A Guide to Problems in Modern Electrochemistry: 1: Ionics

296 Pages·2001·6.856 MB·English

by  Maria E. Gamboa-Adelco, Robert J. Gale (auth.)

A GUIDE
TO PROBLEMS
IN MODERN
ELECTROCHEMISTRY
1: /onics
A GUIDE
TO PROBLEMS
IN MODERN
ELECTROCHEMISTRY
1: /onics
Maria E. Gamboa-Adelco
Superior, Colorado
and
Robert J. Gale
Louisiana State University
Baton Rouge, Louisiana
SPRINGER SCIENCE+BUSINESS MEDIA,LLC
ISBN 978-0-306-46668-7 ISBN 978-1-4419-8600-9 (eBook)
DOI 10.1007/978-1-4419-8600-9
©2001 Springer Science+Business Media New York
Originally published by Kluwer Academic / Plenum Publishers, New York in 2001
http://www.wkap.nl/
10 9 8 7 6 5 4 3 2 1
A C.I.P. record for this book is available from the Library of Congress
AII rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted in
any form or by any means, electronic, mechanical, photocopying, microfilming, recording,
or otherwise, without writtenpermission from the Publisher
To all students of Electrochemistry
PREFACE
The main goal when writing the textbook Modern Electrochemistry -in its
original version of 1970 (by Bockris and Reddy), and later in its second edition
of 1998 (by Bockris, Reddy and Gamboa-Aldeco)- was to present, in a lucid
way, the complex and multidisciplinary area of Electrochemistry. The aim was
to start at a low level and increase the complexity of concepts, theories, and their
applications. The result is a detailed presentation of topics such as ion-solvent
and ion-ion interactions (Volume 1: lonics), and thermodynamics and kinetics of
electrodic processes (Volumes 2A and 2B: Electrodics). In this effort, the
involvement of various other disciplines -such as mathematics, biology and
engineering- were considered as well as numerous applications, such as fuel
cells, production of metals, batteries, soil remediation and photo-splitting of
water, to mention a few.
The textbook is addressed to anyone interested in learning
Electrochemistry, with occasional previews of advancing frontier topics. It is
written for students or anyone who, because of their work or personal interests,
would be presented with the challenge of learning Electrochemistry. Since the
goal was to teach, the authors followed the format of an excellent textbook,
Physical Chemistry, written by Peter Atkins (W.H. Freeman). Therefore, in the
second edition of Modem Electrochemistry, exercise headings addressed to
assimilate the acquired knowledge were included at the end of each chapter.
Thus, any student willing to improve hislher understanding of this field could be
challenged by solving the many exercises found through the book.
It has been always an incentive for students to find whether hislher efforts
to solve exercises give correct results, or to find tips for problems that he/she
finds more difficult. These are the main reasons for the appearance of the
present book. As part of the textbook Modern Electrochemistry J: /onics, A
Guide to Problems in Modem Electrochemistry: Part 1 Ionics compiles many
vii
viii PREFACE
of the solutions to the exercises and problems presented in the text, as well as
many new problems. During its preparation, the authors wanted to emphasize
three points; first, the variation in complexity of the exercises, which allows the
student to acquire the knowledge in little steps; second, the numerous exercises
and problems that give the student plenty of practice to assimilate the concepts
in the book; and third, the variety of topics presented in the book, which covers
fundamental concepts through applications in modern technology.
The exercises in each chapter have been divided into three categories. The
fIrst category contains simple Exercises, which can be completed with a basic
understanding of the related text. These Exercises allow for practice in using the
chapter's equations and should take about 15 minutes each to solve. Exercises
represents 37% of the total number of exercises and problems, with an average
of 30 exercises per chapter. In the second category, the degree of complexity
increases. This is not because of the length of the answers, but because of a
more profound understanding of the concepts is required. Because of their
higher complexity, the Problems require more time to solve, but can each be
completed within one hour. There are about 44 of these Problems in each
chapter, representing 60% of the total number. Finally, the third category
includes tasks that are more difficult. To solve these Micro-Research Problems,
a further effort of the student is needed. This may imply research on his/her own
