Quantities, Units and Symbols in Physical Chemistry - Hardcover

Hardcover

ISBN 10: 0854044337 ISBN 13: 9780854044337

Publisher: Royal Society of Chemistry, 2007

Synopsis

The first IUPAC Manual of Symbols and Terminology for Physicochemical Quantities and Units (the Green Book) of which this is the direct successor, was published in 1969, with the object of 'securing clarity and precision, and wider agreement in the use of symbols, by chemists in different countries, among physicists, chemists and engineers, and by editors of scientific journals'. Subsequent revisions have taken account of many developments in the field, culminating in the major extension and revision represented by the 1988 edition under the simplified title Quantities, Units and Symbols in Physical Chemistry. This 2007, Third Edition, is a further revision of the material which reflects the experience of the contributors with the previous editions. The book has been systematically brought up to date and new sections have been added. It strives to improve the exchange of scientific information among the readers in different disciplines and across different nations. In a rapidly ex

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From the Back Cover

Quantities, Units and Symbols in Physical Chemistry Third Edition The first IUPAC Manual of Symbols and Terminology for Physicochemical Quantities and Units (the "Green Book") of which this is a successor, was published in 1969, with the objective of 'securing clarity and precision, and wider agreement in the use of symbols, by chemists in different countries, among physicists, chemists and engineers, and by editors of scientific journals'. Subsequent revisions have taken account of many developments in the field, culminating in the major extension and revision represented by the 1988 edition under the title Quantities, Units and Symbols in Physical Chemistry. This third edition (2007) is a further revision of the material which reflects the experience of the contributors and users with the previous editions. The book has been systematically brought up to date and new sections have been added. It strives to improve the exchange of scientific information between different disciplines in the international pursuit of scientific research. In a rapidly expanding scientific literature where each discipline has a tendency to retreat into its own jargon, this book attempts to provide a compilation of widely used terms and symbols from many sources together with brief understandable definitions and explanations of best practice. Tables of important fundamental constants and conversion factors are included. Precise scientific language encoded by appropriate definitions of quantities, units and symbols is crucial for the international exchange in science and technology, with important consequences for modern industrial economy. This is the definitive guide for scientists, science publishers and organizations working across a multitude of disciplines requiring internationally approved nomenclature in the area of Physical Chemistry.

Excerpt. © Reprinted by permission. All rights reserved.

Quantities, Units and Symbols in Physical Chemistry

By E. Richard Cohen, Tomislav Cvitas, Jeremy G. Frey, Bertil Holmström, Kozo Kuchitsu, Roberto Marquardt, Ian Mills, Franco Pavese, Martin Quack, Jürgen Stohner, Herbert L. Strauss, Michio Takami, Anders J Thors

The Royal Society of Chemistry

Copyright © 2007 The Royal Society of Chemistry
All rights reserved.

ISBN: 978-0-85404-433-7

Contents

PREFACE, ix, 
HISTORICAL INTRODUCTION, xi, 
1 PHYSICAL QUANTITIES AND UNITS, 1, 
2 TABLES OF PHYSICAL QUANTITIES, 11, 
3 DEFINITIONS AND SYMBOLS FOR UNITS, 83, 
4 RECOMMENDED MATHEMATICAL SYMBOLS, 101, 
5 FUNDAMENTAL PHYSICAL CONSTANTS, 109, 
6 PROPERTIES OF PARTICLES, ELEMENTS, AND NUCLIDES, 113, 
7 CONVERSION OF UNITS, 129, 
8 UNCERTAINTY, 149, 
9 ABBREVIATIONS AND ACRONYMS, 155, 
10 REFERENCES, 165, 
11 GREEK ALPHABET, 179, 
12 INDEX OF SYMBOLS, 181, 
13 SUBJECT INDEX, 195, 
NOTES, 231, 
PRESSURE CONVERSION FACTORS, 233, 
NUMERICAL ENERGY CONVERSION FACTORS, 

CHAPTER 1

PHYSICAL QUANTITIES AND UNITS

1.1 PHYSICAL QUANTITIES AND QUANTITY CALCULUS

The value of a physical quantity Q can be expressed as the product of a numerical value {Q} and a unit [Q]

Q = {Q}[Q] (1)

Neither the name of the physical quantity, nor the symbol used to denote it, implies a particular choice of unit (see footnote, p. 4).

