J O U R N A L OF T H E AMERICAN CHEMICAL SOCIETY (Registered in U. S. Patent Office)
VOLUME82
(0Copyright, 1960, by the American Chemical Society)
NUMBER 21
NOVEMBER 9, 1960
INTERNATIONAL UNION O F PURE AND APPLIED CHEMISTRY PHYSICAL CHEMISTRY SECTION: COMMISSION ON PHYSICO-CHEMICAL SYMBOLS AND TERMINOLOGY
Manual of Physico-Chemical Symbols and Terminology Prepared from the $ubEuations of the Commission by i t s President
J. A. CHRISTIANSEN Printed by permission of the Committee on Publications of the International Union of Pure and Applied Chemistry.
CONTENTS PAGE
CHEMICAL ELEMENTS AND NUCLIDES. . . . . . . . . . . . . . 5517 CONVENTIONS CONCERNING THE SIGNOF THE ELECTROMOTIVE FORCES AND ELECTRODE POTENTIALS. . 5517 THEQUANTITY pH. ............................. 5518 SYMBOLS AND USAGESIN PHYSICAL CHEMISTRYI. NUDERS AND MATHEMATICAL OPERATIONS.5519 11. ABBREVIATIONS FOR WORDS.. . . . . . . . . . . . . . 5519 111. SYMBOLS FOR PHYSICAL AND CHEMICAL ......................... 5519 QUANTITIES.. IV. SYMBOLS FOR SVESIDIARY QUANTITIES.. .... 5521
The right superscript place remains for indicating, if required, a state of ionization or a nuclear excited The practice of American chemists and physicists in general has been to Put the number at the upper right of the symbol.
CONVENTIONS CONCERNING THE SIGN OF ELECTROMOTIVE FORCES AND ELECTRODE POTENTIALS S Y ~ ~ BIN O REACTION L~ KINETICS... . . . . . . . . . . . . . . . 5522 At the XVIIth Conference of the International Union of Pure and Applied Chemistry in StockCHEMICAL ELEMENTS AND NUCLIDES holm, 1953, the Commission on Physico-Chemical Recommendations adopted by the Symbols and Terminology and the Commission Symbols, Units and Nomenclature on Electrochemistry reached complete agreement Commission of the International Union of on the sign conventions to be recommended with a Pure and Applied physics, September, 1958 view to removing the serious confusion that has Apart from minor differences these conventions long existed in this field, especially in the specificawere adopted by the Physical Chemistry Section tion of so-called “electrode potentials.” of the Commission on Physico-Chemical Symbols The following statement of the recommendations and Terminology of the IUPAC in Stockholm, has been drawn up by the Chairmen of the two 1953. On behalf of the Commission its Chairman Commissions on the basis of a draft prepared by recommends them to be used by chemists. the Commission on Physico-Chemical Symbols and + Comments concerning present contlicts with the pracand Of Some modifications Of the text tice of American chemists and the rules of Chemical Abstracts proposed by the Conmission on Electrochemistry. have been interpolated in the text. It is hoped that the me Electromotive Force of a Ce&-The cell necessity for such comments can be reduced in future years. be represented by a diagram, e.g, These comments, in smaller type, are preceded by the syrnbo1 +. ZnlZn++llCu++lCu Symbols for chemical elements should be written The electromotive force is equal in sign and in roman type* The symbol is not followed by a magnitude to the electrical potential of the metallic period. conducting lead on the right when that of the simExamples: Ca, C, H, He ilar lead on the left is taken as zero, the cell being open. The attached numerals specify a nuclide: When the reaction of the cell is written as mass number 14 N 32n $Cu++ -++Zn++ )Cu atomic number 7 2 atoms/molecule Remark.-It may be of advantage to omit the this implies a diagram so drawn that this reaction atomic number when there is no special reason for takes place when positive electricity flows through indicating it. the cell from left to right. If this is the direction 5517
+
+
5518
INTERNATIONAL UNIONOF PUREAND APPLIED CHEMISTRY
Vol. 82
of the current when the cell is short-circuited, as in the present example, the electromotive force will be positive (unless the ratio Cu++/Zn++ is extremely small). If, however, the reaction is written as 4/31 +Zn++ +*Cu++ +Zn this implies the diagram Cu 1 Cu ++IIZn++ 1 Zn