for data or deeper concepts in reference or more advanced texts. There is only
one of these problems included in each chapter.
At this point it is important to stress that, in addition to the efforts of the
authors, more than thirty Electrochemistry professionals contributed to the
preparation of the problems. Thanks to them, the authors, with substantial
assistance from J. O'M. Bockris, were able to compile and organize more than
500 exercises and problems for the whole book, including those in A Guide to
Problems in Modern Electrochemistry: Part 2 Electrodics. Just writing this
many questions -without considering their solutions, complexity, and variety of
topics- constitutes a tremendous effort. The authors would like to thank each
one of the participants of this volume who make this book an asset for the
student of Electrochemistry: Bock, Bockris, Casidar, Constantinescu,
Contractor, Herbert, Kim, Mussini, Tejada, Trassati, and Xu.
Finally, one of the authors (Gamboa-Aldeco) thanks Prof. John O'M.
Bockris, for his encouragement, guidance, insistence, and recompilation of the
problems ofthis book.
CONTENTS
CHAPTER 1
NOMENCLATURE ............................................................... ..
CHAPTER 2
ION-SOLVENT INTERACTIONS.............................................. 9
Exercises ........................................................................ 9
Problems ...... '" . .. . . . . .. ... .. ... . ... .. . .. . . .. ... . . . ... .. . ... .. . . . . ... . . . . .. ... 43
Micro-Research Problems .................................................... 84
CHAPTER 3
ION-ION INTERACTIONS.................. ... ... ... ... ...... ...... ... ... ... .... 89
Exercises ........................................................................ 89
Problems ...... . .. . .. ... . .. . . . . . . . .. .. . .. . . .. . . . .. . . .. ... .. . .. . .. . . .. .. . . .. . .. . .. 119
Micro-Research Problems ....................................... '" ... ....... 150
CHAPTER 4
ION TRANSPORT IN SOLUTIONS ............ .................. ............ 155
Exercises ....................................... '" ... ... ... ...... ... ... ... ... ... 155
Problems ............. " ... .. . . . . .. . ... .. . . .. .. . .. . .. . .. . .. . .. . ... .. . .. . ... . .. .. . 186
Micro-Research Problems ......... '" .. . . .. ... . .. ... . . . .. . ... .. . . .. .. . ... . ... 219
ix
x CONTENTS
CHAPTER 5
IONIC LIQUIDS... ... ... ... ... ... .... .. ..... ... ... . .. ... ... ... ... ... ... ... ... ... ... 225
Exercises ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Problems ........................................................................ 252
Micro-Research Problems .................................................... 282
INDEX ................................................................................ 287
CHAPTER 1
NOMENCLATURE
For each symbol the appropriate SI unit is given. Multiples and
submultiples of these units are equally acceptable, and are often more
convenient. For example, although the SI unit of concentration is mol m-3,
concentrations are frequently expressed in mol dm-3 (or M). The abbreviation SI
units comes from Systeme International d'Unites, a system developed by the
General Conference on Weights and Measures based on the mksa (meter
kilogram-second-ampere) system.
Symbol Name SI unit Other units
frequently used
GENERAL
A area of an electrode-solution interface m2
OJ activity of species i
Cj concentration of species i molm-3 M,N
c" bulk concentration mol m-3 M,N
E energy J
F force N
glJ radial pair distribution function
v frequency Hz, S-l
m mass kg
n number of moles
N number of molecules
M. E. Gamboa-Adelco et al., A Guide to Problems in Modern Electrochemistry
© Springer Science+Business Media New York 2001
2 CHAPTER 1
Symbol Name SI unit Other units
frequently used
P pressure Pa atm
r, d, I distance m A
T thennodynamic temperature K °c
t time s
U potential energy J
V volume m3
v velocity m S-I
W work J
Xi molar fraction of species i
Ji reduced mass
p density Kgm-3
A. wavelength m
v
wavenumber m-I
() angle 0
y surface tension Nm-I dyncm-I
ION AND MOLECULE-RELATED QUANTITIES
a distance of closest approach m A
q Bjerrum parameter m
Zi charge number of an ion i
ai polarizability of species i m3 molecule-I
fJ compressibility Pa -I
j.J dipole moment Cm D (debye)
esucm
tel Debye-HUckel reciprocal length m-I
THERMODYNAMICS OF A SIMPLE PHASE
energy of activation J mol-I
relative molar Gibbs free energy Jmol-I
relative molar enthalpy Jmol-I
equilibrium constant of the reaction
charge C
relative entropy J K -I mol -1 eu