Physical quantities, numerical values, and units may all be manipulated by the ordinary rules of algebra. Thus we may write, for example, for the wavelength λ of one of the yellow sodium lines

λ = 5.896 × 10-7 m = 589.6 nm (2)

where m is the symbol for the unit of length called the metre (or meter, see Sections 3.2 and 3.3, p. 86 and 87), nm is the symbol for the nanometre, and the units metre and nanometre are related by

1 nm = 10-9 m or nm = 10-9 m (3)

The equivalence of the two expressions for λ in Equation (2) follows at once when we treat the units by the rules of algebra and recognize the identity of 1 nm and 10-9 m in Equation (3). The wavelength may equally well be expressed in the form

λ/m = 5.896 × 10-7 (4)

or

λ/nm = 589.6 (5)

It can be useful to work with variables that are denned by dividing the quantity by a particular unit. For instance, in tabulating the numerical values of physical quantities or labeling the axes of graphs, it is particularly convenient to use the quotient of a physical quantity and a unit in such a form that the values to be tabulated are numerical values, as in Equations (4) and (5).

Example

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Algebraically equivalent forms may be used in place of 103 K/T, such as kK/T or 103 (T/K)-1. Equations between numerical values depend on the choice of units, whereas equations between quantities have the advantage of being independent of this choice. Therefore the use of equations between quantities should generally be preferred.

The method described here for handling physical quantities and their units is known as quantity calculus [11–13]. It is recommended for use throughout science and technology. The use of quantity calculus does not imply any particular choice of units; indeed one of the advantages of quantity calculus is that it makes changes between units particularly easy to follow. Further examples of the use of quantity calculus are given in Section 7.1, p. 131, which is concerned with the problems of transforming from one set of units to another.

1.2 BASE QUANTITIES AND DERIVED QUANTITIES

By convention physical quantities are organized in a dimensional system built upon seven base quantities, each of which is regarded as having its own dimension. These base quantities in the International System of Quantities (ISQ) on which the International System of units (SI) is based, and the principal symbols used to denote them and their dimensions are as follows:

Base quantity Symbol for quantity Symbol for dimension

length l L
mass m M
time t T
electric current I I
thermodynamic temperature T Θ
amount of substance nN N
luminous intensity Iv J

All other quantities are called derived quantities and are regarded as having dimensions derived algebraically from the seven base quantities by multiplication and division.

Example dimension of energy is equal to dimension of M L2 T-2 This can be written with the symbol dim of dimension (see footnote, below) dim(E) = dim(m x l2 x t-2) = M L2T-2

The quantity amount of substance is of special importance to chemists. Amount of substance is proportional to the number of specified elementary entities of the substance considered. The proportionality factor is the same for all substances; its reciprocal is the Avogadro constant (see Section 2.10, p. 47, Section 3.3, p. 88, and Chapter 5, p. 111). The SI unit of amount of substance is the mole, denned in Section 3.3, p. 88. The physical quantity "amount of substance" should no longer be called "number of moles", just as the physical quantity "mass" should not be called "number of kilograms". The name "amount of substance", sometimes also called "chemical amount", may often be usefully abbreviated to the single word "amount", particularly in such phrases as "amount concentration" (see footnote, below), and "amount of N2". A possible name for international usage has been suggested: "enplethy" [10] (from Greek, similar to enthalpy and entropy).

The number and choice of base quantities is pure convention. Other quantities could be considered to be more fundamental, such as electric charge Q instead of electric current I.

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However, in the ISQ, electric current is chosen as base quantity and ampere is the SI base unit. In atomic and molecular physics, the so-called atomic units are useful (see Section 3.9, p. 94).