+
+
and the electromotive force of the cell so specitied will be negative (unlessthe ratio Cu++/Zn++is extremely small). The Electromotive Force of a H alf Cell and the So-called “Electrode Potential.”--When we speak of the electromotive forces of the half cells
Zn++lZn
a - I Cl2,Pt C1-1 AgC1,Ag Fe++,Fe+++lPt we mean the electromotive forces of the cells Pt,H2l H+IIZn++lZn implying Pt,H2IH+IICl-I Clz,Pt the R,J& I H+llCl-I AgCLAg reactions Pt,H*IH+I/Fe++,Fe+++l Pt
qH2
+ @n++ H + + 3% + 4C12 +H+ + C1+ AgCl+ H + + C1- + Ag + Fe+++-+-H+ + Fe++ --f
3Hz #HZ 3H2
where the electrode on the left is a standard hydrogen electrode. These electromotive forces may also be called relotwe electrode poterztzbls or, in brief, electrode potmtiais. When, on the other hand, we speak of the electromotive forces of the half cells ZnlZn++ Pt,Cl*1 c1Ag,AgCl IC1Pt I Fe++,Fe+++ we mean the electromotive forces of the cells Zn I Zn++IIH+IH2,Pt implying Pt,Cl2)Cl-JIH+)Ho,Pt the reactions Ag,AgCl I Cl-llH+l H2,Pt Pt 1 Fe++,Fe+++llH+IH2,Pt
+ + + +
+
@n H + -+ )Zn++ $HI C1H + --+ aC12 433% Ag C1-+ H + + A g C l + *H2 Fe++ H+-Fe+ ++ $HI
+
+
where the electrode on the right is a standard hydrogen electrode. These electromotiveforces should NOT be called electrode potentials.
THE QUANTITY pH Paris, 1957
pH has been defined on an eXperimental bask in a number of papers in the J w r d of Research of thc United States National Bureau of Standurds and in the British Standards Institute’s Standard 1647 (1950). The CommisSion notes that these alternative definitions are equivalent for all (or almost all) practical purposes. The Commission recommends that these dehitions of pH (printed in roman type) be accepted internationally.
SYMBOLS AND USAGES M PHYSICAL CHEMISTRY Prepared in Ziirich, 1955, mended in Paris, 1967. and in Copenhagen. 1958. by the Commiss~onon Physico-Chemical Symbols and Terrmnologg.
The recommendations on the following pa es are mainly those agreed upon in Amsterdam (194$, with modifications which subsequent discussions in the Commission have made desirable. The Commbsion refers to the report of 1949 concerning the history and concerning the agreement with recom-
mendations from related bodies, especially the Symbols,Units and Nomenclature Commission of IUPAP. Referring to setion I11 below, the Commission has found it desirable, however, to quote two paragraphs from the Introduction to the report of 1949. “It is recognized that recommendations by an international body must involve compromises and will sometimes have to include alternative usages for particular quantities from which the various national organizations can select those most closely in accord with their established practices. The proposals now made are not therefore intended to prescribe rigidly usages that should be Universally adopted, but to give guidance in seeking a wider measure of international agreement and warning of instances where existing diversities may cause misunderstandings.” “Even among chemists in Werent countries, or belonging to Merent schools, complete agreement has not been attained on the use of symbols for certain quantities and in a few instances it may be necessary,at leasttemporarily, to agree to disagree and to say so.”
MANUALOF PHYSICO-CHEMICAL SYMBOLS AND TERMINOLOGY
Nov. 5, 1960
I. Numbers and Mathematical Operations Numbers should be printed in roman figures, with a period or comma only separating whole numbers from the decimals. To facilitate reading of long numbers the figures may be grouped together in threes without using commas or periods to separate the groups.
+ Ch.emiua2 Abstracts prefers the use of the comma when there are five or more figures, c.g., 63,122. In some countries a comma is used instead of a period for the decimal point, hence the recommendation for the use of spaces in an international system.
