Commentary Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX
pubs.acs.org/jchemeduc
What Chemistry Teachers Should Know about the Revised ̀ e International) International System of Units (System Carmen J. Giunta*
J. Chem. Educ. Downloaded from pubs.acs.org by 91.243.93.226 on 01/31/19. For personal use only.
Department of Chemistry, Le Moyne College, Syracuse, New York 13214, United States ABSTRACT: In November 2018, a revision of the International System of Units (Système International, SI) was approved at the 26th meeting of the General Conference on Weights and Measures (CGPM). What are the implications of the revision of all seven definitions of SI base units for the teaching of chemistry? (1) No names of base units or their corresponding physical quantities have changed. For the precision typically employed in educational settings (say six or fewer significant figures), no values of base units have changed either. (2) The mole is officially defined as a definite number (6.02214076 × 1023) of elementary entities. (3) The kilogram is defined by setting a fixed value for the Planck constant. (4) The revision defines units indirectly by assigning fixed values to key physical constants (explicit-constant definitions rather than explicit-unit definitions). (5) Some quantities previously regarded as exact now have small uncertainties and vice versa. KEYWORDS: First-Year Undergraduate/General, High School/Introductory Chemistry, History/Philosophy, Misconceptions/Discrepant Events, Nomenclature/Units/Symbols, Mathematics/Symbolic Mathematics
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INTRODUCTION
meter (m), and candela (cd) have also been revised, recast in explicit-constant forms. The new definitions of these three are exactly equivalent to their most recent previous definitions, which had already been formulated in terms of previously fixed constants: the hyperfine transition frequency of 133Cs (ΔνCs), the speed of light in a vacuum (c), and the luminous efficacy3 of monochromatic 540 THz radiation (Kcd), respectively.4 The revision has been in the works for more than a decade,5,6 prompted mainly by the problem and opportunity provided by the then-current definition of the kilogram, the SI base unit of mass. The kilogram was the only base unit still defined by an artifact, a platinum−iridium ingot known as the International Prototype Kilogram (IPK) maintained at the International Bureau of Weights and Measures (Bureau International de Poids et Mesures, BIPM). It had long been considered desirable to use invariant standards as the basis for units,7 and despite stringently careful storage conditions, the IPK was not unchangeable. In fact, the masses of prototype kilograms maintained at various national metrology laboratories that had been calibrated against the IPK were observed to have masses slightly but detectably different from it,8,9 as can be seen in Figure 2. Meanwhile, technical advances in a variety of fields reduced the uncertainties in fundamental constants, such as h and NA, to a point where the kilogram could be defined more precisely in terms of one of those constants. The metrology community saw an opportunity to redefine three other base units, the mole, kelvin, and ampere, at the same time, thereby constructing a system in which all seven base units were defined in terms of constants of nature, including several fundamental constants.
In November 2018, the 26th meeting of the General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM) approved a revision to the International System of Units (Système International, SI) to go into effect May 20, 2019.1 This revision, sometimes referred to as the “New SI”,2 formulates explicit-constant definitions of all seven SI base units and newly fixes numerical values for four important physical constants. The four newly fixed constants, the Planck constant (h), Avogadro constant (NA), elementary charge (e), and Boltzmann constant (k), are used as the basis for the definitions of four base units, the kilogram (kg), mole (mol), ampere (A), and kelvin (K), respectively (Figure 1). The definitions of the other three base units, the second (s),
Received: September 16, 2018 Revised: December 6, 2018
Figure 1. Logo for the revised International System (SI) of units. Courtesy of the Bureau International de Poids et Mesures (BIPM). © XXXX American Chemical Society and Division of Chemical Education, Inc.
