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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
A Comprehensive Reference for Electrochemical Engineering Theory and Application
From chemical and electronics manufacturing, to hybrid vehicles, energy storage, and beyond, electrochemical engineering touches many industries—any many lives—every day. As energy conservation becomes of central importance, so too does the science that helps us reduce consumption, reduce waste, and lessen our impact on the planet. Electrochemical Engineering provides a reference for scientists and engineers working with electrochemical processes, and a rigorous, thorough text for graduate students and upper-division undergraduates.
Merging theoretical concepts with widespread application, this book is designed to provide critical knowledge in a real-world context. Beginning with the fundamental principles underpinning the field, the discussion moves into industrial and manufacturing processes that blend central ideas to provide an advanced understanding while explaining observable results. Fully-worked illustrations simplify complex processes, and end-of chapter questions help reinforce essential knowledge.
With in-depth coverage of both the practical and theoretical, this book is both a thorough introduction to and a useful reference for the field. Rigorous in depth, yet grounded in relevance, Electrochemical Engineering:
- Introduces basic principles from the standpoint of practical application
- Explores the kinetics of electrochemical reactions with discussion on thermodynamics, reaction fundamentals, and transport
- Covers battery and fuel cell characteristics, mechanisms, and system design
- Delves into the design and mechanics of hybrid and electric vehicles, including regenerative braking, start-stop hybrids, and fuel cell systems
- Examines electrodeposition, redox-flow batteries, electrolysis, regenerative fuel cells, semiconductors, and other applications of electrochemical engineering principles
Overlapping chemical engineering, chemistry, material science, mechanical engineering, and electrical engineering, electrochemical engineering covers a diverse array of phenomena explained by some of the important scientific discoveries of our time. Electrochemical Engineering provides the critical understanding required to work effectively with these processes as they become increasingly central to global sustainability.