Symbols for mathematical operations should be printed in roman type. II. Abbreviations for Words
+ General agreement a t an international level on abbreviations is =cult to attain. Slight variations seem relatively unimportant in view of other language ditlerences. Periods or no periods after abbreviations is a matter for editorial discretion. A Chemical Abstracts approved list of abbreviations is published in each annual Subject Index and in the "Directions for Abstractors and Section Editors of Chemical Abstracts." Chmicd Abstracts uses periods after abbreviations in order to standardize on unambiguous forms. thus m. (meter). 1. (liter), sec. (second), min. (minute), hr. (hour), g. (gram), (ton, dyne, bar)o(not abbreviated), j. (joule), w. (watt), cal. (calorie), OC., F., OK.,amp. (ampere), v. (volt), f. (farad). Chcmicnl Abstracts prefers italic M (for molar concentration) and N (for normal concentration). To be printed in roman type. Abbreviations for the Names of Units.-Abbreviations for units named after persons begin with a capital letter. Single capital letters used as abbreviations may be printed in smaller type than is used in the body of the text, but practice in this varies and no recommendation is made. meter
micron Hngstram liter second minute hour hertz gram ton dyne
m
OC
p
degreeCelsius. degreeFahrenheit. A degreeKelvius 1 lumen 9 lux min stilb h candela
O F
Hz coulomb
g t dyn N b P J
amphe volt
ohm
OK
Im lx sb cd C A
V 0 F H
farad henry molal (concentration), m molar(concentrationp M W normal(conantration N watt calorie c d fod(concentrationj' F Prefixes to abbreviations for the names of units indicating: Multiples Submultiples tFa 10'' T deci 10-1 d grga 101 G mti 10c mega lo" M milli 10-1 m kilo 10' k micro 10p n-ano 10n p1Co " ' 0 1 p The sign and the letter following form me symbol and there should be no space between them, c.g., 2 6 O C or 26 OC but not 25O C. * Used only when preceded by numerals to indicate the magnitude of a concentration in the specified terms and not as symbols for concentrations in equations.
newton baf
: L
Abbreviations for Other Words.-These will vary with the language used and no attempt is therefore made to secure uniformity of practice a t an international level. III. Symbols for Physical and Chemical Quantities Symbols for physical and chemical quantities, in contrast to abbreviations for units, should be
5519
printed in italic type whenever these symbols are letters of the Latin alphabet and if practicable when they are letters of the Greek alphabet. A bold-face italic type may be used to represent certain specified physical constants or conversion factors. Symbols separated by commas represent equivalent recommendations. Symbols preceded by three dots are alternatives to be used only when there is some reason for not using a symbol before the three dots. Space, time, mass and related quantities 1 h
1 length 2 height 3 radius 4 diameter 5 path, length of arc
6 plane angle 7 solid angle 8 area 9 volume 10 specific volume 11 wave length 12 wave number 13 time 14 period or other characteristic interval 15 frequency 16 angular frequency (27rv) 17 velocity 18 angular velocity 19 acceleration 20 acceleration of free fall 21 mass 22 moment of inertia 23 density 24 relative density
Y
d S
8, ~ AIS
v... v
Y
x 6,
t
v
T,7
v, f W
u . . .u, w W
a g
m
I
:
Molecular and related quantities
101 molecular mass 102 molar mass 103 Avogadro's number 104 number of molecules 105 number of moles 106 mole fraction 107 molality 108 concentration 109 molar concentration of substance B 110 molecular concentration 111 partition function 112 statistical weight 113 symmetry number 114 characteristic temperature 115 diameter of molecule 116 mean free path 117 diffusion coefficient 118 osmotic pressure 119 surface concentration
m M No, L,N N n x..
.x, y
Mechanical and related quantities F G. . .W M
201 force 202 force due to gravity (weight) 203 moment of force 204 power 205 pressure
P
PI
p
+
~p, 8
W
,
INTERNATIONAL UNIONOF PUREAND APPLIEDCHEMISTRY
5520 206 207 208 209 210 211 212 213 214 215 216 217
traction U shear stress 7 modulus of elasticity E shear modulus G compressibility K compression modulus ( 1 / ~ ) K viscosity 9 fluidity P kinematic viscosity V friction coefficient f surface tension 7.. . U angle of contact e
301 302 303 304 305 306
Thermodynamic and related quantities temperature e . . .t temperature, absolute T gas constant R,R Boltzmann constant k, k heat 4, Q work w, A b
a
307 energy (Gibbs
E)
U... E
.
