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Beschreibung

Supercapacitors are a relatively new energy storage system that provides higher energy density than dielectric capacitors and higher power density than batteries. They are particularly suited to applications that require energy pulses during short periods of time, e.g., seconds or tens of seconds. They are recommended for automobiles, tramways, buses, cranes, fork-lifts, wind turbines, electricity load leveling in stationary and transportation systems, etc. Despite the technological maturity of supercapacitors, there is a lack of comprehensive literature on the topic. Many high performance materials have been developed and new scientific concepts have been introduced. Taking into account the commercial interest in these systems and the new scientific and technological developments now is the ideal time to publish this book, capturing all this new knowledge. The book starts by giving an introduction to the general principles of electrochemistry, the properties of electrochemical capacitors, and electrochemical characterization techniques. Electrical double layer capacitors and pseudocapacitors are then discussed, followed by the various electrolyte systems. Modelling, manufacture of industrial capacitors, constraints, testing, and reliability as well as applications are also covered. 'Supercapacitors - Materials, Systems, and Applications' is part of the series on Materials for
Sustainable Energy and Development edited by Prof. G.Q. Max Lu. The series covers advances in materials science and innovation for renewable energy, clean use of fossil energy, and greenhouse gas mitigation and associated environmental technologies.

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Table of Contents

Related Titles

Title Page

Copyright

Editorial Board

Series Editor Preface

Preface

About the Series Editor

About the Volume Editors

List of Contributors

Chapter 1: General Principles of Electrochemistry

1.1 Equilibrium Electrochemistry

1.2 Ionics

1.3 Dynamic Electrochemistry

Further Reading

Chapter 2: eneral Properties of Electrochemical Capacitors

2.1 Introduction

2.2 Capacitor Principles

2.3 Electrochemical Capacitors

2.4 Summary

Acknowledgments

References

Chapter 3: Electrochemical Techniques

3.1 Electrochemical Apparatus

3.2 Electrochemical Cell

3.3 Electrochemical Interface: Supercapacitors

3.4 Most Used Electrochemical Techniques

References

Chapter 4: Electrical Double-Layer Capacitors and Carbons for EDLCs

4.1 Introduction

4.2 The Electrical Double Layer

4.3 Types of Carbons Used for EDLCs

4.4 Capacitance versus Pore Size

4.5 Evidence of Desolvation of Ions

4.6 Performance Limitation: Pore Accessibility or Saturation of Porosity

4.7 Beyond the Double-Layer Capacitance in Microporous Carbons

4.8 Conclusions

References

Chapter 5: Modern Theories of Carbon-Based Electrochemical Capacitors

5.1 Introduction

5.2 Classical Theories

5.3 Recent Developments

5.4 Concluding Remarks

Acknowledgments

References

Chapter 6: Electrode Materials with Pseudocapacitive Properties

6.1 Introduction

6.2 Conducting Polymers in Supercapacitor Application

6.3 Metal Oxide/Carbon Composites

6.4 Pseudocapacitive Effect of Heteroatoms Present in the Carbon Network

6.5 Nanoporous Carbons with Electrosorbed Hydrogen

6.6 Electrolytic Solutions – a Source of Faradaic Reactions

6.7 Conclusions – Profits and Disadvantages of Pseudocapacitive Effects

References

Chapter 7: Li-Ion-Based Hybrid Supercapacitors in Organic Medium

7.1 Introduction

7.2 Voltage Limitation of Conventional EDLCs

7.3 Hybrid Capacitor Systems

7.4 Material Design for NHC

7.5 Conclusion

Abbreviations

References

Chapter 8: Asymmetric and Hybrid Devices in Aqueous Electrolytes

8.1 Introduction

8.2 Aqueous Hybrid (Asymmetric) Devices

8.3 Aqueous Asymmetric Electrochemical Capacitors

8.4 Tantalum Oxide–Ruthenium Oxide Hybrid Capacitors

8.5 Perspectives

References

Chapter 9: EDLCs Based on Solvent-Free Ionic Liquids

9.1 Introduction

9.2 Carbon Electrode/Ionic Liquid Interface

9.3 Ionic Liquids

9.4 Carbon Electrodes

9.5 Supercapacitors

9.6 Concluding Remarks

Ionic Liquid Codes

Glossary

References

Chapter 10: Manufacturing of Industrial Supercapacitors

10.1 Introduction

10.2 Cell Components

10.3 Cell Design

10.4 Module Design

10.5 Conclusions and Perspectives

References

Chapter 11: Supercapacitor Module Sizing and Heat Management under Electric, Thermal, and Aging Constraints