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CONTENTS
Cover
Title Page
Copyright
Preface
List of Symbols
Greek Symbols
Subscripts and Superscripts
About the Companion Website
Chapter 1: Introduction and Basic Principles
1.1 Electrochemical Cells
1.2 Characteristics of Electrochemical Reactions
1.3 Importance of Electrochemical Systems
1.4 Scientific Units, Constants, Conventions
1.5 Faraday's Law
1.6 Faradaic Efficiency
1.7 Current Density
1.8 Potential and OHM'S Law
1.9 Electrochemical Systems: Example
Closure
Further Reading
Problems
Chapter 2: Cell Potential and Thermodynamics
2.1 Electrochemical Reactions
2.2 Cell Potential
2.3 Expression for Cell Potential
2.4 Standard Potentials
2.5 Effect of Temperature on Standard Potential
2.6 Simplified Activity Correction
2.7 Use of the Cell Potential
2.8 Equilibrium Constants
2.9 Pourbaix Diagrams
2.10 Cells with a Liquid Junction
2.11 Reference Electrodes
2.12 Equilibrium at Electrode Interface
2.13 Potential in Solution Due to Charge: Debye–Hückel Theory
2.14 Activities and Activity Coefficients
2.15 Estimation of Activity Coefficients
Closure
Further Reading
Problems
Chapter 3: Electrochemical Kinetics
3.1 Double Layer
3.2 Impact of Potential on Reaction Rate
3.3 Use of the Butler–Volmer Kinetic Expression
3.4 Reaction Fundamentals
3.5 Simplified forms of the Butler–Volmer Equation
3.6 Direct Fitting of the Butler–Volmer Equation
3.7 The Influence of Mass Transfer on the Reaction Rate
3.8 Use of Kinetic Expressions in Full Cells
3.9 Current Efficiency
Closure
Further Reading
Problems
Chapter 4: Transport
4.1 Fick's Law
4.2 Nernst–Planck Equation
4.3 Conservation of Material
4.4 Transference Numbers, Mobilities, and Migration
4.5 Convective Mass Transfer
4.6 Concentration Overpotential
4.7 Current Distribution
4.8 Membrane Transport
Closure
Notes
Further Reading
Problems
Chapter 5: Electrode Structures and Configurations
5.1 Mathematical Description of Porous Electrodes
5.2 Characterization of Porous Electrodes
5.3 Impact of Porous Electrode on Transport
5.4 Current Distributions in Porous Electrodes
5.5 The Gas–Liquid Interface in Porous Electrodes
5.6 Three-Phase Electrodes
5.7 Electrodes with Flow
Closure
Further Reading
Problems
Chapter 6: Electroanalytical Techniques and Analysis of Electrochemical Systems
6.1 Electrochemical Cells, Instrumentation, and Some Practical Issues
6.2 Overview
6.3 Step Change in Potential or Current for a Semi-Infinite Planar Electrode in a Stagnant Electrolyte
6.4 Electrode Kinetics and Double-Layer Charging
6.5 Cyclic Voltammetry
6.6 Stripping Analyses
6.7 Electrochemical Impedance
6.8 Rotating Disk Electrodes
6.9 iR Compensation
6.10 Microelectrodes
Closure
Further Reading
Problems
Chapter 7: Battery Fundamentals
7.1 Components of a Cell
7.2 Classification of Batteries and Cell Chemistries
7.3 Theoretical Capacity and State of Charge
7.4 Cell Characteristics and Electrochemical Performance
7.5 Ragone Plots
7.6 Heat Generation
7.7 Efficiency of Secondary Cells
7.8 Charge Retention and Self-Discharge
7.9 Capacity Fade in Secondary Cells
Closure
Further Reading
Problems
Chapter 8: Battery Applications: Cell and Battery Pack Design
8.1 Introduction to Battery Design
8.2 Battery Layout Using a Specific Cell Design
8.3 Scaling of Cells to Adjust Capacity
8.4 Electrode and Cell Design to Achieve Rate Capability
8.5 Cell Construction
8.6 Charging of Batteries
8.7 Use of Resistance to Characterize Battery Peformance
8.8 Battery Management
8.9 Thermal Management Systems
8.10 Mechanical Considerations
Closure
Further Reading
Problems
Chapter 9: Fuel-Cell Fundamentals
9.1 Introduction
9.2 Types of Fuel Cells
9.3 Current–Voltage Characteristics and Polarizations
9.4 Effect of Operating Conditions and Maximum Power
9.5 Electrode Structure
9.6 Proton-Exchange Membrane (PEM) Fuel Cells
9.7 Solid Oxide Fuel Cells
Closure
Further Reading
Problems
Chapter 10: Fuel-Cell Stack and System Design
10.1 Introduction and Overview of Systems Analysis
10.2 Basic Stack Design Concepts
10.3 Cell Stack Configurations
10.4 Basic Construction and Components
10.5 Utilization of Oxidant and Fuel
10.6 Flow-Field Design
10.7 Water and Thermal Management
10.8 Structural–Mechanical Considerations
10.9 Case Study
Closure
Further Reading
Problems
Chapter 11: Electrochemical Double-Layer Capacitors
11.1 Capacitor Introduction
11.2 Electrical Double-Layer Capacitance
11.3 Current–Voltage Relationship for Capacitors
11.4 Porous Edlc Electrodes
11.5 Impedance Analysis of EDLCs
11.6 Full Cell Edlc Analysis
11.7 Power and Energy Capabilities
11.8 Cell Design, Practical Operation, and Electrochemical Capacitor Performance
11.9 Pseudo-Capacitance
Closure
Further Reading
Problems
Chapter 12: Energy Storage and Conversion for Hybrid and Electrical Vehicles
12.1 Why Electric and Hybrid-Electric Systems?
12.2 Driving Schedules and Power Demand in Vehicles
12.3 Regenerative Braking
12.4 Battery Electrical Vehicle
12.5 Hybrid Vehicle Architectures
12.6 Start–Stop Hybrid
12.7 Batteries for Full-Hybrid Electric Vehicles
12.8 Fuel-Cell Hybrid Systems for Vehicles
Closure
Note
Further Reading
Problems
Chapter 13: Electrodeposition
13.1 Overview
13.2 Faraday's Law and Deposit Thickness
13.3 Electrodeposition Fundamentals
13.4 Formation of Stable Nuclei
13.5 Nucleation Rates
13.6 Growth of Nuclei
13.7 Deposit Morphology
13.8 Additives
13.9 Impact of Current Distribution
13.10 Impact of Side Reactions
13.11 Resistive Substrates
Closure
Further Reading
Problems
Chapter 14: Industrial Electrolysis, Electrochemical Reactors, and Redox-Flow Batteries
14.1 Overview of Industrial Electrolysis
14.2 Performance Measures
14.3 Voltage Losses and the Polarization Curve
14.4 Design of Electrochemical Reactors for Industrial Applications
14.5 Examples of Industrial Electrolytic Processes
14.6 Thermal Management and Cell Operation
14.7 Electrolytic Processes for a Sustainable Future
14.8 Redox-Flow Batteries
Closure
Further Reading
Problems
Chapter 15: Semiconductor Electrodes and Photoelectrochemical Cells
15.1 Semiconductor Basics
15.2 Energy Scales
15.3 Semiconductor–Electrolyte Interface
15.4 Current Flow in the Dark
15.5 Light Absorption
15.6 Photoelectrochemical Effects
15.7 Open-Circuit Voltage for Illuminated Electrodes
15.8 Photoelectrochemical Cells
Closure
Further Reading
Problems
Chapter 16: Corrosion
16.1 Corrosion Fundamentals
16.2 Thermodynamics of Corrosion Systems
16.3 Corrosion Rate for Uniform Corrosion
16.4 Localized Corrosion
16.5 Corrosion Protection
Closure
Further Reading
Problems
Appendix A: Electrochemical Reactions and Standard Potentials
Appendix B: Fundamental Constants
Appendix C: Thermodynamic Data
Appendix D: Mechanics of Materials
D.1 Stress and Strain
D.2 Thermal Expansion
4.3 Creep and Fracture
Further Reading
Index
End User License Agreement
List of Tables
Table 1.1
Table 1.2
Table 3.1
Table 3.2
Table 3.3
Table 6.1
Table 6.2
Table 6.3
Table 6.4
Table 7.1
Table 7.2
Table 8.1
Table 8.2
Table 9.1
Table 9.2
Table 9.3
Table 9.4
Table 10.1
Table 10.2
Table 10.3
Table 12.1
Table 12.2
Table 13.1
Table 14.1
Table 16.1
Table C.1
Table C.2
Table D.1
List of Illustrations
Figure 1.1
Figure 1.2
Figure 1.3
Figure 1.4
Figure 1.5
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 2.7
Figure 2.8
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 3.8