E...U
a Recommended by IUPAP (without. .E),European practice. * American practice. 308 entropy (Gibbs 9) S S
309 Helmholtz free energy F (Gibbs $) 310 enthalpy (Gibbs x) H G 311 Gibbs function (c) American practice is F...G , the opposite of
A H G...F the listing
shown.
312 313 314 315 316 317 318 319 320 321 401
402 403 404 405 406 407 408 409 410 41 1
heat capacity specific heats ratio cp/cv chemical potential activity, absolute activity (relative) activity coefficient osmotic coefficient thermal conductivity Joule-Thomson coefficient
C GpJ cV
YJ
I.r
x
a
fJ gJ x p
Chemical reactions stoichiometric number of molecules (negative for reactants, positive for products) V standLrd equation of chemical reaction ZVBB= 0 affinity ( - Z V B ~ B )of a reA action K equilibrium constant equilibrium quotient or equilibrium product (of molalities) Q extent of reaction (dnB = E VBdO degree of reaction (e.g., deff gree of dissociation) k rate constant collision number (collisions per unit volume and unit z time) rate constant corresponding 2 to the rate Z rate of reaction v . . . r , s, J
Light 501 Planck’s constant 502 Planck’s constant divided by 2?r 503 quantity of light 504 radiant power, flux of light (dQ/dt) 505 luminous intensit (d@/dw) 506 illumination (d9jrdS) 507 luminance 508 luminous emittance 509 absorption factor (fraction of incident radiant power which is absorbed) 510 reflection factor (fraction of incident radiant power which is reflected) 511 transmission factor (fraction of incident radiant power which is transmitted) 512 transmittance ( T = 1/10) 513 absorption (extinction) coefficient (KZC = In (I/T)) 514 absorbance (extinction) ( A = log10 ( I I T ) ) 515 absorptivity (specificabsorbance) (decadic absorption or extinction coefficient) 516 molar absorptivity (molar decadic absorption or extinction coefficient) (elc =
A)
517 refraction index 518 refractivity 519 angle of optical rotation
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hJ
A
Q cp
I E L, B H CL
P
7
T K
A . . .E a
E
n Y CY
Electricity and magnetism 601 elementary charge e, e 602 quantity of electricity Q 603 charge density P 604 surface charge density U 605 electric current 1.. .i 606 electric current density J 607 electric potential V E 608 electric field strength D 609 electric disdacement 610 electrokineh potential c 611 capacity C 612 permittivity (dielectric constant) € 613 dielectric polarization P 614 dipole moment CI 615 electric polarizability of a molecule Y 616 magnetic field strength H 617 magnetic induction B 618 magnetic permeability I.c 619 magnetization M 620 magnetic susceptibility 621 resistance 622 resistivity 623 self inductance 624 mutual inductance M , L12 625 reactance X 626 impedance z 627 admittance Y ff,
T i
2
M ~ AOFLPHYSICO-CHEMICAL SYMBOLS AND TERMINOLOGY
Nov. 5, 1960
Electrochemistry 701 Faraday's constant (the faraday) 702 charge number of an ion, plus or minus 703 degree of electrolytic dissociation 704 ionic strength 705 electrolytic conductivity (specilic conductance) 706 equivalent or molar conductance of electrolyte or ion 707 transport number 708 electromotive force 709 overpotentid
F,F z a
I... p K
A
4 T E ?f
IV. Symbols for Subsidiary Quantities It is much more diEcult to make detailed recommendations on symbols for subsidiary quantities than on symbols for the principal quantities. The reason is the incompatibility between the need for specifying numerous details and the need for keeping the printing reasonably simple. Among the most awkward things to print are superscripts to subscripts and subscripts to subscripts. Examples of symbols to be avoided are ANO,- and HWC The problem is vastly reduced if it is recognized that two different kinds of notation are required for two different purposes. In the formulation of general fundamental relations the most important requirement is a notation easy to understand and easy to remember. In applications to particular cases, in quoting numerical values and in tabulation the most important requirement is complete elimination of any possible ambiguity even a t the cost of an elaborate notation. The advantage of a dual notation already is accepted to some extent in the case of concentration. The best notation for formulating the laws of homogeneous chemical equilibrium is something such as A + ... e L + ...