A
DOI: 10.1021/acs.jchemed.8b00707 J. Chem. Educ. XXXX, XXX, XXX−XXX
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Commentary
Figure 2. Change in mass of various official copies of the IPK as a function of time since 1889 (when several of the copies were first calibrated). Reprinted from ref 9 under the terms of a Creative Commons Attribution 3.0 Unported license (https://creativecommons.org/licenses/by/3.0/).
chemistry students understand the mole10 than did the former definition, which specified the mole as the amount of substance that had as many elementary entities as 0.012 kg of 12C.11 The new definition also recognizes the Avogadro number (better known to chemists as Avogadro’s number) as well as the Avogadro constant, a term not often used by chemists.12 The International Union of Pure and Applied Chemistry (IUPAC) is primarily responsible for the revised definition.10,13 It consulted its member organizations around the world and used the responses gathered to publish a recommendation on the redefinition of the mole. When the definitions were being finalized ahead of the 2018 meeting of CGPM, IUPAC’s representative argued forcefully against alternatives favored by some in the metrology community.14 The physical quantity for which the mole is the SI base unit continues to be called “amount of substance”, at least in English. The fact that this name is problematic for chemists has been much discussed in the pages of this journal,15 and the desirability of a different name has been recognized by IUPAC and other international bodies as well.10 Next to the mole, the kilogram is the SI base unit most relevant to chemistry education, especially at the introductory stage, because the balance is among the earliest and most frequently used instruments in the teaching laboratory. (The kilogram is the SI base unit of mass, but the gram is the unit more frequently encountered in the lab.) The kilogram is now defined by setting a fixed value for the Planck constant:4 The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10−34 when expressed in the unit J s, which is equal to kg m2 s−1... the meter and second having already been defined. The revision has thus converted the kilogram from one of the conceptually simplest SI units to grasp into one of the most complex. To be sure, the old artifact had serious drawbacks for precise work, and the primary considerations of the redefinition were rightfully precision rather than pedagogical clarity. Still, the definition of the kilogram by the IPK had the pedagogical advantage of embodying the notion of measurement as a comparison to a standard very directly.
This paper focuses on those aspects of the revision that affect quantities and concepts taught in chemistry courses at the high-school and undergraduate level.
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WHAT HAS NOT CHANGED Given that the revision has been more than a decade in the making and has involved several international research efforts and scientific bodies, it is worth noting what has not changed. No names of base units or their corresponding physical quantities have changed. To the precision typically employed in educational settings (say six or fewer significant digits), no values of base units or of the constants connected to them have changed either, nor have the practical procedures for making measurements in the teaching laboratory. Furthermore, notwithstanding some of the philosophical shifts to be discussed below, the idea of measurement as comparison to a standard remains unchanged.
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UNITS FOR CHEMISTRY All four of the units defined in terms of newly fixed constants are relevant to chemistry, namely, the mole, the kilogram, the kelvin, and the ampere; however, most of the attention chemists have paid to the revision was focused on the mole and the kilogram. The mole in particular is the SI base unit that came specifically out of chemistry and is used primarily by chemists. The revised mole is officially defined as a specified number of elementary entities. The new definition reads4 The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in mol−1, and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles. The revised definition is a much closer match than the old definition to the way the mole has been described in many textbooks for some time. That is, the new definition better matches the way that many chemists, chemistry teachers, and B
DOI: 10.1021/acs.jchemed.8b00707 J. Chem. Educ. XXXX, XXX, XXX−XXX
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PHILOSOPHY: EXPLICIT CONSTANTS VERSUS EXPLICIT UNITS In the classroom or laboratory, ideas of units are readily connected to ideas about the nature of measurement and uncertainty. The concept of measurement as a comparison to a standard is easily illustrated for length (comparing the distance between two marks to a standard measuring stick) and mass (using a two-pan balance with a sample mass and standard masses). Standards are easily related to units; indeed, standards often come in a size equivalent to one unit (gram, foot, meter, etc.) or graduated in such units (milliliter, centimeter, etc.). None of this conceptual apparatus changes with the revised SI. What has changed philosophically, though, is the relationship of the standard to the definition of the unit. The revised SI defines its base units