Figure 3.9
Figure 3.10
Figure 3.11
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 4.9
Figure 4.10
Figure 4.11
Figure 4.12
Figure 4.13
Figure 4.14
Figure 4.15
Figure 4.16
Figure 4.17
Figure 4.18
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6
Figure 5.7
Figure 5.8
Figure 5.9
Figure 5.10
Figure 5.11
Figure 5.12
Figure 5.13
Figure 5.14
Figure 5.15
Figure 5.16
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8
Figure 6.9
Figure 6.10
Figure 6.11
Figure 6.12
Figure 6.13
Figure 6.14
Figure 6.15
Figure 6.16
Figure 6.17
Figure 6.18
Figure 6.19
Figure 6.20
Figure 6.21
Figure 6.22
Figure 6.23
Figure 6.24
Figure 6.25
Figure 6.26
Figure 6.27
Figure 6.28
Figure 6.29
Figure 6.30
Figure 7.1
Figure 7.2
Figure 7.3
Figure 7.4
Figure 7.5
Figure 7.6
Figure 7.7
Figure 7.8
Figure 7.9
Figure 7.10
Figure 7.11
Figure 7.12
Figure 7.13
Figure 8.1
Figure 8.2
Figure 8.3
Figure 8.4
Figure 8.5
Figure 8.6
Figure 8.7
Figure 8.8
Figure 8.9
Figure 8.10
Figure 8.11
Figure 8.12
Figure 8.13
Figure 8.14
Figure 9.1
Figure 9.2
Figure 9.3
Figure 9.4
Figure 9.5
Figure 9.6
Figure 9.7
Figure 9.8
Figure 9.9
Figure 9.10
Figure 9.11
Figure 9.12
Figure 9.13
Figure 9.14
Figure 9.15
Figure 9.16
Figure 9.17
Figure 9.18
Figure 9.19
Figure 10.1
Figure 10.2
Figure 10.3
Figure 10.4
Figure 10.5
Figure 10.6
Figure 10.7
Figure 10.8
Figure 10.9
Figure 10.10
Figure 10.11
Figure 10.12
Figure 10.13
Figure 10.14
Figure 10.15
Figure 10.16
Figure 10.17
Figure 10.18
Figure 10.19
Figure 10.20
Figure 10.21
Figure 11.1
Figure 11.2
Figure 11.3
Figure 11.4
Figure 11.5
Figure 11.6
Figure 11.7
Figure 11.8
Figure 11.9
Figure 11.10
Figure 11.11
Figure 11.12
Figure 11.13
Figure 11.14
Figure 11.15
Figure 11.16
Figure 11.17
Figure 11.18
Figure 11.19
Figure 11.20
Figure 11.21
Figure 11.22
Figure 12.1
Figure 12.2
Figure 12.3
Figure 12.4
Figure 12.5
Figure 12.6
Figure 12.7
Figure 12.8
Figure 12.9
Figure 12.10
Figure 12.11
Figure 12.12
Figure 12.13
Figure 12.14
Figure 12.15
Figure 12.16
Figure 12.17
Figure 12.18
Figure 13.1
Figure 13.2
Figure 13.3
Figure 13.4
Figure 13.5
Figure 13.6
Figure 13.7
Figure 13.8
Figure 13.9
Figure 13.10
Figure 13.11
Figure 13.12
Figure 13.13
Figure 13.14
Figure 13.15
Figure 13.16
Figure 13.17
Figure 14.1
Figure 14.2
Figure 14.3
Figure 14.4
Figure 14.5
Figure 14.6
Figure 14.7
Figure 14.8
Figure 14.9
Figure 14.10
Figure 14.11
Figure 14.12
Figure 14.13
Figure 14.14
Figure 14.15
Figure 14.16
Figure 14.17
Figure 15.1
Figure 15.2
Figure 15.3
Figure 15.4
Figure 15.5
Figure 15.6
Figure 15.7
Figure 15.8
Figure 15.9
Figure 15.10
Figure 15.11
Figure 15.12
Figure 15.13
Figure 15.14
Figure 15.15
Figure 15.16
Figure 15.17
Figure 15.18
Figure 15.19
Figure 15.20
Figure 15.21
Figure 15.22
Figure 15.23
Figure 15.24
Figure 16.1
Figure 16.2
Figure 16.3
Figure 16.4
Figure 16.5
Figure 16.6
Figure 16.7
Figure 16.8
Figure 16.9
Figure 16.10
Figure 16.11
Figure 16.12
Figure 16.13
Figure 16.14
Figure 16.15
Figure 16.16
Figure 16.17
Figure 16.18
Figure D.1
Figure D.2
Figure D.3
Figure D.4
Figure D.5
Figure D.6
Figure D.7
Guide
Cover
Table of Contents
Begin Reading
Chapter 1
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Electrochemical Engineering
Thomas F. Fuller
Georgia Institute of Technology, US
John N. Harb
Brigham Young University, US
This edition first published 2018
© 2018 John Wiley & Sons, Inc
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The right of Thomas F Fuller and John N Harb to be identified as the author(s) of this work has been asserted in accordance with law.
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In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
Library of Congress Cataloging-in-Publication Data
Names: Fuller, Thomas Francis, author. | Harb, John Naim, 1959- author.
Title: Electrochemical engineering / Thomas F. Fuller & John N. Harb.
Description: First edition. | Hoboken, NJ, USA : Wiley, 2018. | Includes index. | Identifiers: LCCN 2017044994 (print) | LCCN 2017047266 (ebook) | ISBN 9781119446583 (pdf) | ISBN 9781119446590 (epub) | ISBN 9781119004257 (hardback)
Subjects: LCSH: Electrochemistry, Industrial. | BISAC: SCIENCE / Chemistry / Physical & Theoretical.
Classification: LCC TP255 (ebook) | LCC TP255 .F85 2018 (print) | DDC 660/.297–dc23
LC record available at https://lccn.loc.gov/2017044994
Cover image: Courtesy of Thomas F. Fuller; © crisserbug / Getty Images
Cover design by Wiley
Preface
Given the existing books on electrochemistry and electrochemical engineering, what do we hope to accomplish with this text? The answer is twofold. First, it is our goal to provide enough of the fundamentals to enable students to approach interesting problems, but not so much that new students are overwhelmed. In doing this, we have attempted to write with the student in mind, and choices regarding content, examples, and applications have been made with the aim of helping students understand and experience the important and exciting discipline of electrochemical engineering. The text has a large number of worked out examples, includes homework problems for each chapter, and uses consistent nomenclature throughout in order to facilitate student learning. Our second objective is to integrate key applications of electrochemical engineering with the relevant fundamentals in a single book. We have found applications to be of great interest to students. Importantly, applications provide students with the opportunity to practice in a meaningful way the fundamentals that they have learned. We have made a deliberate effort to tie the investigation of the applications directly back to the fundamental principles.
The book is intended for senior-level engineering students and entering graduate students in engineering and the sciences. No knowledge of electrochemistry is assumed, but an undergraduate training in thermodynamics, transport, and freshman chemistry is needed. A basic knowledge of differential equations is also recommended. Historically, electrochemical engineering is closely associated with chemical engineering and chemistry. However, the lines between disciplines are becoming increasingly blurred, and today we find mechanical engineers, material science engineers, and physicists engaged in electrochemical engineering. We have attempted to broaden our view of electrochemical engineering both to appeal to a larger audience and to expand the exposure of students to new areas and opportunities.
The text is divided into two parts. The first six chapters cover essential topics in a familiar order: an introduction, thermodynamics, kinetics, and mass transport. Also included in these fundamentals is a chapter on electrode structures and one on electroanalytical techniques. The remaining chapters cover applications of electrochemical engineering. It is assumed that the student will have mastered the fundamental chapters before starting on the applications. The application-focused chapters comprise batteries, fuel cells, double-layer capacitors, energy storage systems for vehicles, electrodeposition, industrial electrolysis, semiconductor electrodes, and corrosion. For the most part, the instructor can pick and choose which application chapters to cover; and these applications can be presented in any order. Although not exhaustive, the applications selected represent important applications of electrochemical engineering.