11.1 Introduction

11.2 Electrical Characterization

11.3 Thermal Modeling

11.4 Supercapacitor Lifetime

11.5 Supercapacitor Module Sizing Methods

11.6 Applications

References

Chapter 12: Testing of Electrochemical Capacitors

12.1 Introduction

12.2 Summaries of DC Test Procedures

12.3 Application of the Test Procedures to Carbon/Carbon Devices

12.4 Testing of Hybrid, Pseudocapacitive Devices

12.5 Relationships between AC Impedance and DC Testing

12.6 Uncertainties in Ultracapacitor Data Interpretation

12.7 Summary

References

Chapter 13: Reliability of Electrochemical Capacitors

13.1 Introduction

13.2 Reliability Basics

13.3 Cell Reliability

13.4 System Reliability

13.5 Assessment of Cell Reliability

13.6 Reliability of Practical Systems

13.7 Increasing System Reliability

13.8 System Design Example

References

Chapter 14: Market and Applications of Electrochemical Capacitors

14.1 Introduction: Principles and History

14.2 Commercial Designs: DC Power Applications

14.3 Energy Conservation and Energy Harvesting Applications

14.4 Technology Combination Applications

14.5 Electricity Grid Applications

14.6 Conclusions

References

Index

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The Editors

Prof. François Béguin

Poznan University of Technology

Faculty of Chemical Technology

u1. Piotrowo 3

Poznan, 60-965

Poland

Prof. Elżbieta Frąckowiak

Poznan University of Technology

Institute of Chemistry and Technical Electrochemistry

u1. Piotrowo 3

Poznan, 60-965

Poland

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No.: applied for

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.

© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form — by photoprinting, microfilm, or any other means — nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.

Print ISBN: 978-3-527-32883-3

ePDF ISBN: 978-3-527-64669-2

ePub ISBN: 978-3-527-64668-5

mobi ISBN: 978-3-527-64667-8

oBook ISBN: 978-3-527-64666-1

Materials for sustainable energy and development (Print) ISSN: 2194-7813

Materials for sustainable energy and development (Internet) ISSN: 2194-7821

Editorial Board

Members of the Advisory Board of the “Materials for Sustainable Energy and Development” Series

Professor Huiming Cheng

Professor Calum Drummond

Professor Morinobu Endo

Professor Michael Grätzel

Professor Kevin Kendall

Professor Katsumi Kaneko

Professor Can Li

Professor Arthur Nozik

Professor Detlev Stöver

Professor Ferdi Schüth

Professor Ralph Yang

Series Editor Preface

The Wiley Series on New Materials for Sustainable Energy and Development

Sustainable energy and development is attracting increasing attention from the scientific research communities and industries alike, with an international race to develop technologies for clean fossil energy, hydrogen and renewable energy as well as water reuse and recycling. According to the REN21 (Renewables Global Status Report 2012 p. 17) total investment in renewable energy reached $257 billion in 2011, up from $211 billion in 2010. The top countries for investment in 2011 were China, Germany, the United States, Italy, and Brazil. In addressing the challenging issues of energy security, oil price rise, and climate change, innovative materials are essential enablers.

In this context, there is a need for an authoritative source of information, presented in a systematic manner, on the latest scientific breakthroughs and knowledge advancement in materials science and engineering as they pertain to energy and the environment. The aim of the Wiley Series on New Materials for Sustainable Energy and Development is to serve the community in this respect. This has been an ambitious publication project on materials science for energy applications. Each volume of the series will include high-quality contributions from top international researchers, and is expected to become the standard reference for many years to come.

This book series covers advances in materials science and innovation for renewable energy, clean use of fossil energy, and greenhouse gas mitigation and associated environmental technologies. Current volumes in the series are:

Supercapacitors. Materials, Systems, and Applications
Functional Nanostructured Materials and Membranes for Water Treatment
Materials for High-Temperature Fuel Cells
Materials for Low-Temperature Fuel Cells
Advanced Thermoelectric Materials. Fundamentals and Applications
Advanced Lithium-Ion Batteries. Recent Trends and Perspectives
Photocatalysis and Water Purification. From Fundamentals to Recent Applications

In presenting this volume on Supercapacitors, I would like to thank the authors and editors of this important book, for their tremendous effort and hard work in completing the manuscript in a timely manner. The quality of the chapters reflects well the caliber of the contributing authors to this book, and will no doubt be recognized and valued by readers.

