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Quantities, Units and Symbols in Physical Chemistry Third Edition INTERNATIONAL UNION OF PURE AND APPLIED CHEMISTRY Physical and Biophysical Chemistry Division 1 7 2 ) + Quantities, Units and Symbols in Physical Chemistry Third Edition Prepared for publication by E. Richard Cohen Tomislav Cvitaš Jeremy G. Frey Bertil Holmström Kozo Kuchitsu Roberto Marquardt Ian Mills Franco Pavese Martin Quack Jürgen Stohner Herbert L. Strauss Michio Takami Anders J Thor The first and second editions were prepared for publication by Ian Mills Tomislav Cvitaš Klaus Homann Nikola Kallay Kozo Kuchitsu IUPAC 2007 Professor E. Richard Cohen Professor Tom Cvitaš 17735, Corinthian Drive University of Zagreb Encino, CA 91316-3704 Department of Chemistry USA Horvatovac 102a email: [email protected] HR-10000 Zagreb Croatia email: [email protected] Professor Jeremy G. Frey Professor Bertil Holmström University of Southampton Ulveliden 15 Department of Chemistry SE-41674 Göteborg Southampton, SO 17 1BJ Sweden United Kingdom email: [email protected] email: [email protected] Professor Kozo Kuchitsu Professor Roberto Marquardt Tokyo University of Agriculture and Technology Laboratoire de Chimie Quantique Graduate School of BASE Institut de Chimie Naka-cho, Koganei Université Louis Pasteur Tokyo 184-8588 4, Rue Blaise Pascal Japan F-67000 Strasbourg email: [email protected] France email: [email protected] Professor Ian Mills Professor Franco Pavese University of Reading Instituto Nazionale di Ricerca Metrologica (INRIM) Department of Chemistry strada delle Cacce 73-91 Reading, RG6 6AD I-10135 Torino United Kingdom Italia email: [email protected] email: [email protected] Professor Martin Quack Professor Jürgen Stohner ETH Zürich ZHAW Zürich University of Applied Sciences Physical Chemistry ICBC Institute of Chemistry & Biological Chemistry CH-8093 Zürich Campus Reidbach T, Einsiedlerstr. 31 Switzerland CH-8820 Wädenswil email: [email protected] or Switzerland [email protected] email: [email protected] or [email protected] Professor Herbert L. Strauss Professor Michio Takami University of California 3-10-8 Atago Berkeley, CA 94720-1460 Niiza, Saitama 352-0021 USA Japan email: [email protected] email: [email protected] Dr. Anders J Thor Secretariat of ISO/TC 12 SIS Swedish Standards Institute Sankt Paulsgatan 6 SE-11880 Stockholm Sweden email: [email protected] CONTENTS v PREFACE ix HISTORICAL INTRODUCTION xi 1 PHYSICAL QUANTITIES AND UNITS 1 1.1 Physical quantities and quantity calculus . 3 1.2 Base quantities and derived quantities . 4 1.3 Symbols for physical quantities and units . 5 1.3.1 General rules for symbols for quantities . 5 1.3.2 General rules for symbols for units . 5 1.4 Use of the words “extensive”, “intensive”, “specific”, and “molar” . 6 1.5 Products and quotients of physical quantities and units . 7 1.6 The use of italic and Roman fonts for symbols in scientific publications . 7 2 TABLES OF PHYSICAL QUANTITIES 11 2.1 Space and time . 13 2.2 Classical mechanics . 14 2.3 Electricity and magnetism . 16 2.4 Quantum mechanics and quantum chemistry . 18 2.4.1 Ab initio Hartree-Fock self-consistent field theory (ab initio SCF) . 20 2.4.2 Hartree-Fock-Roothaan SCF theory, using molecular orbitals expanded as linear combinations of atomic-orbital basis functions (LCAO-MO theory) . 21 2.5 Atoms and molecules . 22 2.6 Spectroscopy . 25 2.6.1 Symbols for angular momentum operators and quantum numbers . 30 2.6.2 Symbols for symmetry operators and labels for symmetry species . 31 2.6.3 Other symbols and conventions in optical spectroscopy . 32 2.7 Electromagnetic radiation . 34 2.7.1 Quantities and symbols concerned with the measurement of absorption intensity 38 2.7.2 Conventions for absorption intensities in condensed phases . 40 2.8 Solid state . 42 2.8.1 Symbols for planes and directions in crystals . 44 2.9 Statistical thermodynamics . 45 2.10 General chemistry . 47 2.10.1 Other symbols and conventions in chemistry . 49 2.11 Chemical thermodynamics . 56 2.11.1 Other symbols and conventions in chemical thermodynamics . 59 2.12 Chemical kinetics and photochemistry . 63 2.12.1 Other symbols, terms, and conventions used in chemical kinetics . 68 2.13 Electrochemistry . 70 2.13.1 Sign and notation conventions in electrochemistry . 73 2.14 Colloid and surface chemistry . 77 2.14.1 Surface structure . 79 2.15 Transport properties . 81 2.15.1 Transport characteristic numbers: Quantities of dimension one . 82 v 3 DEFINITIONS AND SYMBOLS FOR UNITS 83 3.1 The International System of Units (SI) . 85 3.2 Names and symbols for the SI base units . 86 3.3 Definitions of the SI base units . 87 3.4 SI derived units with special names and symbols . 89 3.5 SI derived units for other quantities . 90 3.6 SI prefixes and prefixes for binary multiples . 91 3.7 Non-SI units accepted for use with the SI . 