SI Stands for Sfudenf lmprovemenf
I
One would have thought that the recently developed International Svstem of Units (SI units)'.2 would have been welcomed with open arms by chemical educators. For the first time, the chemists' own unit, the mole, has been recognized not only as a valid unit for describing the properties of matter, but as one of onlv seven hase units from which all others should be derived Instead, the response bas been less than lukewarm. Based on our informal (and admittedly small) survey of chemical educators, the general impression seems to be that SI units may be fine for more advanced classes such as Physical Chemistry, but they are much too esoteric for General Chemistry. Who wants to measure pressures in kilopascals, volumes in cuhic decimeters, and energy in joules? In our minion. such an attitude is douhlv unfortunate. In the first piace, it puts the U.S. out of step with the rest of the scientific world. where SI units are now widelv adooted. In the second place, i t fails to appreciate that ~ i u n i t sprovide a simnle and uneauivocal entrv into elementarv chemical arithmetic, far superior to the potpourri of ambiguities which may be found by an enterprising student in the first 50 pages of almost any introductory chemistry text. The seven base units of the SI are: the meter to measure length; the kilogram for mass; the second for time; the ampere for electric current: the keluin for thermodynamic temperature; the candela for luminous intensity; and the mole for amount of substance. In the interest of improving communication among scientists it is suggested that measured quantities be reported in these hase units, other units derived from them (J = kg m2 s-2), or decimal multiples and fractions of base or derived units. (The latter are to be indicated by prefixes such a s k (kilo, 103). p (pico, 10-12), T (tera, 1012),etc.) Adoption of the SI in all sciences would therefore free students from the necessity of learning one set of units in physics and another in chemistry. Use of the SI is also advantageous because relationships among different quantities are easier to establish when all units derive from a limited hase. Consider. for examole, the product, PV, for an ideal gas. When SI unigof conven:ent size (kilopascal and cuhic decimeter) are used, we find that ~~
~
1kPaXldm~lX103Nm-2X10-3m3=1Nm=1J
Thus it is quite simple to show that PV has units corresoondine" to enerev. Althowh this does not guarantee that the constancy of PV a t agiven temperature and amount of gas is due to the constancv of some energv, it is suggestive. When the relationship between PV and kinetic energy of the gas molecules is derived rigorously, students will certainly find it more plausible than if atmospheres and liters had been used. From a strictly chemical point of view, of course, a far more important advantage of the SI is the recognition it gives to the mole. It is recommended that we use this unit exclusively and abandon the plethora of older alternatives such as gram-atom, gmm-molecule,gram-mole,gram atomic weight, P a m formula weight, equivalent, and qam equivalent weight, together with the auaint svmhols 1e.e.. GF:\V. GA\Y, that often nccomDanv them. The really original aspect of the International system, though, is its suggestion of a specific term, the amount of substance, for describing that quantity which the mole measures. The IUPAC committee on symbols and terminology has further recommended use of the symbol n to indicate the amount of s u b ~ t a n c e . ~ . ~
--
provocative opinion I'erhape berause of its novelty the amount of suhstance has sometimes been misunderstood. Its use and significance are best explained by an example. Suppose we have a sample of oxygen gas which contains 3.011 X loz3molecules of 0 2 . We can refer to the "amount of substance" in this sample as 0.5000 moles of 02, in exactly the same way as we can refer to its "mass" as 16.00 erams and its "volume" as 11.21 cubic deci~ can also describe the amount of submeters (at S T P We stance in the form of a very succinct equation nol = 0.5000 mol in the same way that the mass, temperature, pressure, and volume of the sample are given by Toz= 273.16 K, Po, = 101.3 kPa, mo* = 16.00 g, and Vo, = 11.20 dm5 In our experience, the use of the symbol n and the term amount of substance bring a new preciseness to the way in which the subject matter of chemical arithmetic can he described and taught. As matters now stand, most students (and, it seems, many professors) confuse the amount of substance and the mass. A major contributor to this confusion is the widespread habit of writing 1 mole 0% = 32.00 g 0% This "equation" represents an equivalence, hut not an equality in the sense of 1.129 oz 0 2 = 32.00 g 0 2 Almost all students we know assume that the equals signs in both exoressions mean the same thine. Thev naturallv conclude that just as ounces and grams are alteinative units for measuring mass, the mole, too, must be a unit of mass. Another major source of confusion is the use of the term "number of moles" rather than "amount of substance." This older term is clearly ambiguous, it being uncertain whether a pure number or a number multiplied by moles is intended. A survey of currently popular general chemistry texts confirms this ambiguity. While some authors write expressions such as
no. of moles HIS = 0.331 others write them in the form no. of moles H2S = 0.331 moles A third erouo. ~ e r h a othe s maioritv. e m ~ l o vboth conventions. During h e 612 weei of classes mi& of i s make valiant efforts to convince students that checkine for cancellation of units is quite useful in achieving correct solutions to problems. Indiscriminate confusion of the above ex~ressionsleads students to think thatthose efforts were just bisy work to tide us over
I Page, C. H., and Vigoureux, P. (Editors),"The International System of Units (SI)," NBS Special Publication 330, US. Government Printing Office, Washington, D.C., 197%Paul, M. A., J. Chem. Doc.,
11,3 (1971).