1.3 SYMBOLS FOR PHYSICAL QUANTITIES AND UNITS [5.a]

A clear distinction should be drawn between the names and symbols for physical quantities, and the names and symbols for units. Names and symbols for many quantities are given in Chapter 2, p. 11; the symbols given there are recommendations. If other symbols are used they should be clearly defined. Names and symbols for units are given in Chapter 3, p. 83; the symbols for units listed there are quoted from the Bureau International des Poids et Mesures (BIPM) and are mandatory.

1.3.1 General rules for symbols for quantities

The symbol for a physical quantity should be a single letter (see footnote , below) of the Latin or Greek alphabet (see Section 1.6, p. 7). Capital or lower case letters may both be used. The letter should be printed in italic (sloping) type. When necessary the symbol may be modified by subscripts and superscripts of specified meaning. Subscripts and superscripts that are themselves symbols for physical quantities or for numbers should be printed in italic type; other subscripts and superscripts should be printed in Roman (upright) type.

Examples

Cp for heat capacity at constant pressure

pi for partial pressure of the ith substance

but CB for heat capacity of substance B

μBα for chemical potential of substance B in phase α

Ek for kinetic energy

μr for relative permeability

ΔrHθ for standard reaction enthalpy

Vm for molar volume

A10 for decadic absorbance

The meaning of symbols for physical quantities may be further qualified by the use of one or more subscripts, or by information contained in parentheses.

Examples ΔfSθ (HgCl2, cr 25 °C) = -154.3 J K-1 mol- 1

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Vectors and matrices may be printed in bold-face italic type, e.g. A, a. Tensors may be printed in bold-face italic sans serif type, e.g. S, T. Vectors may alternatively be characterized by an arrow, [??] and second-rank tensors by a double arrow, [??].

1.3.2 General rules for symbols for units

Symbols for units should be printed in Roman (upright) type. They should remain unaltered in the plural, and should not be followed by a full stop except at the end of a sentence.

Example r = 10 cm, not cm. or cms.

Symbols for units shall be printed in lower case letters, unless they are derived from a personal name when they shall begin with a capital letter. An exception is the symbol for the litre which may be either L or 1, i.e. either capital or lower case (see footnote, below).

Examples m (metre), s (second), but J (joule), Hz (hertz)

Decimal multiples and submultiples of units may be indicated by the use of prefixes as defined in Section 3.6, p. 91.

Examples nm(nanometre), MHz (megahertz), kV(kilovolt)

1.4 USE OF THE WORDS "EXTENSIVE", "INTENSIVE", "SPECIFIC", AND "MOLAR"

A quantity that is additive for independent, noninteracting subsystems is called extensive; examples are mass m, volume V, Gibbs energy G. A quantity that is independent of the extent of the system is called intensive; examples are temperature T, pressure p, chemical potential (partial molar Gibbs energy) μ.

The adjective specific before the name of an extensive quantity is used to mean divided by mass. When the symbol for the extensive quantity is a capital letter, the symbol used for the specific quantity is often the corresponding lower case letter.

Examples volume, V, and specific volume, v = V/m = 1/ρ (where ρ is mass density); heat capacity at constant pressure, Cp, and specific heat capacity at constant pressure, cp and Cp/m

ISO [5.a] and the Clinical Chemistry Division of IUPAC recommend systematic naming of physical quantities derived by division with mass, volume, area, and length by using the attributes massic or specific, volumic, areic, and lineic, respectively. In addition the Clinical Chemistry Division of IUPAC recommends the use of the attribute entitic for quantities derived by division with the number of entities [14]. Thus, for example, the specific volume could be called massic volume and the surface charge density would be areic charge.

The adjective molar before the name of an extensive quantity generally means divided by amount of substance. The subscript m on the symbol for the extensive quantity denotes the corresponding molar quantity.

