E. A. Guggenheim The university, Reading England
I The I
Mole and Related Quadties
The scale of "atomic weights" based on
0 = 16 was introduced under the influence of Berzelius early in the nineteenth century and has been used ever since by chemists. I n 1929 Giauque and Johnston (1) discovered the isotopes l8Oand "0 of the hitherto only known oxygen nuclide ' 8 0 . From that time physicists have for obvious reasons used the scale 'Q = 16. The chemical scale and the physical scale diier by the factor 1.000275. The difference between the two scales has been a source of increasing inconvenience and indeed irritation to both chemists and physicists. For nearly four years there have been discussions ( 2 ) on the possibility of finding a scale acceptable to both, discussions which a t last have resulted in success. The physicists for technical reasons which need not be elaborated required a scale based on a pure nuclide with mass number a multiple of four. The chemists on the other hand, in order not to have to scrap the extensive tables of molar quantities, were prepared to accept a change only if it was less than 1 part in lo4. These conditions ruled out both existing scales. I n 1957 Olander and Nier independently proposed (2) the scale 12C = 12 and this has now been accepted by both chemists and physicists. The International Union of Chemistry at its meeting of 1959 in Munich decided (3) that it would formally introduce the scale
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Journol o f Chemicol Education
1% = 12 a t its next biennial meeting of 1961 in Montreal provided that meanwhile the scale was formally endorsed by the International Union of Physics. This was done (4) a t the latter Union's meet,ingin September, 1960, in Ottawa. A comparison betu.een the two obsolescent scales and the new unified scale is summarized in the following tahle:
"0
0
'$C
C Ag
Old physical male
Old chemical scale
New unified scale
16 exactly
15.99560 16 exactly 12.00052 12.011 107.880" 107.873b
15.99491 15.9999 12 exactly 12.010 107.875 107.868
..... 12.Kl382 . ... . . ... .
Value given in the 1959 International Table of Atomic Weights. Value obtained from the recent coulometric determination a t the National Bureau of Standards (7) of the electrochemical equivalent of alvcr.
It will be observed that the change for chemists is only 43 parts per million and this is numerically trivial, but this change is a tremendous triumph of reasonableness over confusion. The change also provides an occasion for tidying up nomenclature related to the scale. In particular it is hoped that the term "atomic weieht"
may fall into disuse so that eventually it may become unnecessary to explain to every novice that "atomic weight" does not mean weight of an atom. The following text is an outline of recommendat,ions on terminology and notation already endorsed (4) by the International Union of Physics. Some of these have also been endorsed by the International Union of Chemistry; it seems probable that this body will make similar if not identical recommendations. Most of these recommendations have also been endorsed by the Internat,ional Standards Organization's Technical Committee on Quantities, Units, Symhols, Conversion Factors,'and Conversion Tables.
where m, =
lu = 1.66037 X
g
The mole i s the amount of substance containing the same number of molecules (or atoms or radicals or ions or electrons as the case m a y be) as there are atoms in 18 grams of 12C. Avogadro's constant denot,ed by L or N , describes the number of molecules per amount of substance. Its value on the unified scale is L
=
6.02278 X 10'8 mole-'
L-' = 1.66037 X 10-la mole
Mole:
Chemists' "Amount of Substance"
We have all been taught at an early age that mass and weight are different quantities although at a given place their ratio is constant. During the past score of years the view has been accepted by a rapidly increasing number of physicists and chemists that there is a third quantity different from mass and weight but proportional to both. This quantity was first named (5) "St,offmenge" in German and the English translation is "amount of substance." Admittedly the amount of a pure dry solid substance is usually measured by weighing, but t,here are numerous other ways of measuring amount of substance. The amount of a gas (or beer!) is often determined by a measurement of volume. The amount of a substance in solution is often determined by titration or by colorimetry or by polarography. The amount of a radioactive substance may be determined by a Geiger count,er. The amount of a drug may he determined by its physiological action. This list is not exhaustive. Weight is a measure of gra~it~ational pull and mass determines the redistribution of momentum in a collision. It is clear t,hat amount of substance determinable by any of the mentioned techniques is no more identical with mass or with weight t,han t,hese two quantities are identical with each ot,her. The unit of amount of substance most used and among chemists almost universally used is the mole. We cont,inue with a list of definitions related to the mole and to the new unified scale. A nuclide is an atomic species defined by bot,h atomic number and mass. Two or more nuclides having the same atomic number but different atomic masses are called isotopes. (A single isotope is, like a single tvin, a contradiction in t,erms.) The mass of an ahom of a nuclide, or the average mass of an atom in an element, is for convenience expressed as the rat,io of this mass to one-twelfth of the mass of a neut,ral at,om of I2C. This rat,io is called t,he relative nuclidic mass of the nuclide or the relative atomic mass of t,he element. The mass equal to one-twelfth t,hat of a neut,ral atom of 12Cis denot,ed by muin analogy with m, for the mass of a prot,on, m. for the mass of a neut,ron, and m. for the mass of an electron. Alternatively this same quantity may be regarded as a unit of mass for the new unified scale and it is then denoted by u. We may thus writ.e either for the relative atomic mass of ordinary silver
Faraday's constant, denoted by F, describes the charge of a mole of electrons and is equal to the product of Avogadro's constant L and the elementary charge e. On the unified scale F
=
The gas constant denoted by R is equal to the product of Avogadro's constant L and Boltzmann's constant k. On the unified scale and on the temperature scale prescribed hy the General Conference on Weights and Measures wit,h the triple point of water defmed (6) as 273.16'K: erg OK-' R = L k = (6.02278 X lo2' mole-') (1.38049 X = 8.3144 X 107 erg OK-' mole-' =
8.3144 joules OK-' mole-'
Terminology Still Needed
There remains a t least one unresolved question of terminology. There is a need for a word to denote per amount of suhst,ance analogous to spec@ meaning per mass and density meaning per volume. This need has been st,ressed especially by French-speaking scientists but no proposal has yet been made to fill the gap. The present aut,hor n+th some diffidence suggests the word proper (French "propre," German "eigen") because he knows of no better word. If this suggestion \\.ere adopted we should say that the "proper energy" of a substance was so many joules per mole rather than saying that t,he "molar energy" is so many joules per mole, which is as clumsy as if we spoke of "gram energy" inst,ead of "specific energy." I am grateful to Dr. Stille for expert. advice concerning t,he new values of the general constants. Literature Cited (1) (2) (3) (4) 15) , ,
(6) (7)
or for the mass of an at,om of ordinary silver
Le = (6.02278 x loPSmole-') (1.60209 X lo-'*) coulombs
F..*\-a J o x r s ~ o s H. , L.,Nalure, 123,318, 831 (1929): A , Science, 127, Korr~ax,T., MATTACCH, J., .AXD WAPSTRA, 14.11 IlR.5R). See . also .-.~ ~ - THIS JOURNAL. ,~~ , 36.. 103 119591 and references there cited. "Comptes Rendus, Twentieth Conference of IUPAC," 1959, p. 202. "Report of the Ninth General .4ssemhly of IUPAC. Otr tawa," 1960, to be published. STILLE.U.. "Messen und Rechnen in der Physik," Vieweg, ~ r a k h w e i g 1955, , Section 3.8. "Comptes Rendus des S6ances de la Dixihme Conference Gh6rale des Poids e t Mesures," 1954. SHIELDS,W. R., CRAIG,D. N., A N D DIBELER,V. H., J . Amer. Chem. Soe., 82, 5033 (1960). GIAVQUE.W.
Volume 38, Number 2, Febrvcry 1961
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