P. G. Wright
I
AnA
As one from the Eastern side of the Atlantic hut not as a member of any supposed "magic circle" instrumental in devising and propagating SI, (and as one who would indeed have preferred to see 4a's where Adamson (I) would like to see them), might I present something of a counter-argument to the contentions of Adamson ( I ) and Lamhert (2)against SI? I propose to speak primarily of some of the larger issues involved, and not of such issues as whether the word "mole" shall he spelled with or without an "en-issues which could he decided either way without significantly affecting the main concepts. In the light of the principal issues involved, it seems to me entirely reasonable (even for people who would retain the atm as a unit, and write sec-1 rather than s-') to accept a practice that is fairly close to SI. I would prefer not to accept SI in every detail, hut it seems to me that there are only afew respects in which departure from SI would be desirable. There are several quite distinct issues involved, and (3)it is largely a historical accident that most of them tend a t the moment to he lumped together as if they were a single issue "SI uersus non-SI." For example, in those which I take up below, it would have heen possible to insist on (1).without raising any of the others. Issue (I): Symbolism for Physlcal Quantities
There is one point which Adamson and Lambertdonot say much about in their articles, hut on which some SI manuals (4,5) are very definite. This is that symbols shall normally denote complete physical quantities-that is, that "Let m denote the mass" may mean m = 0.784 kg
(the difference in sign reflecting the physical fact that like charges, in contrast to like masses, repel); and, when written as a corresponding equality, this becomes F = + K - QIQZ 9
where K is some constant of proportionality. SI then writes the constant of proportionality in a form K=- 1
4sfa
which Adamson and numbers of other chemists find obtuse (in contrast to what seem to he the feelings of most physicists and electrical engineers). The issue involved, however, is one of the actual aGehraic form employed fo; a dimensional constant of orooortionalitv. It is not one of conversion factors: . . as (1)ahove implies, no conuersion factor can euer appear in any physical equation written in conformity with SZ. The physical significance of €0, in the context of Coulomb's law, is that it relates to how large electrostatic forces are; just as G ahove relates to how large gravitational forces are. It (and the po for magnetic phenomena) should seem no more mysterious than the fact that there is a definite natural constant co-that light has a certain velocity when propagated in a vacuum. It is not entirely absurd to say that a vacuum has the property co; and, if so, i t equally has such properties as G. There are several alternatives to the S I form (3).The particular one to which Adamson makes the most reference involves a re-definition of charge as a quantity q equal to K'IZQ
There is then an expression for the force
J.=m
but will never mean m = 0.784
The issue of adoption or non-adoption of SZ is not reducible : to a mere adoption or non-adoption of S I units ( 4 , 5 , 6 ) the point involved here is logically independent of whether the gram or the kilogram shall he taken as the basic unit of mass. Issue (2): Coulomb's Law
The prototype of the various inverse square laws is Newton's law of gravitation that the gravitational force between two point masses is an attraction proportional to the product of the two masses and inversely proportional to the square of the distance between them:
-2
-an expression which departs from that for the analogous aravitarional case a roo(l (Ira1 more drastically than the SI . expression does. The use of q instead of Q is not uncommonly associated with a generally slovenly and cavalier attitude to units and dimensions (as reflected, for example, in the frequency with which the use of q is mis-characterized as ause of "c g s units"). That is one respect in which SI is better. As for the specific algebraic form 1/4aro, is this not a context in which there is more reason for chemists to defer to electrical engineers, than there is for electrical engineers to defer to chemists? In terms of Adamson's criterion (4), as applied to electrical engineers, they cannot he expected to restore the 4a's to where he (and indeed I) would prefer the 4a's to he. lssue (3): The Mole as a Unit of Amount of Substance
When written as an equality F = -Gmlmz r2
this expression involves a constant of proportionality G which has apparently not been a source of trouble. I t would appear natural to employ a directly analogous mode of writing any other inverse square law. Coulomb's law asserts that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them:
There is twice as much copper in 480 mg of copper as there is in 240 mg of copper; hut is there twice as much copper in 480 me of conoer as there is silver in 240 me of silver? 'if thisquestion refers toanything 0th; than the mass, then the answer is "No." There is as much coooer in 0.0'714 ITIO~(Q) of copper as there is silver in 0.0714 moiie) of silver, in what is in many ways a much more meaningful sense than that in which there is as much copper in 49.6 mg of copper as there is silver in 49.6 mg of silver. "Amount of substance," in the sense just indicated, is a physical quantity in much the same way that length, mass, and temperature are. Like them, "amount of substance in this
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sense" can be specified in terms of a unit; and the size of this unit is open to he chosen arbitrarily. The mole is one such choice; the kilomole would he a conceivable alternative; and so forth. The status of the mole is entirely different from that of the molecule. The mole is one particular choice out of infinitely many that could conceivably have been made; the molecule, in contrast. is somethine which actuallv exists as such in nature, and cannot be vari;?d arbitrarily by decree. As such, the molecule is not, and never can he, a unit; and, as Adamson indicates, a volume per molecule has the dimensions of (IengthP and an area per molecule has the dimensions of (length)2.The mole, however, is different from this. I t is an arbitrarily chosen unit of amount of substance, inasmuch as a different arbitrary choice would have been possible. There are two equations which might be meant if is written. In one. M denotes the mass of some portion of matter in which there are a certain number of mol&es, and N is this number. The dimensions of the quantities involved are then: length)^ M:(mass) N:none