Finally, I would like to thank the editorial board members. I am grateful to their excellent advice and help in terms of examining coverage of topics and suggesting authors, and evaluating book proposals.

I would also like to thank the editors from the publisher Wiley-VCH with whom I have worked since 2008, Dr Esther Levy, Dr Gudrun Walter, and Dr Bente Flier for their professional assistance and strong support during this project.

I hope you will find this book interesting, informative and valuable as a reference in your work. We will endeavour to bring to you further volumes in this series or update you on the future book plans in this growing field.

Brisbane, Australia

G.Q. Max Lu

31 July 2012

Preface

Currently, our planet faces huge challenges related to energy. How to reduce CO2 emissions and fossil fuel consumption? How to introduce renewable energies in the energy mix? Of course these are not new questions, but simply, until the end of the last century, no one cared about the scarcity of fossil fuels even if some warnings appeared during the successive oil crises.

The answer to the above questions is energy saving as well as energy management. It is exactly the role that can be played by electrochemical capacitors, so-called supercapacitors, because of their ability to store larger amounts of energy than the traditional dielectric capacitors. Such exceptional properties originate from the nanometric scale capacitors built from the polarized electrode material and a layer of attracted ions on its surface. The thickness of the electrode–electrolyte interface is directly controlled by the size of ions. Supercapacitors are able to harvest energy in very short periods (less than one minute) and to subsequently provide burst of energy when needed. They are now a reality in the market, where they are applied in automotive and stationary systems, and allow energy savings ranging from 10 to 40%. They can also play a role in the stabilization of current when intermittent renewable energies are introduced in the energetic mix.

Although supercapacitors are now commercially available, they still require improvements, especially for enhancing their energy density. It requires a fundamental understanding of their properties and exact operating principles, in addition to improving electrode materials, electrolytes past and integration in systems. All these topics led to a very strong motivation of academics and industry during the decade.

When Max Lu invited us to suggest a book in his series Materials for Sustainable Energy and Development, we immediately thought about Supercapacitors. Indeed, since the fantastic pioneer book Electrochemical supercapacitors: Scientific Fundamentals and Technological Applications published by B.E. Conway in 1999, no other comprehensive book was dealing extensively with the topic of supercapacitors, and until now the book is generally referred in almost all scientific publications concerning this subject. During the past 10 years new ideas appeared, such as a better description of what is really the double-layer in these systems and hybrid and asymmetric capacitors, requiring a comprehensive review.

Our book entitled Supercapacitors: materials and systems does not intend to substitute but be a complement to the Conway's book taking advantage of the developments which appeared in the past decade. It is dedicated to researchers and engineers involved with supercapacitor science, its developments, and implementation. The book is also intended for graduate and undergraduate students wanting to special in energy storage systems.

For these reasons, it has been written in collaboration with scientists world-wide renowned in supercapacitors science and also with contributors from the industry. The book includes 14 chapters: 3 being dedicated to general principles of electrochemistry, electrochemical characterization techniques and general properties of supercapacitors in order to allow reading the book without any prerequisite knowledge; 3 to fundamentals, general properties, and modelling of electrical double-layer capacitors, and pseudo-capacitors; 3 to new trends such as asymmetric and hybrid capacitors, and the use of ionic liquid electrolytes; 2 to manufacturing and modules sizing; 3 to testing, reliability, and applications of supercapacitors. Each chapter aims at giving the most detailed information using familiar terms.

We are very happy and proud that we could gather, in this book, the greatest names in supercapacitors science and technology. All are colleagues and friends who we met in international conferences or with whom we have had the pleasure to collaborate. They all kindly accepted to devote their time for contributing chapters; we sincerely and warmly thank them for their help. We also would like to thank our friend Max Lu for giving us this wonderful opportunity and also the Wiley staff for being patient. Finally, we would like to dedicate this book to our solve parents who would be very proud to see our small contribution in helping solve humanity problems.

