooctanoic acidPFOS perfluorooctane sulfonic acidPFR plug-flow reactorPON particulate organic nitrogenPOP persistent organic pollutantPP particulate phosphorusPPC products of proton consumptionPPCPs pharmaceutical and personal care productsPPR products of proton releaseRPHPLC reverse-phase high-performance liquid chromatographyS salinitySC specific conductance (same as EC)SD standard deviationSEC size-exclusion chromatographySII specific ion interactionSMILES Simplified Molecular Input Line Entry SystemSMP soluble microbial productsSRFA Suwannee River fulvic acidSRP soluble reactive phosphate (expressed as P)STP standard temperature and pressureSUVA specific ultraviolet absorptionTCE trichloroethyleneTCP 2,4,6-trichlorophenolTDP total dissolved phosphorusTDS total dissolved solidsTH total hardnessTHM trihalomethaneThOC threshold odor concentrationTLM triple-layer modelTMA trimethylamineTNT trinitrotolueneTOC total organic carbonTON total organic nitrogenTP total phosphorusTST transition state theoryUF ultrafiltrationU.S. EPA U.S. Environmental Protection AgencyUSGS U.S. Geological SurveyUV ultravioletVB valence bandVOC volatile organic compoundWWTP wastewater treatment plantXANES x-ray absorption near-edge spectroscopy

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Units and Constants

Units for physical quantities

Fundamental quantities Some derived quantities

Quantity SI units Quantity SI unitsLength meter, m Force newton (kg·m·s−2)Mass kilogram, kg Volume cubic meters (m3)∗Time second, s Electric charge coulomb, C = A · sElectric current ampere, A Power watt, W = J · s−1

Temperature Kelvin, K Electric potential volt, V = W ·A−1

Amount of material mole, mol Electric resistance ohm, � = V ·A−1

Conductance Siemens, S = A ·V−1

Important constants

Atomic mass unit 1.6605 × 10−27 kgAvogadro’s constant (number) 6.022 × 1023 mol−1

e (the “natural” number) 2.71828Electron charge 1.602 × 10−19 coulombs (C) or 4.803 × 10−10 esuElectron mass 9.109 × 10−31 kg

*The liter (L) is not an SI unit but is widely used as the unit of volume in freshwater studies. 1 L = 10−3 m3

= 1 dm3. Some scientific journals use SI units only and use m3 for volumetric measurements.

xxiv UNITS AND CONSTANTS

Fundamental frequency, vf(reciprocal of molecularvibration period)

6.2 × 1012 s−1

Faraday, F 96,485 C mol−1

Gas constant per mole, R 8.314 J mol−1 K−1 or 1.987 cal mol−1 K−1

Gas constant per molecule, k,called the Boltzmann constant

1.3805 × 10−23 J K−1

Gravitation constant (of theEarth)

9.806 m s−2

Melting point of water 0◦C or 273.15 KMolar volume of an ideal gas at

0◦C and 1 atm22.414 L mol−1 or 22.414 × 103 cm−3 mol−1

Molecular vibration period 1.5 × 10−13 sPermittivity of a vacuum, ε0 8.854 × 10−12 J−1 C2 m−1

� 3.14159Planck’s constant, h 6.626 × 10−34 J sRelative static permittivity of

water, D, also called thedielectric constant)

80 (dimensionless) at 20◦C

Speed of light (in a vacuum), c 2.998 × 108 m s−1

Conversion Factors

Energy-related quantities

1 newton (unit of force) = 1 N = kg m s−2

1 joule (unit of energy) = 107 erg = 1 N m = kg m2 s−2 = 1 volt coulomb (V C) =0.239 calories (cal) = 9.9 × 10−3 L atm−1 = 6.242 × 1018 eV

1 cal = 4.184 J1 watt = 1 kg m2 s−3 = 1 J s−1 = 2.39 × 10−4 kcal s−1 = 0.86 kcal h−1

1 entropy unit = 1 cal mol−1 K−1 = 4.184 J mol−1 K−1

Pressure

1 atm = 760 mm Hg = 1.013 × 105 Pa (pascals) = 1.013 bars1 mm Hg = 1 torr1 Pa = 10−5 bars = 1 N m−2

Some useful relationships

RT ln x = 2.303RT log x = 5.709 log x (kJ mol−1) = 1.364 log x (kcal mol−1) at 25◦C(298.15 K)

(RT/F) ln x = 2.303RT/F log x = 0.05916 log x (V at 25◦C, or 59.16 mV at 25◦C)

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Water Chemistry

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IPrologue