Examples volume, V molar volume, Vm = V/n (Section 2.10, p. 47) enthalpy, H molar enthalpy, Hm = H/n

If the name enplethy (see Section 1.2, p. 4) is accepted for "amount of substance" one can use enplethic volume instead of molar volume, for instance. The word "molar" violates the principle that the name of the quantity should not be mixed with the name of the unit (mole in this case). The use of enplethic resolves this problem. It is sometimes convenient to divide all extensive quantities by amount of substance, so that all quantities become intensive; the subscript m may then be omitted if this convention is stated and there is no risk of ambiguity. (See also the symbols recommended for partial molar quantities in Section 2.11, p. 57, and in Section 2.11.1 (iii), p. 60.)

There are a few cases where the adjective molar has a different meaning, namely divided by amount-of-sub stance concentration.

Examples absorption coefficient, a molar absorption coefficient, ε = a/c (see Section 2.7, note 22, p. 37) conductivity, κ molar conductivity, Δ = κ/c (see Section 2.13, p. 73)

1.5 PRODUCTS AND QUOTIENTS OF PHYSICAL QUANTITIES AND UNITS

Products of physical quantities may be written in any of the ways

a b or ab or a · b or a × b

and similarly quotients may be written

a/b or a/b or by writing the product of a and b-1, e.g. ab-1

Examples F = ma, p = nRT/V

Not more than one solidus (/) shall be used in the same expression unless parentheses are used to eliminate ambiguity.

Examples (a/b)/c or a/(b/c) (in general different), not a/b/c

In evaluating combinations of many factors, multiplication written without a multiplication sign takes precedence over division in the sense that a/bc is interpreted as a/(bc) and not as (a/b)c; however, it is necessary to use parentheses to eliminate ambiguity under all circumstances, thus avoiding expressions of the kind a/bcd etc. Furthermore, a/b + c is interpreted as (a/b) + c and not as a/(b + c). Again, the use of parentheses is recommended (required for a/(b + c)).

Products and quotients of units may be written in a similar way, except that the cross (x) is not used as a multiplication sign between units. When a product of units is written without any multiplication sign a space shall be left between the unit symbols.

Example 1 N = 1 m kg s-2 = 1xkgxs-2 = 1 m kg/s2, not 1 mkgs-2

1.6 THE USE OF ITALIC AND ROMAN FONTS FOR SYMBOLS IN SCIENTIFIC PUBLICATIONS

Scientific manuscripts should follow the accepted conventions concerning the use of italic and Roman fonts for symbols. An italic font is generally used for emphasis in running text, but it has a quite specific meaning when used for symbols in scientific text and equations. The following summary is intended to help in the correct use of italic fonts in preparing manuscript material.

1. The general rules concerning the use of italic (sloping) font or Roman (upright) font are presented in Section 1.3.2, p. 5 and in Section 4.1, p. 103 in relation to mathematical symbols and operators. These rules are also presented in the International Standards ISO 31 (successively being replaced by ISO/IEC 80000) [5], ISO 1000 [6], and in the SI Brochure [3].

2. The overall rule is that symbols representing physical quantities or variables are italic, but symbols representing units, mathematical constants, or labels, are roman. Sometimes there may seem to be doubt as to whether a symbol represents a quantity or has some other meaning (such as label): a good rule is that quantities, or variables, may have a range of numerical values, but labels cannot. Vectors, tensors and matrices are denoted using a bold-face (heavy) font, but they shall be italic since they are quantities.

Examples The Planck constant h = 6.626 068 96(33) × 10-34 J s.

The electric field strength E has components Ex, Ey, and Ez.

The mass of my pen is m = 24 g = 0.024 kg.

3. The above rule applies equally to all letter symbols from both the Greek and the Latin alphabet, although some authors resist putting Greek letters into italic.

Examples When the symbol μ is used to denote a pyhsical quantity (such as permeability or reduced mass) it should be italic, but when it is used as a prefix in a unit such as microgram, µg, or when it is used as the symbol for the muon, μ (see paragraph 5 below), it should be roman.