Each chapter begins with a short biography of one of the founders in electrochemistry and electrochemical engineering from the twentieth century. Even though not essential to the technical material presented, writing these short sketches was often personal and deeply satisfying. In general, our focus was on the accomplishments and impact of these remarkable individuals. The selection of whom to profile was also personal and, without question, subjective. Other than space limitations, there can be no justification for omitting pioneers such as Alan Bard and Norbert Ibl.
The authors have used this material to teach introductory electrochemical engineering courses at Georgia Institute of Technology and Brigham Young University. Many of the chapters were drastically revised after the first teaching. Again, our objective was to create a textbook suitable for classroom teaching. Many of the problems presented at the end of the chapters have been honed through homework assignments and on examinations. In fact, these problems and our lectures guided what content to include in the text—we sought to eliminate from the book content not addressed in class or not suitable for practice in the form of problems. Our experience has been that in a one semester course only a couple of the application chapters can be completed in addition to the first six fundamental chapters. We have purposely included references only sparingly in the text itself. While important references for each topic are found at the end of each chapter, we made no attempt to meticulously ascribe credit—our thinking was a highly annotated text is not important to beginning students and actually presents an additional barrier to learning.
The journey of writing this book has been immensely rewarding and not surprisingly a bit longer than anticipated. We have so many colleagues, students, friends, and family members to thank. Their support and encouragement was beyond heartening.
Thomas F. Fuller
2017
John N. Harb
List of Symbols
specific interfacial area, m
−1
activity of species
i
, unitless
A
area, m
2
A
c
cell or electrode area, m
2
Ar
Archimedes number, unitless
b
Tafel slope, V per decade
B
Debye constant for solvent, (kg/mol)
½
m
−1
c
total concentration or salt concentration, mol m
−3
c
speed of light, 2.99792 × 10
8
m s
−1
c
i
concentration of species
i
, mol m
−3
C
capacitance, F
C
d
differential capacitance, F
C
DL
double layer capacitance per unit area, F m
−2
C
p
battery capacity offset, unitless
distance, m
hydraulic diameter, m
molecular diffusivity of species
i
, m
2
·s
−1
E
energy for battery or double layer capacitor, J or W·h
E
elastic modulus, Pa
E
a
activation energy, J/mol
E
g
energy gap, eV
f
frequency, Hz
f
i
fugacity of species
i
, Pa
F
Faraday's constant, 96485 C per equivalent
F
x
component of force, N
acceleration of gravity, m s
−2
G
Gibbs energy, J mol
−1
G
conductance, Ω
−1
Gr
Grashof number, unitless
h
thickness, gap in electrolysis cells, m
h
Planck's constant, J-s
H
Enthalpy, J mol
−1
i,
i
current density, A m
−2
current, A
exchange current density, A·m
−2
photon flux, s
−1
·m
−2
J
i
molar flux of species
i
, mol m
−2
s
−1
k
a
, k
c
anodic and cathodic reaction rate constants
k
c
mass transfer coefficient, m s
−1
k
thermal conductivity, W·m
−1
·K
−1
K
equilibrium constant, unitless
L
characteristic length, m
L
p
diffusion length, m
m
mass, kg
m
molality, mol kg
−1
mass flow, kg s
−1
M
i
molecular weight, g·mol
−1
or kg·mol
−1
n
number of electrons transferred
n
number density of electrons, m
−3
n
i
number of moles of species
i
, mol
n
i
number density of electrons in intrinsic semiconductor, m
−3
N
AV
Avogadro's number
N
A
number density of acceptor atoms, m
−3
N
D
number density of donor atoms, m
−3
N
i
molar flux of species
i
relative to stationary coordinates, mol m
−2
s
−1
p
pressure, Pa
p
number density of holes, m
−3
P
power, W
P
perimeter, m
q
fundamental charge, 1.602 × 10
−19
C
q
charge per unit surface area, C·m
−2
rate of heat generation, W
Q
charge, C or A·h
r
radius, m
R
universal gas constant, 8.314 J mol
−1
K
−1
R
Ω
ohmic resistance, Ω or Ω-m
2
Re
Reynolds number, unitless
homogeneous reaction rate, mol m
−3
s
−1
stoichiometric coefficient, unitless
S
electrical conductance, S
S
entropy, J mol
−1
K
−1
Sh
Sherwood number, unitless
Sc
Schmidt number, unitless
t
time, s
transference number of species
i
, unitless
T
Temperature, K, or °C
U
equilibrium potential, V
u
i
mobility of ion, m
2
mol J
−1
s
−1
v
velocity, m s
−1
V
electric potential or voltage, V
v
s
superficial velocity, m s
−1
volumetric flowrate m
3
s
−1
volume, m
3
W
work, J
W
width of depletion layer, m
w
molar flowrate, mol s
−1
Wa
Wagner number, unitless
x
i
mole fraction of species
i
in condensed phase, unitless
y
i
mole fraction of species
i
in gas phase, unitless
z
i
charge number
Greek Symbols
α
Debye constant for solvent, (kg/mol)
½
α
relative permeability, unitless
α
absorption coefficient, m
−1
α
a
,
α
c
transfer coefficient for anodic and cathodic reactions, unitless
β
symmetry factor, unitless
activity coefficient, unitless
ɛ
porosity, unitless
ɛ
o
permittivity of free space, 8.854 × 10
−12
C V
−1
m
−1
ɛ
permittivity, C V
−1
m
−1
or F m
−1
ɛ
r
relative permittivity, unitless
strain, unitless
η
c
current efficiency
η
coul
coulombic efficiency, unitless
η
f
faradaic efficiency, unitless
surface overpotential, V
κ
electrical conductivity, S m
−1
Debye length, or wavelength, m
absolute activity
equivalent conductance, S m
−2
equivilent
−1
conductance, S m
−1
viscosity, Pa-s
chemical potential, J mol
−1
kinematic viscosity, m
2
s
−1
scan rate, V s
−1
stoichiometric coefficient, unitless
electro-osmotic drag coefficient, unitless
mass density, kg m
−3
charge density, C m
−3
σ
electrical conductivity of solid, S m
−1
; or surface energy, J m
−2
τ
characteristic time, s
τ
tortuosity, dimensionless
ϕ
potential, V
Φ
quantum yield
gas holdup, osmotic coefficient, unitless
angular frequency, rad s
−1
Subscripts and Superscripts
a
anode
avg
average value
b
bubble
c
charge, cathode, or cutoff frequency
cb
conduction band
ct
charge transfer
d
discharge
e
electrolyte
eff
effective quantity
f
formation
fb
flat band
h
electrical portion of hybrid system
i
species
int
interface
lim
limiting value
M
metal
o
value at standard or reference conditions
ocv
open circuit voltage
ph
photon
Rx
reaction
s
solution, separator, or surface
sc
space charge
vb
valence band
∞
bulk value far from electrode
o
initial value
θ
equilibrium potential at reference conditions
*
ideal gas
About the Companion Website
This book is accompanied by a companion website:
www.wiley.com/go/fuller/electrochemicalengineering