5521
but when it comes to giving values in particular cases a much more appropriate notation is A(&Mg++)= 53 cm2 equiv-' a t 25OC A(C1-) = 76 3-l cm2 equiv-' a t 25OC A(&MgC12)= 129 3-l cm2 equiv-' at 25OC A(MgC12) = 258 3-' cm2 mole-' a t 25OC In both notations the meaning of the symbols is so obvious and so well suited to the purpose that it is hardly necessary even to deiine them. Again partial quantities are most simply denoted by the use of a subscript, for example Vl for partial volume and the general relation between the partial volumes of the two components of a binary system is written most simply ( T , P const.) nl dVl n2 dV2 = 0 and this relation holds whether the partial volumes Vl, V2 are expressed per mole or per gram or per kilogram according as the quantities nl, n2 are measured in moles or grams or kilograms. When it is desired to emphasize the contrast between partial quantities, which are intensive, and the extensive properties from which they are derived, this may be achieved either by use of a bar over the symbol or by use of the corresponding lower case letter. Thus in these notations ( T , P const.) nl dP1 n 2 d P z = 0 (TIP const.) nl der] n2 der2 = 0
+
+ +
+ In journals of the American Chemical Society partial molal quantities are indicated almost exclusively by an italic letter surmounted by a bar, e.g., 9. VI and VZare not regarded as adequate. But when it comes to specifying values a completely different notation is called for such as V (KS04, aq., 0.1 MI 25OC) = 48 ml mole-' = 24 ml equiv-1 = 0.27 ml g-I Each kind of notation is appropriate to its purpose. Incidentally the notation for extensive and partial quantities need not be restricted to purely thermodynamic quantities but is also appropriate to such quantities as refraction. Thus if we define the refraction R (an extensive property) by R=- n2 - 1 V n2 2 then it becomes natural to denote the derived partial refractivity by Ri or & or ri. A last example will be given relating to optical rotation. The relations between the angle a of rotation of the plane of polarization and the total number n of moles or N of molecules in the path of a light beam of cross-section A can be clearly expressed in the form n N a = -A a,,= 2 aN
+
but when we turn to a particular example it is better to use a notation such as HOBr H + BrBr2 H 2 0 [HOBr][H+][Br-] = K, [Bra1 mole2 1-2 KC(25"C) = 6 X Once the principle of dual notation is accepted, its adaptability and usefulness become manifest in all fields of physical chemistry. It will be illustrated here by just a few examples. The general relation between the equivalent conductance of an electrolyte and the eqdvalent conductance of the two ions is written most simply and most clearly as A = A+ A-
+
+
e
+
+
where a,, is the molar optical rotatory power and q the molecular optical rotatory power (a molecular cross-sectional area). When on the other hand it is desired to record an experimental measurement, an appropriate notation would be a(5900 A, 25"C, D-sucrose, aq., 10 g/l, 10 cm) = . . .O
INTERNATIONAL UNIONOF PIIREAND APPLIEDCHEMISTRY
5522
These superscripts are recommended: = pure substance = infinite dilution id = ideal * = standard in general t = pressure independent term The superscripto is not specifically recommended because it has been used with several meanings.
v = - -1 d[BI VB
a
SYMBOLS IN REACTION KINETICS Paris, 1957
The Commission decided to recommend : (a) Each reaction should be represented by a formulation which may be written in either of two forms 2HI -+ Hz I2 or 0 = H t I* - 2HI 11+2HI or 0 = 2HI HI 11 H, and in general YAA+ ... + n L + ... or 0 = ZmB where V A , a,vg are integral stoichiometric numbers. VB is negative for reactants, positive for products. The rate of reaction is then defined by
+
+
+
-
-
Vol. 82
where [B] denotes the concentrations of any of the substances, either reactant or product. (b) If experimentally y a [QIWI' then the reaction is described as of order q with re ect to Q and of order r with respect to R. Elementory processes should be labeled in such a manner that reverse processes are immediately recognizable, for example, either 2 and -2, or 3+5 and 5+3. (d) Elemenfury processes are called unimolecular, bimolecular, trimolecular according to the number of molecules involved. (e) The collision number defined as the number of collisions per unit time and per unit volume is a rate and should be denoted by 2. The collision number divided by the product of the two relevant concentrations (or by the square of the relevant concentration) is a second-order rate constant and should be denoted by z. Nom BY THE CHAIR", OCTOBER, 1958.--Some of these
T)
recommendations,particularly (b), may be subject to later revision.