4. Numbers, and labels, are roman (upright).

Examples The ground and first excited electronic state of the CH2 molecule are denoted ... (2ai)2(1b2)2(3a1)1(1b1)1, X 3B1 and ... (2a1)2(1b2)2(3a1)2, a 1A1 respectively. The π-electron configuration and symmetry of the benzene molecule in its ground state are denoted: ... (a2u)(e1g)4, X 1A1g. All these symbols are labels and are roman.

5. Symbols for elements in the periodic system shall be roman. Similarly the symbols used to represent elementary particles are always roman. (See, however, paragraph 9 below for use of italic font in chemical-compound names.)

Examples H, He, Li, Be, B, C, N, O, F, Ne, ... for atoms; e for the electron, p for the proton, n for the neutron, μ for the muon, α for the alpha particle, etc.

6. Symbols for physical quantities are single, or exceptionally two letters of the Latin or Greek alphabet, but they are frequently supplemented with subscripts, superscripts or information in parentheses to specify further the quantity. Further symbols used in this way are either italic or roman depending on what they represent.

Examples H denotes enthalpy, but Hm denotes molar enthalpy (m is a mnemonic label for molar, and is therefore roman). Cp and Cy denote the heat capacity at constant pressure p and volume V, respectively (note the roman m but italic p and V). The chemical potential of argon might be denoted μAr or μ(Ar), but the chemical potential of the ith component in a mixture would be denoted μi, where iis italic because it is a variable subscript.

7. Symbols for mathematical operators are always roman. This applies to the symbol Δ for a difference, δfor an infinitesimal variation, d for an infinitesimal difference (in calculus), and to capital Σ and Π for summation and product signs, respectively. The symbols π (3.141 592 ...), e (2.718 281 ..., base of natural logarithms), i (square root of minus one), etc. are always roman, as are the symbols for specified functions such as log (lg for log10, ln for loge, or lb for log2), exp, sin, cos, tan, erf, div, grad, rot, etc. The particular operators grad and rot and the corresponding symbols V for grad, [nabla]x for rot, and [nabla] for div are printed in bold-face to indicate the vector or tensor character following [5.k]. Some of these letters, e.g. e for elementary charge, are also sometimes used to represent physical quantities; then of course they shall be italic, to distinguish them from the corresponding mathematical symbol.

Examples ΔH = H(final) - H(initial); (dp/dt) used for the rate of change of pressure; δx; used to denote an infinitesimal variation of x. But for a damped linear oscillator the amplitude F as a function of time t might be expressed by the equation F = F0 exp(- δt)] sin(ωt) where δ is the decay coefficient (SI unit: Np/s) and ω is the angular frequency (SI unit: rad/s). Note the use of roman δ for the operator in an infinitesimal variation of x, δx, but italic δ for the decay coefficient in the product δT. Note that the products δt and ωt are both dimensionless, but are described as having the unit neper (Np = 1) and radian (rad = 1), respectively.

(Continues...)

Excerpted from Quantities, Units and Symbols in Physical Chemistry by E. Richard Cohen, Tomislav Cvitas, Jeremy G. Frey, Bertil Holmström, Kozo Kuchitsu, Roberto Marquardt, Ian Mills, Franco Pavese, Martin Quack, Jürgen Stohner, Herbert L. Strauss, Michio Takami, Anders J Thors. Copyright © 2007 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Edition details

• Publisher: Royal Society of Chemistry
• Publication date: 2007
• ISBN 10: 0854044337
• ISBN 13: 9780854044337
• Binding: Hardcover
• Language: English
• Edition number: 3
• Number of pages: 248
• Editor: Cohen E Richard, Cvitas Tom, Frey Jeremy G, Holström Bertil, Kuchitsu Kozo, Marquardt Roberto, Mills Ian, Pavese Franco, Quack Martin, Stohner Jüergen, Strauss Herbert L, Takami Michio, Thor Anders J