Poznan

François Bèguin and Elzbieta Frackowiak

November 2012

About the Series Editor

Professor Max Lu

Editor, New Materials for Sustainable Energy and Development Series

Professor Lu's research expertise is in the areas of materials chemistry and nanotechnology. He is known for his work on nanoparticles and nanoporous materials for clean energy and environmental technologies. With over 500 journal publications in high-impact journals, including Nature, Journal of the American Chemical Society, Angewandte Chemie, and Advanced Materials, he is also coinventor of 20 international patents. Professor Lu is an Institute for Scientific Information (ISI) Highly Cited Author in Materials Science with over 17 500 citations (h-index of 63). He has received numerous prestigious awards nationally and internationally, including the Chinese Academy of Sciences International Cooperation Award (2011), the Orica Award, the RK Murphy Medal, the Le Fevre Prize, the ExxonMobil Award, the Chemeca Medal, the Top 100 Most Influential Engineers in Australia (2004, 2010, and 2012), and the Top 50 Most Influential Chinese in the World (2006). He won the Australian Research Council Federation Fellowship twice (2003 and 2008). He is an elected Fellow of the Australian Academy of Technological Sciences and Engineering (ATSE) and Fellow of Institution of Chemical Engineers (IChemE). He is editor and editorial board member of 12 major international journals including Journal of Colloid and Interface Science and Carbon.

Max Lu has been Deputy Vice-Chancellor and Vice-President (Research) since 2009. He previously held positions of acting Senior Deputy Vice-Chancellor (2012), acting Deputy Vice-Chancellor (Research), and Pro-Vice-Chancellor (Research Linkages) from October 2008 to June 2009. He was also the Foundation Director of the ARC Centre of Excellence for Functional Nanomaterials from 2003 to 2009.

Professor Lu had formerly served on many government committees and advisory groups including the Prime Minister's Science, Engineering and Innovation Council (2004, 2005, and 2009) and the ARC College of Experts (2002–2004). He is the past Chairman of the IChemE Australia Board and former Director of the Board of ATSE. His other previous board memberships include Uniseed Pty Ltd., ARC Nanotechnology Network, and Queensland China Council. He is currently Board member of the Australian Synchrotron, National eResearch Collaboration Tools and Resources, and Research Data Storage Infrastructure. He also holds a ministerial appointment as member of the National Emerging Technologies Forum.

About the Volume Editors

Prof. François Béguin

Poznan University of Technology

Faculty of Chemical Technology

Piotrowo 3, 60-965 Poznan, Poland

[email protected]

tel. ++48 61 665 3632

fax ++48 61 665 2571

François Béguin is a professor at the Poznan University of Technology (Poland), where he was recently awarded the WELCOME stipend from the Foundation for Polish Science. His research activities are devoted to chemical and electrochemical applications of carbon materials, with special attention to the development of nanocarbons with controlled porosity and surface functionality for applications to energy conversion/storage and environment protection. The main topics investigated in his research group are lithium batteries, supercapacitors, electrochemical hydrogen storage, and reversible electrosorption of water contaminants. He published over 250 publications in high-ranking international journals, and his works are cited in 8300 papers, with Hirsch index 46. He is also involved in several books dealing with carbon materials and energy storage. He is a member of the International Advisory Board of the Carbon Conferences and has launched the international conferences on Carbon for Energy Storage and Environment Protection (CESEP). He is a member of the editorial board of the journal Carbon. He was Professor of materials science in the Orléans University (France) until 2012 and was Director of national programmes on Energy Storage (Stock-E), Hydrogen and Fuel Cells (H-PAC), and electricity management (PROGELEC) in the French Agency for Research (ANR).

Elżbieta Frąckowiak

Poznan University of Technology, Institute of Chemistry and Technical Electrochemistry,

Piotrowo 3, 60-965 Poznan, Poland

[email protected]

tel. ++48 61 665 3632

fax ++48 61 665 2571

Elżbieta Frąckowiak is a full professor at the Institute of Chemistry and Technical Electrochemistry at the Poznan University of Technology. Her main research topics are devoted to energy storage in electrochemical capacitors, Li-ion batteries, and hydrogen electrosorption. She is especially interested in the development of electrode materials (nanoporous carbons, template carbons, carbon nanotubes, graphene, etc.), composite electrodes from conducting polymers, and doped carbons and transition-metal oxides for supercapacitors, as well as in new concepts of supercapacitors based on the carbon/redox couples interface.