The website features:
Powerpoint slides for figures from the text
Complete solution manual to end of chapter problems
Excel files for data sets used in student problems and chapter illustrations
Charles W. Tobias was born on November 2, 1920 in Budapest, Hungary and died in 1996 in Orinda, California. He describes his family as an “engineering family” and realized that he would be an engineer from the age of 4 or 5. Music was a lifelong passion, but engineering was his career. Tobias was inspired to select chemical engineering by his high school chemistry teacher. He attended the University of Technical Sciences in Budapest, where he obtained his Ph.D. in 1946. He was part of the Hungarian diaspora, fleeing Hungary in 1947 as the Communists were taking over the government. He traveled to Berkeley to pursue postdoctoral studies at the University of California where his brother was already working for Ernest O. Lawrence at the University's radiation laboratory. W.M. Latimer, a pioneer in the thermodynamics of electrolytes and Tobias's new boss, directed him to “…build up engineering electrochemistry here, and it should be the best in the world.” By all measures, he succeeded. He began as an instructor in the newly formed Department of Chemical Engineering and then became an Assistant Professor in 1950 and Professor in 1960. He also chaired the department from 1967 until 1972.
Charles Tobias is considered by many to be the father of modern electrochemical engineering. He added discipline and rigor, putting many of the principles on a sound theoretical footing. He studied fluid flow, electric potential fields, thermodynamic and materials properties, and mass transfer, linking his findings into a new discipline. Tobias was instrumental in moving the field from largely empirical approaches to a quantitative science that addressed scale-up and optimization. Professor Tobias is also credited with founding the electrochemical research program at Lawrence Berkeley National Laboratory, which for decades was the most influential electrochemistry group. He is reported to have started the first “electrochemical engineering” course. Professor Tobias joined with Paul Delahay in 1961 to edit a new monograph series entitled Advances in Electrochemistry and Electrochemical Engineering.
Professor Tobias had a long and productive involvement in the Electrochemical Society. He won several awards, including the Society's highest honor, the Acheson award. He served as President of the Electrochemical Society from 1970 to 1971 as well as an editor for the Journal of the Electrochemical Society for many years. As a result, he had a large influence on the structure and operation of the Society. Tobias brought the same philosophy of increasing the scientific rigor and quantitative engineering to the Society. He was also President of the International Society of Electrochemistry (1977–1978). In 2003, the Tobias Award of the Electrochemical Society was established to recognize outstanding scientific and/or engineering work in fundamental or applied electrochemistry by a young investigator.
Although Tobias had an immeasurable impact on the field of electrochemical engineering and was elected a member of the National Academy of Engineering, he was not particularly aggressive in publishing. One of his most significant findings was the use of propylene and ethylene carbonates for lithium batteries, but it was never published beyond a laboratory report. Nonetheless, Dr. Tobias believed that knowledge should always be shared—only ignorance needs secrecy. Much of the information here was derived from the chemical heritage foundation's oral history, which delivers an excellent portrait of his life.
http://www.chemheritage.org/discover/collections/oral-histories/details/tobias-charles-w.aspx
Image Source: Courtesy of UC Berkeley College of Chemistry.
Chapter 1Introduction and Basic Principles
Welcome to this introductory text about electrochemical engineering. If you are like most people, you probably have little idea of what “electrochemical engineering” is and why it is important. That's okay. This book is to help you answer those questions and to prepare you to work in this exciting area. Electrochemistry is a branch of chemistry that studies the chemical changes that occur due to the flow of electrical current or, conversely, the production of electricity from chemical changes. As engineers, we are interested in the application of scientific knowledge, mathematical principles, and economic analyses to the design, manufacture, and maintenance of products that benefit society. It's not surprising, then, that electrochemical engineering has strong historical ties to the profession of chemical engineering.
Almost invariably, application of the principles of electrochemistry to develop products or devices requires consideration of an electrochemical system. An engineering system consists of multiple components that work together in a concerted manner. In addition to electrochemistry, other topics such as heat transfer, structural analysis, and materials science are critical to the design and operation of electrochemical systems. Today, we find engineers and scientists of all disciplines engaged in electrochemistry and collaborating in the design of electrochemical systems.
As with any topic, electrochemical engineering includes a new set of terminology that must be learned. There are also several conventions of practical importance. Hence, this chapter will introduce you to the key vocabulary of the discipline, as well as to some of the central aspects of electrochemical systems. In order to do this, we begin by looking at an electrochemical cell.
1.1 Electrochemical Cells
Electrochemical cells, such as the cell illustrated in Figure 1.1, lie at the heart of electrochemical systems. A typical electrochemical cell consists of two electrodes: an anode where oxidation occurs and a cathode where reduction takes place. Electrons move through an external circuit via an electronic conductor that connects the anode and cathode. The liquid solution that is between the two electrodes is the electrolyte. The electrolyte does not conduct electrons and does not contain any free electrons. It does, however, contain a mixture of negatively charged ions (anions) and positively charged ions (cations). These ions are free to move, which allows them to carry current in the electrolyte.
Figure 1.1 A Daniell cell is an example of an electrochemical cell. During steady operation, a constant current flows throughout the cell. For any given volume, the current entering and leaving must sum to zero since charge is conserved.
