Truman P. Kohman Carnegie-Mellon Unlversity, Pittsburgh, PA 15213 Several recent communications ( 1 3 ) have addressed the question, "What do we measure in moles?", or more technically, "What is the quantity of which the mole is the unit?" Related to this is the auestion. "What are the auantities of which molar and n~,rmalare units?" 'I'he traditional answer UI the first auestion has been number of mols ( 4 , 5 ) , although the spefiing change in English from mol to mole is now widely accepted. This, however, is subject to the same objections as number of g r a m for mass, number of liters for volume, etc.: we are dealing.with a quantity that is not evaluated by counting. In 1967 the International Committee on Weights and Measures recommended the use of amount of substance for this concept (6).Gorin (I) has raised valid objections to this usage: unqualified amount can refer indiscriminately to mass, volume, or number of entities. However, Gorin's own ~ r o ~ o s achemical l. amount. is also vaeue. as will he shown. - The IUPAC Manual o f ' ~ y m h o l sa n d Terminology for Physical Quantities and Units (7) defines the fundamental quantity of which the mole is one unit in a general way, in terms of the number of discrete particles (molecules, atoms, ions, etc), independently of any particular unit. Its value might be expressed in any unit implying number . . .aparticular . of particlesisuch as particle itself, dozen, or mole (the Avomdr0 number of particles). Tykodi (2)makes the point that, since this auantitv is defined with reference to the oarticulate nature of matter, its name ought to have particle as a root. An appropriate name for this general quantity might then he particulate amount. For the special case of particulate amount in which the unit is the mole, the qualifier molar can he used. An appropriate name of the quantity is then molar amount. This is certainly more self-descriptive than amount of substance and chemical amount. There is a t least one other similar restricted quantity which is also en amount of substance and a chemical amount. When the unit of amount is the equivalent, the qualifier equiva1er.t can he used, the resulting special kind of ~
~
~
~~
~~
~
.~ ~~
246
Journal of Crsmlcal Education
~
~
~~
particulate amount becoming equivalent amount. Of course, in cases where the equiualence (= equivalent amountlmolar amount) is not equal to 1 equivalent/mole, this requires the formalism of considering the "particle" in question (an Avogadro number of which comprises an equivalent) as a fraction of an atom, molecule, or ion: for Ba2+as a precipitant, '/z Ba2+;for HC104 as an oxidant with C1- as the reduction product, 1's HC104; etc. With respect to the other question in the introduction, the general quantity is concentration (= amount/volume). When the amount is expressed in terms of its particles, this becomes particulate concentration. In the special case where the amount is expressed in mole(s), this becomes molar concentration. Likewise, when the amount is expressed in equivalent(s), the concentration becomes e q i v a lent concentration. In the even more restricted cases where the volume is expressed in liter(s), these become respectively molarity (unit molelliter = molar) and normality (unit equiualentlliter = normal). T o summarize, amount includes particulate amount, which includes molar amount and equivalent amount; and concentration includesparticulate concentration, which includes molar concentration (which includes molaritv) ". and equiualent concentration (which includes normality). Thus the questions in the introduction can be answered naturallv witheself-defining names based on simpler or more gene12 concepts or with already accepted names suitably defined. Literature Cited 1. Gorin, G. J. Chern. Educ 1982,59,508. 2. Tyk0di.R. J. J. Chern.Educ. 1983,60,782. 3. G& I. J. c h p m .E ~ U C 1983,60, . 782. 4. Noyes, A . A,; Sherrill, M. S. Chemical Plincipler, 1sted.; Mscmillan: New Yark, 1922: 2nd sd., 1938. N.:Randall. M. Thermodynamics and the Free Emorgy of Chernicol Sub. Mfficaw-Hill:New York, 1923. 6. The I n t o r ~ t i o n o lSystem of Units ( S O , Nat. Bur. Stand. Spe. Publ. 330: U. S. Government Printing Onice: Washington, DC, 1981 ad.; pp 4-5, 34-35. See for chmnology. 7. IUPAC, Manual of Symbola and Terminology for Phyaieochemieal Quantities end Unih, Pure Appl Chem. 1979.51.1. (Revision of 1969 and 1973 versions.) 5. Lewis, G.
stonres;