92 3.8 Coherent units and checking dimensions . 93 3.9 Fundamental physical constants used as units . 94 3.9.1 Atomic units . 94 3.9.2 The equations of quantum chemistry expressed in terms of reduced quantities using atomic units . 95 3.10 Dimensionless quantities . 97 3.10.1 Fractions (relative values, yields, and efficiencies) . 97 3.10.2 Deprecated usage . 97 3.10.3 Units for logarithmic quantities: neper, bel, and decibel . 98 4 RECOMMENDED MATHEMATICAL SYMBOLS 101 4.1 Printing of numbers and mathematical symbols . 103 4.2 Symbols, operators, and functions . 105 5 FUNDAMENTAL PHYSICAL CONSTANTS 109 6 PROPERTIES OF PARTICLES, ELEMENTS, AND NUCLIDES 113 6.1 Properties of selected particles . 115 6.2 Standard atomic weights of the elements 2005 . 117 6.3 Properties of nuclides . 121 7 CONVERSION OF UNITS 129 7.1 The use of quantity calculus . 131 7.2 Conversion tables for units . 135 7.3 The esu, emu, Gaussian, and atomic unit systems in relation to the SI . 143 7.4 Transformation of equations of electromagnetic theory between the ISQ(SI) and Gaussian forms . 146 8 UNCERTAINTY 149 8.1 Reporting uncertainty for a single measured quantity . 151 8.2 Propagation of uncertainty for uncorrelated measurements . 153 8.3 Reporting uncertainties in terms of confidence intervals . 154 9 ABBREVIATIONS AND ACRONYMS 155 10 REFERENCES 165 10.1 Primary sources . 167 10.2 Secondary sources . 169 vi 11 GREEK ALPHABET 179 12 INDEX OF SYMBOLS 181 13 SUBJECT INDEX 195 NOTES 231 PRESSURE CONVERSION FACTORS 233 NUMERICAL ENERGY CONVERSION FACTORS IUPAC PERIODIC TABLE OF THE ELEMENTS vii viii PREFACE The purpose of this manual is to improve the exchange of scientific information among the readers in different disciplines and across different nations. As the volume of scientific literature expands, each discipline has a tendency to retreat into its own jargon. This book attempts to provide a readable compilation of widely used terms and symbols from many sources together with brief understandable definitions. This Third Edition reflects the experience of the contributors with the previous editions and we are grateful for the many thoughtful comments we have received. Most of the material in this book is “standard”, but a few definitions and symbols are not universally accepted. In such cases, we have attempted to list acceptable alternatives. The references list the reports from IUPAC and other sources in which some of these notational problems are discussed further. IUPAC is the acronym for International Union of Pure and Applied Chemistry. A spectacular example of the consequences of confusion of units is provided by the loss of the United States NASA satellite, the “Mars Climate Orbiter” (MCO). The Mishap Investigation Board (Phase I Report, November 10, 1999)1 found that the root cause for the loss of the MCO was “the failure to use metric units in the coding of the ground (based) software file”. The impulse was reported in Imperial units of pounds (force)-seconds (lbf-s) rather than in the metric units of Newton (force)-seconds (N-s). This caused an error of a factor of 4.45 and threw the satellite off course.2 We urge the users of this book always to define explicitly the terms, the units, and the symbols that they use. This edition has been compiled in machine-readable form by Martin Quack and Jürgen Stohner. The entire text of the manual will be available on the Internet some time after the publication of the book and will be accessible via the IUPAC web site, http://www.iupac.org. Suggestions and comments are welcome and may be addressed in care of the IUPAC Secretariat PO Box 13757 Research Triangle Park, NC 27709-3757, USA email: [email protected] Corrections to the manual will be listed periodically. The book has been systematically brought up to date and new sections have been added. As in previous editions, the first chapter describes the use of quantity calculus for handling physical quantities and the general rules for the symbolism of quantities and units and includes an expanded description on the use of roman and italic fonts in scientific printing. The second chapter lists the symbols for quantities in a wide range of topics used in physical chemistry. New parts of this chapter include a section on surface structure. The third chapter describes the use of the International System of units (SI) and of a few other systems such as atomic units. Chapter 4 outlines mathematical symbols and their use in print. Chapter 5 presents the 2006 revision of the fundamental physical constants, and Chapter 6 the properties of elementary particles, elements and nuclides. Conversion of units follows in Chapter 7, together with the equations of electri- city and magnetism in their various forms. Chapter 8 is entirely new and outlines the treatment of uncertainty in physical measurements.
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