The reactions take place at the electrode surface and are called heterogeneous electron-transfer reactions. For example, the electrodeposition of copper in the cell shown in Figure 1.1 can be written as
Copper ions in solution accept two electrons from the metal and form solid copper. The reaction is described as heterogeneous because it takes place at the electrode surface rather than in the bulk solution; remember, there are no free electrons in the solution. Importantly, then, we see that electrochemical reactions are surface reactions. The metal that accepts or supplies electrons is the electrode. As written, copper ions gain electrons and therefore are reduced to form copper metal. When reduction occurs, the electrode is called the cathode.
In the same cell, the reaction that takes place on the other electrode is
The zinc metal is oxidized, giving up two electrons and forming zinc ions in solution. When oxidation occurs at the surface, the electrode is called the anode.
Both the copper and zinc reactions written above (Equations 1.1 and 1.2) are half-cell reactions, meaning that they describe a reaction that takes place at one of the electrodes. Half-cell reactions always have electrons as either a reactant or a product. Also, charge is always balanced in half-cell reactions. Charge balance means that the net charge on one side of the equation must equal the net charge on the other side of the equation. For example, in the above equation, the net charge on the Zn (left side of the equation) is zero. This value is equal to the net charge for the other side, which is (+2) + 2(−1) = 0. Charge balance is no surprise since electrochemical reactions simply add or remove electrons.
The cell illustrated in Figure 1.1 is called a Daniell cell and is named after John Frederic Daniell, who invented the cell in 1836. In this cell, the electrodes themselves (solid Zn and Cu) participate in the electrochemical reactions as either a reactant or a product. This is not always the case, as we shall see later. The electrons for the reduction of Cu2+ come from the other electrode where the oxidation of Zn takes place. The electrons that are liberated from zinc oxidation at the anode travel through an external circuit to participate in the reduction reaction at the cathode. The movement of electrons corresponds to an electrical current flowing through the external circuit. The anode and cathode reactions can be combined to give an overall cell reaction, also called the full-cell reaction. Note that there are no electrons in the overall reaction, but charge is still balanced.
In other words, the exact number of electrons released from oxidation is used for reduction. Similarly, for each copper ion that is reduced, one zinc ion is formed. Because there is a production of charge at the anode and a consumption of charge at the cathode, there is a net movement of charge in solution from the anode to the cathode. Thus, there is also a current flowing in the solution, but the net charge in the solution is unchanged.
The flow of current in an electrochemical cell is shown in Figure 1.1. Note that, by definition, current in the external circuit is opposite (cathode to anode) to the direction that electrons flow. As illustrated in the figure, current flows counterclockwise in a continuous circuit that includes the solution and the external circuit. The electrochemical reactions are the means by which current flows from the electrode to the solution (anode) and from the solution to the electrode (cathode) as part of this circuit. These reactions will not take place if the circuit is broken. This circuit is most commonly “broken” by disconnecting the external connection between the electrodes. In the absence of this external connection, the cell is at open circuit, and there is no net reaction at either electrode. Finally, we note that the name “electrochemical” refers to the fact that the chemical changes are connected to the flow of electric current. Some of the additional aspects of electrochemical reactions are discussed in the next section.
1.2 Characteristics of Electrochemical Reactions
Electrochemical reactions are reactions where electrons are transferred through a conductor from the species being oxidized to that being reduced. Most of the unique and important properties of electrochemical reactions are the result of the way that these electrons are transferred. These characteristics include the following:
Separation of the oxidation (anodic) and reduction (cathodic) reactions
. Because electrons are transferred through a conductor, the oxidation and reduction can take place on two different electrodes. This situation is the most common type of configuration for an electrochemical cell, as already illustrated.
Use of electrons to perform work
. In cells like the Daniell cell introduced in
Section 1.1
, electrons move spontaneously from the anode to the cathode when the circuit is closed (completed), because the energy of electrons in the anode is higher than the energy of electrons in the cathode. Some of that extra electron energy can be used to perform work by passing the electrons (current) through a load (e.g., an electronic device). Perhaps the most familiar application of this concept is in the battery that you use to power your phone or computer, where you are using electron energy to send messages to your friends or to complete your homework.
Direct measurement of reaction rates
. Typically, it is difficult to measure directly the rates of chemical reactions. However, since electron transfer in electrochemical reactions takes place through a conductor, the reaction rate is easy to measure—you just measure the electric current passing in the wire between the electrodes. That current is directly related to the reaction rate at each of the two electrodes. We will explore this later in the chapter when we discuss Faraday's law.
Control of the direction and rate of reaction
. Because electrons participate in both the oxidation and reduction reactions as either a product or a reactant, we can change the rate of reaction by changing the difference in potential between the electrodes. The electric potential is a measure of the electron energy. By adjusting the potential, we can speed up the reactions, slow them down, or even make them go in the reverse direction.
This textbook will help you to understand and to use the powerful properties of electrochemical reactions to design useful products. In the application chapters of the book, you will have the opportunity to see what others have done with electrochemical systems to create devices and processes that benefit humankind. In preparation, the next section of this chapter provides a brief overview of the applications that will be considered in order to illustrate the importance of electrochemical systems. However, before doing that, let's consider some additional aspects of electrochemical reactions.
In the Zn/Cu cell considered previously, the electrodes participated directly as either a reactant (Zn) or a product (Cu). In many instances, the electrodes do not participate beyond supplying or removing electrons. In these instances, the electrodes are called inert. Each of the electrochemical reactions considered in the Daniell cell involved one solid species and one aqueous species. This is by no means a requirement or even typical. Reactants and products in electrochemical reactions can be solids, liquids, dissolved species, or gases. The evolution of hydrogen gas, for instance,
is a reduction (cathodic) reaction that occurs at an inert electrode. Here, the reactant is dissolved in solution and the product is a gas. The oxidation of iron(II) to iron(III) provides another example:
In this case, both the reactant and product are dissolved species.