She serves as Chair of Division 3 “Electrochemical Energy Conversion and Storage” of the International Society of Electrochemistry (2009–2014). She is a member of International Advisory Boards – Electrochimica Acta from 2011 and Energy & Environmental Science from 2008. She was chair/cochair of a few international conferences (12th International Symposium on Intercalation Compounds (ISIC 12) Poznań, Poland, 1–5 June 2003; 2nd International Symposium on Enhanced Electrochemical Capacitors (ISEECap'11), Poznań, Poland, 12–16 June 2011; and the World CARBON conference in Krakow, 17–22 June 2012. She was the winner of the Foundation for Polish Science Prize, the so-called Polish Nobel (December 2011) and was also decorated with the Order of Polonia Restituta (December 2011) and the Order Sapienti Sat (October 2012).

She is the author of 150 publications, a few chapters, and tens of patent applications. The number of her citations is about 6000, with Hirsch index 36.

List of Contributors

Catia Arbizzani
Alma Mater Studiorum
Università di Bologna
Dipartimento di Scienza
dei Metalli
Elettrochimica e Tecniche Chimiche
Via San Donato 15
40127 Bologna
Italy
Philippe Azaïs
Batscap Supercapacitor Business Unit
Odet, Ergue-Gaberic
29556 Quimper Cedex 9
France
and
Commissariat à l'Energie Atomique (CEA)
LITEN (Laboratoire d'Innovation pour les Technologies des Energies Nouvelles)
17 rue des Martyrs
38054 Grenoble Cedex 9
France
Daniel Bélanger
Université du Québec à Montréal
Département de Chimie
case postale 8888
succursale centre-ville
Montréal
Québec H3C 3P8
Canada
François Béguin
Poznan University of Technology
Faculty of Chemical Technology
u1. Piotrowo 3
60-965 Poznan
Poland
Thierry Brousse
Université de Nantes
Institut des Matériaux Jean Rouxel (IMN)
CNRS/Université de Nantes
Polytech Nantes
BP50609
44306 Nantes Cedex 3
France
Andrew Burke
University of California-Davis
Institute of Transportation Studies
One Shields Avenue
Davis, CA 95616
USA
Scott W. Donne
University of Newcastle
School of Environmental and Life Sciences
Office C325, Chemistry
Callaghan
New South Wales 2308
Australia
Guang Feng
Clemson University
Department of Mechanical Engineering
Clemson, SC 29634-0921
USA
Elżbieta Frąckowiak
Poznan University of Technology
Faculty of Chemical Technology
Institute of Chemistry and Technical Electrochemistry
u1. Piotrowo 3
60-965 Poznan
Poland
Roland Gallay
Garmanage
Clos-Besson 6
CH-1726
Farvagny-le-Petit
Switzerland
Hamid Gualous
Université de Caen Basse Normandie
Esplanade de la Paix
BP 5186
14032, Caen Cedex 5
France
Daniel Guay
INRS-Énergie
Matériaux et Télécommunications
1650 Boulevard Lionel Boulet
case postale 1020
Varennes
Québec J3X 1 S2
Canada
Jingsong Huang
Center for Nanophase Materials Sciences, and Computer Science and Mathematics Division
Oak Ridge National Laboratory
Bethel Valley Road
Oak Ridge, TN 37831-6367
USA
Mariachiara Lazzari
Alma Mater Studiorum
Università di Bologna
Dipartimento di Scienza dei Metalli
Elettrochimica e Tecniche Chimiche
Via San Donato 15
40127 Bologna
Italy
Marina Mastragostino
Alma Mater Studiorum
Università di Bologna
Dipartimento di Scienza dei Metalli
Elettrochimica e Tecniche Chimiche
Via San Donato 15
40127 Bologna
Italy
Vincent Meunier
Center for Nanophase Materials Sciences, and Computer Science and Mathematics Division
Oak Ridge National Laboratory
Bethel Valley Road
Oak Ridge, TN 37831-6367
USA
John R. Miller
JME Inc
23500 Mercantile Road, Suite L
Beachwood, OH 44122
USA
and
Case Western Reserve University
Great Lakes Energy Institute
Electrical Engineering and Computer Science
10900 Euclid Avenue
Cleveland, OH 44106
USA
Yuki Nagano
Tokyo University of Agriculture and Technology
School of Engineering
Division of Applied Chemistry
2-24-16 Naka-cho
Koganei
Tokyo 184-8558
Japan
Katsuhiko Naoi
Tokyo University of Agriculture and Technology
School of Engineering, Division of Applied Chemistry
2-24-16 Naka-cho
Koganei
Tokyo 184-8558
Japan
Jawahr Nerkar
CSIRO Energy Technology
Normanby Rd
Clayton South
Victoria 3169
Australia
Tony Pandolfo
CSIRO Energy Technology
Normanby Rd
Clayton South
Victoria 3169
Australia
Rui Qiao
Clemson University
Department of Mechanical Engineering
Clemson, SC 29634-0921
USA
Vanessa Ruiz
CSIRO Energy Technology
Normanby Rd
Clayton South
Victoria 3169
Australia
Seepalakottai Sivakkumar
CSIRO Energy Technology
Normanby Rd
Clayton South
Victoria 3169
Australia
Patrice Simon
Unviversitè Toulouse III
Institut Carnot CIRIMAT - UMR CNRS 5085
118 route de Narbonne
31062 Toulouse
France
Bobby G. Sumpter
Center for Nanophase Materials Sciences, and Computer Science and Mathematics Division
Oak Ridge National Laboratory
Bethel Valley Road
Oak Ridge, TN 37831-6367
USA
Francesca Soavi
Alma Mater Studiorum
Università di Bologna
Dipartimento di Scienza dei Metalli
Elettrochimica e Tecniche Chimiche
Via San Donato 15
40127 Bologna
Italy
Pierre-Louis Taberna
Unviversitè Toulouse III
Institut Carnot CIRIMAT - UMR CNRS 5085
118 route de Narbonne
31062 Toulouse
France