p:(mass)+' (length)-" In the other eauation. M denotes the mass Der unit amount of substance (';molar mass") and N the number of molecules ner unit amount of substance ("Avoeadro's constant"). The dimensions are then: u:(length)3 M:(mass)+' (amount of substance)-' N:(amount of substance)-' p:(mass)+'(length)P In SI, the two are distinct, and both are consistent. lssue (4): The Demise of the Calorie
Apart from Adamson's point about dislocation involved in re-tabulating data, and so forth, there appear to he three feelings implicit in the reactions of those who would regret the disappearance of the calorie: Is) Pure habit. real physical significance. Of these, (a) is not a sufficient reason for settling the question eithvr way; and (b) is not really warranted, when the two units differ by a n~uncricalfactor uf lws than S.'l'his leave* C I : whirh. onlv I~ ~ , ,inmwcase. it it a u l d he substantiated, w ~ ~ u l d be the most cogent df the three. It is nreciselv in terms of such considerations as (c) that the calori~stands~condemned. The notation of the calorie was natural and appropriate to the notion of caloric, rather than to the notions of energy as we have them today. Moreover. the ioule possesses one characteristic which might be expected to appeal to those who share Lambert's likine for human-sized experience. One newton is not very different from the gravitational force exerted hy the earth on a normal-sized apple, and correspondingly one joule is not very different from the work done when a normal-sized apple is lifted from the ground to a height equal to rather more than half of that of a normal human adult. A
lssue (5) Convenient and lnconvenlent Numerical Magnitudes
I t seems to me that opponents of SI often overstate their case on inconvenience of numerical magnitudes. First, I cannot see that (to take one type of specificexample) i t is grossly more inconvenient to refer to the 0-0 distance in Hz02 as 0.148nm than to refer to it as 1.48 k Neither would it seem grossly inconvenient to refer to a dipole moment as 5.3 gC m, if g were an accepted SI ahhreviation for Secondly, i t seems to me that too much is made of such factors as 10-11. Workers in the field of electronics seem perfectly at home with "47 nanofarad capacitors" a "22 pi664 1 Journal of Chemical Education
cofarad capacitors" (and, for that matter, with the picosecond). Thirdly, concentrations can he expressed in SI with the very same numbers that many opponents of SI would wish to emnlov. The concentration "0.216 molar" can ~erfectlvwell he calied "0.216 kmol(e) m-3" instead of ''0.2i6 mol(e) dm-3" or "0.216 mol(e) I-'.'' Eauallv. . .. a surface tension 72.1 dvne cm-1 is 72.1 &N m-1. Finally, SI does not imply any change in numerical values of such quantities as pK and pH. The numericalvalue of, say, mol(e) -l~e,~(lH+l/ce), --- . . . where c e = 1mol(e) 1-I = 1X m-3, is not altered in any way by changing from one unit of concentration to another; and -log([H+]/ce) is what "-log[H+]" really means. The Influence of Extra-academic Educators and Educational Administrators
Adamson notes the extent to which i t has been schools that have been effective in the propagation of SI. I t is natural that academics would prefer to he in control, instead of educational administrators; hut is it not as well to stick to matters of serious concern when regretting influences which spread from schools? In Britain a t least, the state of preparation of students entering universities gives cause for worries much bigger than any which arise from the fact that they know of no alternative nomenclature to joule and N m-2, propanone and ethanoic acid. For example, some students arrive with no clear understanding of the distinction between concentration and amount of substance. (Those students are numerous and were numerous long before SI1), and their weaknesses in this and many other aspects of stoichiometry pose a very real problem for the teaching of chrmistry in unkersities. Our attention is on the whole more usefull\, directed toward remedsinr thir, rather than toward extollkg any virtues which non-31 no: menclature mav have. Moreover, an intake of students brought up on SI can in some ways he of positive benefit to universities, in the respect that it almost compels us to consider explicitly whether there are any non-SI notations whose retention is genuinely desirable. In contrast to the calorie (whose retention could most charitably he characterized as pointless), the atm is a unit wbose merits and demerits some of us have had to assess verv seriously. The main argument for its partial retention is perhaps that, when the time comes for thermodynamics to he taught, students may cope more adequately (and with less arithmetic) with workine out a AB- from a K, which is equal if it is put to the'm as 0.232 atm to 23.5 k ~ ora 23.5 kN k2 rather than in the more systematic form. T o some extent, however, we have considered this issue seriously because it has been forced upon us. Concluding Remarks
While being prepared in various particular respects to denart from an attitude of rieid conformitv to everv detail of SI. many of us feel that the& no sufficiently cogent reason fa; refusine to acceot at least its eeneral outlines. I t is ~ossihleto retain such measures as the atmosphere and even the Faraday, and to sav N m-2 instead of Pa. while still followine most of the gene& attitude of SI. The s&e has, in effect, n& arrived a t which Adamson's criterion (4) "A new system should not he adopted unless. . . ."has become virtually inapplicable: the abandonment of SI in Western Europe would constitute at least as great an upheaval as would its universal adoption throughout North America. His criteria (1) and (2) remain pertinent enough, hut in terms of those the balance of advantage would appear to lie with the acceptance of at least an
-
1 A fact which in itself casts some doubt on Lamhert's contention that concentrations are understood readily by students taught in terms of the gram and the liter.
Literature Cited (1) Adamson,A. W., J.CHEM.EDUC.66.684 (1976). (2) Lambert. J. L..J. CHEM. EDUC. 55.638 (1918). (3) MeGIashan. M. L..'.Physieo-Chemiealquantitiesand Units," 1st Ed.. 1968.
(4) Ref. (3).P. 29. ( 5 ) Symbols Committee of the Royal Society, "quantities. U n i u and Symbaln." 1971, P.
6. (6) D a v i s , W. G., Moare, J. W., m d Collin%,R. W., J. CHEM. EDUC. 53,681 (1976).
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