In looking at the reactions for the Daniell cell, we note that copper ions gained two electrons, zinc lost two electrons to form zinc ions, hydrogen ions gained one electron each to produce hydrogen gas, and a ferrous ion lost an electron to form a ferric ion. You may be wondering how we know how many electrons will be transferred and the direction in which the reaction will go. The direction depends on potential as we will see in the next two chapters. However, the oxidation and reduction products are determined by the electronic structure of the participating species. You undoubtedly learned about oxidation states in your beginning chemistry class, and those same principles apply here. Let's consider a couple of simple examples just to illustrate the concept. Sodium is an alkali metal and has a single electron in its outer electron shell. Whenever possible, sodium tends to give up that electron, leaving it with a +1 charge and a full outer shell. Thus, the stable state for a sodium ion is Na+. Similar logic can be used for the other alkali metals. In the second column of the Periodic Table you have alkaline-earth metals, such as magnesium or calcium. These elements have two electrons in their outer shell and, therefore, yield ions with a +2 charge such as Mg2+ or Ca2+, using rationale similar to that used for the alkali metals. Moving to the other side of the Periodic Table, we find chlorine that has seven electrons in its outer shell. Chlorine likes to pick up an extra electron in order to complete that shell. Therefore, it forms Cl−. Finally, the electronic structure of some elements (e.g., most transition metals) allows them to form ions with different oxidation states; for example, iron can form Fe2+ or Fe3+.
Fortunately, you don't need to memorize the Periodic Table or to look up the electronic structure of an element every time to determine the relevant oxidation state or half-cell reaction. Tables of known electrochemical reactions are available, and a short list appears in Appendix A of this book. These tables not only show the reactions, but also give the standard potential for each reaction. This standard potential is extremely important as we will see in the next chapter. Note that, by convention, the reactions in Appendix A are written as reduction reactions, but we can treat them as being reversible.
Illustration 1.1
Use the table in Appendix A to find the two half-cell reactions and combine them to determine the full-cell reaction.
Corrosion of iron in an oxygen-saturated acid solution.
On one electrode, iron metal is oxidized to form Fe
2+
; on the other electrode, oxygen is reduced. Entry 18 shows the reduction of iron:
We reverse the direction to get the oxidation of iron:
The reduction of oxygen in acid is given by entry 4:
These two reactions are then combined. The iron oxidation reaction is first multiplied by two so that the electrons cancel out when the equations are added together:
Deposition of silver from an alkaline solution.
The silver reduction reaction is multiplied by four and added to the oxidation reaction to provide the full-cell reaction:
1.3 Importance of Electrochemical Systems
Electrochemical systems are not only essential for our society but are also common in everyday life. Imagine a world without batteries to power your personal electronic devices. How would travel change without low-cost aluminum that is essential for aircraft? What if corrosion of the steel in bridges, the hulls of ships, superstructures of buildings, and pipelines couldn't be controlled? These examples, electrochemical energy storage, industrial electrolysis, and corrosion, are some of the major applications of electrochemical engineering. Following development of the fundamental principles of electrochemical engineering, these and other applications are covered in separate chapters.
We all know that the storage of energy using batteries (Chapters 7 and 8) is an essential feature for countless technologies. The size of the global battery market is more than 50 billion dollars annually. Applications of batteries are widespread in society, ranging from basic consumer electronics, to automobiles, implanted medical devices, and space travel. Energy storage is needed where portability is required, emergency power is desired, or simply when electrical demand and supply are not matched. Batteries store energy chemically and convert that energy to electricity as needed. For many applications, the conversion between chemical and electrical energy must be extremely efficient and, in some cases, nearly reversible in order for batteries to be practical. Electrochemical double-layer capacitors (Chapter 11) can also be used to store energy.
The purpose of industrial electrolysis is to use electrical energy to convert raw materials into desired products. This transformation of raw materials takes place in an electrochemical reactor. Industrial electrolytic processes (Chapter 14) consume about of 6% of the U.S. electricity supply. Although a number of metals and other materials can be produced electrochemically, the main products of electrolysis are aluminum, chlorine, and sodium hydroxide (caustic soda). Low-cost electricity and electrochemical routes for production transformed aluminum from an expensive and rarely used metal to a commodity material that is essential for society. Chlorine and sodium hydroxide, produced simultaneously on a huge scale by electrolysis, are required for the production of a variety of materials, including plastics, paper, soaps, solvents, and a large number of other chemicals.
The many desirable properties of metals have led to their widespread use in industry and, frankly, in nearly every aspect of our lives. Corrosion (Chapter 16) is the unwanted attack of metals by their environment. The manufacture of metals is sometimes done electrochemically as described above for the production of aluminum. We can think of corrosion as the reverse process, by which metals are converted back into their oxide form. This cycle is illustrated in Figure 1.2. The process of corrosion is electrochemical in nature. The global economic cost of corrosion has been estimated to be several trillion dollars annually. Therefore, it is important that engineers understand the conditions under which corrosion is likely to occur. They should also be able to measure, predict, and mitigate the negative impacts of corrosion. Avoidance of corrosion is incorporated into the appliances found in our homes. Additionally, corrosion prevention is essential for maintaining the integrity of the bridges over which we travel, and an integral part of the design of natural gas and oil pipelines that supply our energy. These are just a few of the areas where understanding corrosion is important.
Figure 1.2 Life cycle of metals. Many of the processes are electrochemical.
Electrodeposition is the electrochemical deposition of a metal onto a surface (Chapter 13). Electrodeposition is used for decoration, to provide protective coatings, and is essential in the fabrication of interconnects for large-scale integrated circuits. Most metal fasteners (screws, nails, clips, and bolts to name but a few) are coated for appearance, to improve their corrosion resistance, or to reduce friction. Many of these fasteners use electrochemical processes to provide these coatings.
Roughly 10% of the world's population is afflicted with diabetes. Since treatment requires regular monitoring of blood glucose levels, the measurement of glucose concentration is one of the most frequent tests conducted. Did you know that most of the billions of these tests are done electrochemically? These sensors work by measuring the current generated from electrochemical oxidation of glucose. Modern automobiles use oxygen sensors to allow efficient operation of the fuel injection system. These sensors are also electrochemical devices.
