Chemical Thermodynamics Set
coordinated by
Michel Soustelle
Volume 6
First published 2015 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd
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www.iste.co.uk
John Wiley & Sons, Inc.
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USA
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© ISTE Ltd 2015
The rights of Michel Soustelle to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2016936176
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-84821-869-7
This book – an in-depth examination of chemical thermodynamics – is written for an audience of engineering undergraduates and Masters students in the disciplines of chemistry, physical chemistry, process engineering, materials, etc., and doctoral candidates in those disciplines. It will also be useful for researchers at fundamental- or applied-research labs, dealing with issues in thermodynamics during the course of their work.
These audiences will, during their undergraduate degree, have received a grounding in general thermodynamics and chemical thermodynamics, which all science students are normally taught. This education will undoubtedly have provided them with the fundamental aspects of macroscopic study, but usually the phases discussed will have been fluids exhibiting perfect behavior. Surface effects, the presence of an electrical field, real phases, the microscopic aspect of modeling, and various other aspects, are hardly touched upon (if at all) during this early stage of an academic career in chemical thermodynamics.
This series, which comprises 7 volumes, and which is positioned somewhere between an introduction to the subject and a research thesis, offers a detailed examination of chemical thermodynamics that is necessary in the various disciplines relating to chemical- or material sciences. It lays the groundwork necessary for students to go and read specialized publications in their different areas. It constitutes a series of reference books that touch on all of the concepts and methods. It discusses both scales of modeling: microscopic (by statistical thermodynamics) and macroscopic, and illustrates the link between them at every step. These models are then used in the study of solid, liquid and gaseous phases, either of pure substances or comprising several components.
The different instalments in this series deal with the following subjects:
Appendices in each volume give an introduction to the general methods used in the text, and offer reminders and additional tools.
This series owes a great deal to the feedback, comments and questions from all my students at the Ecole national esupérieure des mines (engineering school) in Saint Etienne who have “endured” my lecturing in thermodynamics for many years. I am very grateful to them, and also thank them for their stimulating attitude. This work is also the fruit of numerous discussions with colleagues who teach thermodynamics in the largest establishments – particularly in the context of the group “Thermodic”, founded by Marc Onillion. My thanks go to all of them for their contributions and kindness.
This sixth volume is made up of two parts: one devoted to ionic equilibria and the other to electrochemical thermodynamics.
In the first part, we discuss the concepts of dissociation of electrolytes and the phenomena of solvation in the different types of solvents – aqueous and non-aqueous. Next, the different families of ionic equilibria are studied, in turn looking at acid–base equilibria, the equilibria of complex formation, redox reactions and equilibria of precipitation. In each case, we examine the phenomena in both an aqueous and a non-aqueous medium. Solid electrolytes are also touched upon.
Part 2 is dedicated to electrochemical thermodynamics with the involvement of charges in electrical fields. A general approach is used to define the electrochemical values, such as the electrochemical potential of a species, the electrochemical Gibbs energy of a system, etc. Then, two different types of electrochemical systems are studied – first, electrodes with the corresponding reactions for the different types, and then galvanic. Applications of the measurements to galvanic cells are described, with a view to determining various thermodynamic values.
Finally, this second part closes with the study of potential/pH diagrams and their generalization in potential/pX diagrams, in aqueous- or non-aqueous media.