MeGIashan, M. L., "Physico-Chemical Quantities and Units," Royal Institute of Chemistry, Monographs for Teachers No. 15, London, 1971. Wanual of Symbols and Terminology for Physicochemical Quantities and Units, Pure Appl. Chem., 21,1(1970). Volume 53. Number 11, November 1976 / 681
until we had shaken off summer vacation and were ready to get down to serious business. Ambiguities like those in the above two paragraphs can be avoided by means of the quantity calculus, a convention for writing symbols and equations described nearly 20 years ago . ~ the SZ in this Journal by the late E. A. G ~ g g e n h e i mBoth units and the IUPAC symbols and terminology have been designed with the quantity calculus in mind, and they lose much of their precision without it. According to this convention, a symbol is used to indicate a quantity (number X units) rather than just the number of units involved, while the equals sign is used only to conned quantities having the same dimensions. Equations like no9= 0.013 moi = 13 rnrnol (ail amounts of 0 2 ) mo, = 32.00 g = 1.129 oz (all masses) P V = nRT = 2.27 kJ = 22.4 liter atm (all energies) conform to this convention, but the following do not 1 ma1 0 2 = 32.00 g 0% (an amount of Oz is not a mass) 1 m o l 0 ~= 22.41 liters (an amount of Oz is not a volume)
d =
c
.rn"
(While g and em3 indicate units, d indicates a quantity,
the density) = no. of moles per liter (The concentration of a solution is a quantity independent of units and not a number)
The great advantage of using the quantity calculus is that it is entirely consistent with algebraic manipulations. If we adhere to it wecan add, subtract, multiply, and divideequations without fear of ambiguity or error. This is not necessarily the case with the mish-mash of conventions we currently teach to freshmen. Suppose, for example, we have one mole of 0 2 gas at S T P with a volume of 22.41 liters and wish to evaluate its density, d. The desired quantity may obviously he obtained as follows 32.00 g d = 22.41 liters However if we also insist on writing "equations" like 1molOz = 32.00 g = 22.4 liters 4
Guggenheirn, E. A., J. CHEM. EDUC., 35,606 (1958).
682 /
Journal of Chemical Education
we can scarcely be surprised if some of our students are able to deduce that the density of oxygen is given by the equation d=l The truth is. that unless we use the auantitv calculus. we can never really be quite certain that any dimen&onal an&& wiU work. If the two sides of an eauation do not have the same dimensions to start with there is little point in cancelling out anv units. Although we have no statistical proof, it is our conviction that ambiguities of the type we have just described are an important source of student confusion regarding chemical calculations. Because the conventions we use are not selfconsistent, each new calculation has slightly different rules. Sometimes a mole can he equated with 22.41 liters and sometimes not. We know the rules (indeed we have prohably iurgotren their explicit statement and use them automaticallv). " .but the student does not. Is it his fault that some of them appear to be completely arbitrary? How much simpler it would be if the single, self-consistent rulehook provided by SI and quantity calculus were used throughout all of the scientific curriculum. We cannot pretend that no difficulties face the instructor who a d o ~ t SI s units. Current introductorv chemistrv textbooks pay little more than lip service to &e S I , usually by means of marginal notes or seldom-read appendices. Furthermore, there is bound to be an "induction period" during which any instructor enterprising enough to use SI units in the classroom will make mistakes in front of his students. In our exp~rienrethis is salutnry for students and profeswr alike. A third difficulty is that of dealing with rhe chemical literalure, the majority of which is in the traditional metric units. This is a which the passage of time and faster (not slower) adoption of SI units will solve. We no longer call KC1 "muriate of potash," and it doesn't bother most of us any more! One difficulty we have not encountered-acceptance of the SI by students! They eat up those kilopascals, the rascals.
William G. Davies, John W. Moore, and Ronald W. Collins Eastern Michigan University Ypsilanti. 48197