We hope that this section has helped you gain an increased appreciation of the importance of electrochemical systems. In addition to the applications noted above, there are other promising technologies in development. These include fuel cells (Chapters 9 and 10), which convert clean fuels into energy at efficiencies much higher than that of a combustion engine. Fuel cells have been essential for manned space flight, but have yet to achieve widespread commercial success. Semiconductor electrochemistry (Chapter 15) offers opportunities for photoelectrochemical processes to convert sunlight into electricity or to produce useful chemicals through artificial photosynthesis. The list of developing applications extends well beyond these two examples, and electrochemistry will undoubtedly continue to provide new products and processes that will improve our quality of life and benefit humankind.
Before we can examine applications in detail, some fundamental principles must be mastered. These fundamental principles provide the foundation for all of the applications mentioned above. We begin by introducing some basic terminology, as well as reviewing scientific units and the conventions adopted in this text.
1.4 Scientific Units, Constants, Conventions
There are seven base units within the International System of Units (SI system), as shown in Table 1.1 for quick reference. Except for luminous intensity, all of the quantities are used extensively in this text. Among the base units is electric current, I, which is critical for the examination of electrochemical systems. Electric current is measured in amperes [A].
Table 1.1 The Seven SI Base Units; All Except Candela Are Used Frequently in This Book
Quantity
Name of unit
Symbol for unit
Nomenclature used in text
Length
meter
[m]
L
Mass
kilogram
[kg]
m
Mole
mole
[mol]
n
i
Time
second
[s]
t
Temperature
kelvin
[K]
T
Current
ampere
[A]
I
Luminous intensity
candela
[cd]
–
Table 1.2 presents derived units that are used widely in this text and are associated with electrochemical engineering. For each quantity, the name and the SI symbol for the quantity is presented. Our general practice will be to place units in brackets, for example, [Pa-s]. When working problems, dimensional consistency is critical; it will also help you to avoid calculation errors. Therefore, for convenience, the table provides the dimensions of these derived quantities written in terms of both the base units and in an alternative form convenient for calculations. For instance, the units for capacitance [m−2·kg−1·s4·A2] can be written more compactly in terms of other derived units [C·V−1], which will usually be more intuitive and easier to remember when checking for dimensional consistency. Finally, the last column provides the variable symbol used in this text to represent the physical quantity. Where possible, we have used the most common nomenclature to represent these quantities. A detailed list of the nomenclature is provided at the beginning of the book. It is important to note that sometimes the nomenclature for a variable may be the same as the unit. To minimize confusion, remember that variables and fundamental physical constants are in italics, whereas the units will not be italicized. Thus, Vrepresents the potential of an electrochemical cell, whose units are volts [V]. Similarly, A is area [m2], whereas [A] is the unit for current in amperes. Most often we will be dealing with scalar quantities. However, occasionally we will encounter vector quantities, ones that have both magnitude and direction. These quantities will be written in bold face. For example, velocity, a vector quantity, is written with the symbol v.
Table 1.2 SI Derived Units That Are Important for This Text
Quantity
Name of unit
Symbol for unit
Expressed in SI base units
Alternative expression
Nomenclature used in text
Electric charge
coulomb
[C]
A·s
[F·V]
Q
Potential
volt
[V]
m
2
·kg·s
−3
·A
−1
[A·Ω], [J·C
−1
]
V
,
ϕ
Capacitance
farad
[F]
m
−2
·kg
−1
·s
4
·A
2
[C·V
−1
]
C
Resistance
ohm
[Ω]
m
2
·kg·s
−3
·A
−2
[V·A
−1
]
R
Ω
Electrical conductance
siemens
[S]
m
−2
·kg
−1
·s
3
·A
2
[A·V
−1
], [Ω
−1
]
S
Force
newton
[N]
m·kg·s
−2
–
F
x
Pressure
pascal
[Pa]
kg·m
−1
·s
−2
[N·m
−2
]
p
Energy
joule
[J]
m
2
·kg·s
−2
[N·m]
E
Power
watt
[W]
m
2
·kg·s
−3
[J·s
−1
]
P
Frequency
hertz
[Hz]
s
−1
–
f
The coulomb [C] is an SI-derived unit of electrical charge—simply the amount of charge that passes with a current of 1 ampere for 1 second. The elementary charge, denoted with q, is a fundamental physical constant. The value of q is 1.602177 × 10−19 C and equal to the charge of a single proton. Additional essential fundamental constants are provided in Appendix B.
1.5 Faraday's Law
In this section, we examine Faraday's law, which is the relationship between the amount of current that flows through the external circuit and the amount of material that is either consumed or produced in a half-cell reaction. To explore how this works, let's return once again to the zinc reaction:
From the half-cell equation, it is apparent that two electrons are produced for every zinc atom that reacts. Typically, it is more convenient to work in terms of moles rather than atoms. Therefore, two moles of electrons are produced for every mole of zinc atoms that is oxidized. As you can see, we can easily relate the moles of electrons to the moles reacted or produced for any species in a given half-cell reaction.
The next step is to relate the moles of electrons to the current that we measure through the external circuit. To do this, it is customary to introduce a new unit of charge—an equivalent. An equivalent is defined as a mole of charge (either positive charge or negative charge, it does not matter). The number of equivalents of a compound is simply the amount of the substance (in moles) multiplied by the absolute value of its charge, zi. For instance, one mole of Na+ is 1 equivalent, whereas one mole of Ca2+ would be 2 equivalents. Because the sign of the charge does not matter, one mole of electrons is equal to 1 equivalent of charge.
The external current is expressed in amperes [A or C·s−1]. Therefore, we need a relationship between coulombs [C] and equivalents. That relationship is called Faraday's constant, F, which has a value of 96,485 C/equivalent. Faraday's constant can also be expressed in terms of two other constants: the fundamental unit of charge, q, and Avogadro's number, NAV,
This expression is another way of stating that an equivalent is a mole of charge, since q is the amount of charge on a proton in coulombs. We also need a relationship between the current, I [A], and the total charge passed in coulombs. That relationship is
where Q is the charge in [C], I in [A], and t in [s]. In situations where the current is constant, Equation 1.8 simplifies to
We now have the pieces that we need to write the relationship between the current in the external circuit and the amount of a substance that is either reacted or produced. Let's apply what we have learned to the zinc electrode.
Illustration 1.2
For the oxidation of zinc, a current of 12 A passes for 2 hours. How much zinc reacts? Provide the answer in terms of mass and the moles of zinc. The reaction is
First, the total charge passed is determined from Equation 1.9.