1

General Principles of Electrochemistry

Scott W. Donne

1.1 Equilibrium Electrochemistry

1.1.1 Spontaneous Chemical Reactions

Chemical reactions move toward a dynamic equilibrium in which both reactants and products are present but have no further tendency to undergo net change. In some cases, the concentration of products in the equilibrium mixture is so much greater than the concentration of the unchanged reactants that for all practical purposes the reaction is complete. However, in many important cases, the equilibrium mixture has significant concentrations of both reactants and products.

1.1.2 The Gibbs Energy Minimum

The equilibrium composition of a reaction mixture can be calculated from the Gibbs energy by identifying the composition that corresponds to a minimum in the Gibbs energy. To elaborate further, consider the simple chemical equilibrium:

1.1

The reaction Gibbs energy (ΔGr) is defined as

1.2

where μ represents the chemical potential or molar Gibbs energy for each species.

Because the chemical potentials vary with composition, the Gibbs energy will change as the reaction proceeds. Moreover, because the reaction runs in the direction of decreasing G, it means that the reaction A → B is spontaneous when μA > μB, whereas the reverse reaction is spontaneous when μB > μA. When the derivative in Eq. (1.2) is zero, the reaction is spontaneous in neither direction, and so

1.3

To generalize these concepts, consider the more generic chemical reaction:

1.4

When the reaction advances by dξ, the amounts of reactants and products change by

1.5

1.6

The general form of this expression is

1.7

It follows that

1.8

To progress further, we note that the chemical potential of a species J is related to its activity (aJ) by

1.9

Substituting an equivalent expression to Eq. (1.9) for each species into Eq. (1.8) gives rise to

1.10

1.11

where K is the thermodynamic equilibrium constant. Furthermore, from Eq. (1.10)

1.12

which is a very important thermodynamic relationship, for it enables us to predict the equilibrium constant of any reaction from tables of thermodynamic data, and hence to predict the equilibrium composition of the reaction mixture.

1.1.3 Bridging the Gap between Chemical Equilibrium and Electrochemical Potential

A cell in which the overall cell reaction has not reached chemical equilibrium can do electrical work as the reaction drives electrons through an external circuit. The work that a given transfer of electrons can accomplish depends on the potential difference between the two electrodes. This potential difference is called the cell potential (V). When the cell potential is large, a given number of electrons traveling between the electrodes can do a large amount of electrical work. When the cell potential is small, the same number of electrons can do only a small amount of work. A cell in which the overall reaction is at equilibrium can do no work, and then the cell potential is zero.

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