Michel SOUSTELLE
Saint-Vallier
March 2016
| A: | area of a surface or an interface. |
 |
Hamaker constant between two media, 1 and 2. |
 |
affinity |
 |
electrochemical affinity. |
| AM: | molar area. |
| Am: | molecular area. |
| a: | pressure of cohesion of a gas or radius of the elementary cell of a liquid. |
| A, B, …: | components of a mixture. |
| C: | concentration or plot concentration of a potential/pH diagram. |
 |
excess molar specific heat capacity at constant pressure. |
| Ci: | molar concentration (or molarity) of component i. |
| C±: | mean concentration of ions in an ionic solution. |
| CV, CP: | specific heat capacity at constant volume and pressure. |
| c: | capacity of a condenser or number of independent components. |
| D: | dielectric constant of the medium. |
| d: | distance between two liquid molecules. |
| deS: | exchange of entropy with the outside environment. |
| di: | degree of oxidation i of an element A. |
| diS: | internal entropy production. |
| E: | energy in the system. |
| E0: | standard electrical potential or standard electromotive force of a cell. |
| Eabs: | reversible electrical voltage of an electrochemical cell. |
 |
set of variables with p intensive variables chosen to define a system. |
| e: | relative voltage of an electrode. |
| e0: | standard electrical potential (or normal voltage) of an electrode. |
| e0: | equi-activity- or equiconcentration voltage of an electrode. |
| eabs: | absolute voltage of an electrode. |
| F: | free energy. |
 |
electrochemical free energy. |
| Fm: | molar free energy. |
 |
faraday (unit). |
 |
electro-capillary Gibbs energy. |
 |
electrochemical Gibbs energy. |
| Gm: | molar Gibbs energy. |
| g: | osmotic coefficient. |
 |
molar Gibbs energy of the pure component i. |
| H0: | Hammett acidity function |
 |
standard molar enthalpy of formation at temperature T. |
 |
enthalpy, partial molar enthalpy of i. |
 |
electrochemical enthalpy. |
| h: | stoichiometric coefficient of the protons in an electrochemical reaction. |
| h: | Planck’s constant. |
 |
molar enthalpy of the pure component i. |
| I: | ionic strength of a solution of ions. |
| Im: | ionic strength expressed in terms of the molalities. |
| i: | van ‘t Hoff factor. |
| KAX: | solubility product of the solid AX. |
| Kd: | dissociation constant. |
 |
equilibrium constant relative to the concentrations. |
 |
equilibrium constant relative to the fugacities. |
 |
equilibrium constant relative to the partial pressures. |
| Kr: | equilibrium constant. |
| Ks: | solubility product. |
| kB: | Boltzmann’s constant. |
| M: | molar mass. |
| ms: | mass of solutes in grams per kg of solvent. |
| m: | total mass. |
| mi: | mass of component i. |
| N: | number of components of a solution. |
| Na: | Avogadro’s number. |
| NA: | number of molecules of component A. |
| n(α): | total number of moles in a phase α. |
| P: | pressure of a gas. |
| Pi: | partial pressure of the component i. |
| p: | number of external physical variables. |
| Qa: | reaction quotient in terms of activities. |
| QP: | heat of transformation at constant pressure; reaction quotient in terms of partial pressures. |
| Qr: | reaction quotient of the transformation r. |
| R: | perfect gas constant. |
| rA: | radius of the ionic atmosphere. |
| S: | oversaturation of a solution. |
 |
electrochemical entropy. |
 |
molar entropy of the pure component i. |
| T: | temperature |
 |
internal electrochemical energy. |
 |
molar internal energy of the pure component i. |
 |
volume, partial molar volume of i. |
| Vm: | molar volume. |
 |
molar volume of the pure component i. |
| v: | quantum number of vibration. |
| wi: | mass fraction of the component i. |
 |
molar fraction of the component k in the α phase. |
| x, y, z: | coordinates of a point in space. |
| xi: | molar fraction of the component i in a solution. |
| <y>: | mean value of y. |
| Yi and Xi: | intensive and extensive conjugate variables. |
| yi: | molar fraction of the component i in a gaseous phase. |
| α: | dissociation coefficient of a weak electrolyte or polarizability of a molecule. |
| αa: | apparent dissociation coefficient of a weak electrolyte. |
 |
characteristic function having the set  as canonical variables. |
| Γ: | characteristic function. |
| γ: | activity coefficient of the component i irrespective of the reference state. |
| γ0: | activity coefficient of a solvent. |
| γi: | activity coefficient of the species i. |
 |
activity coefficient of component i in the pure-substance reference. |
 |
activity coefficient of component i in the infinitely-dilute-solution reference. |
 |
activity coefficient of component i in the molar-solution reference. |
| γ±: | mean activity coefficient of the ions in an ionic solution. |
| γs: | activity coefficient of a solute. |
| ∆r(A): | value of A associated with the transformation r. |
| ε: | electrical permittivity of the medium. |
| ε0: | electrical permittivity of a vacuum. |
| λ0+, λ0: | equivalent ionic conductivities of the cation and the anion. |
| λA: | absolute activity of component A. |
 |
equivalent conductivity of an electrolyte. |
 |
limiting equivalent conductivity of an electrolyte. |
| μi: | chemical potential of component i, electrical dipolar moment of the molecule i. |
 |
chemical potential of the component i in liquid and gaseous form, respectively. |
 |
electrochemical potential. |
| vk(ρ): | algebraic stoichiometric number of component Ak in the reaction ρ. |
| ve: | stoichiometric coefficient of electrons in an electrochemical reaction. |
| ξ: | reaction progress. |
| Φ: | electrical potential. |
| Φi: | fugacity coefficient of component i in a gaseous mixture. |
| ϕ: | conductivity coefficient of a strong electrolyte or number of phases. |
| χ: | electrical conductivity. |
| Ψi: | electrostatic potential of the ionic atmosphere. |
| Ψ(r): | electrostatic potential. |