indirectly by specifying fixed values, not for the units but for related constants of nature. That is, the revised SI is an explicit-constant system of units. The former SI was an explicit-unit system, in which units were defined directly. Take for example the definitions of mass and length in the older and revised systems. In the old system, as noted above, the unit of mass was literally a standard, a particular platinum− iridium ingot known as the IPK. It is conceptually simple to imagine making secondary standards equal in mass to the IPK; subdividing those standards into equal pieces to make secondary standards of fractions of a kilogram; and using a set of such secondary standards to measure the mass of an unknown sample. Of course this conceptual simplicity comes at a cost already mentioned as well: the unit was defined in terms of a changeable artifact rather than an invariant of nature. Now look at the definition of the meter in the old system: “the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second”.11 Conceptually this is also simple, if technically nontrivial to realize. In a thought experiment, at least, one can mark the distance reached by a beam of light in the (very brief) specified time interval. One can then use the spatial interval thus constructed to make secondary standard meter sticks or strings, to make standards for fractions or multiples of a meter, and to use those standards to measure arbitrary lengths. The value of the meter has not changed at all in the revision, but the definition has changed: “It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s−1.”4 Logically, this definition is exactly equivalent to the old one. Philosophically, it is different in that it explicitly fixes the value of the constant c, whereas the old definition explicitly defined the value of the unit meter. Pedagogically, the new definition is a bit more complex than the old one: to solve for the value of the unit requires a (trivial) algebraic operation and some knowledge of the relationship among speed, distance, and time. The situation is similar, but even more complex in the case of the new definition of the kilogram. The value of the unit has not changed within the former uncertainty in the Planck constant. The definition has changed philosophically from a straightforward specification of the unit to an indirect definition in terms of an explicitly valued constant, h. Furthermore, the complexity of the physics that connects the kilogram to h is far beyond the scope of introductory chemistry courses in high school or university.
The new definition can be made explicit formally by using algebra to solve for 1 kg:16 1 kg =
Commentary
h m −2 s 6.62607015 × 10−34
This equation is more direct than the official explicit-constant version above but still rather inadequate pedagogically for several reasons. For one, it is very abstract and therefore unlikely to make any sense to students who learn primarily at the concrete operational stage, to invoke Piaget’s stages of intellectual development. Even for students at the formal operational stage, this equation is poor pedagogy, for it defines what ought to be a familiar quantity, the kilogram, in terms of a less familiar one, the Planck constant. Still the equation is much simpler than the physics needed to connect the Planck constant to mass in any conceptual way. The revised definition of the kilogram was opposed by some chemists partly for pedagogical reasons and partly because a definition in terms of microscopic invariants such as the mass of 12C or 28Si appeared to be a more straightforward and logical alternative.17 Such arguments did not persuade the metrology community, however. Even within the chemistry community they were not universally accepted: they were considered but not adopted by the IUPAC task group.10 Temperature is another physical quantity relevant to chemistry and chemistry education. The revised SI4 defines the kelvin, the unit of thermodynamic temperature, by fixing the value of the Boltzmann constant to be 1.380 649 × 10−23 J K−1. Expressing the joule in terms of base units meters, kilograms, and seconds, all previously defined, the kelvin can be explicitly defined formally, much as the kilogram above.16 The physics connecting the kelvin to the Boltzmann constant is not as complex, in my opinion, as that connecting the kilogram to the Planck constant; however, it is still in the realm of physical chemistry rather than general or high-school chemistry. In an introductory chemistry course, though, the instructor might connect temperature to gas laws and the gas constant. Besides being part of the content of introductory chemistry, a link to gas laws also recapitulates some of the historical path to the concept of absolute temperature. The previous SI definition of the kelvin was in terms of a fraction of the thermodynamic temperature of the triple point of water.11 The other SI base unit whose definition was revised is the ampere, A, the unit of electric current. The closely related quantity electrical charge appears more frequently in elementary chemistry than does current, so the revision affects the definition of the derived unit, the coulomb, through the base unit, the ampere. The revision4 defines the ampere by fixing the value of the elementary charge, e, to be 1.602 176 634 × 10−19 when expressed in the unit coulomb, C, which is equal to amperes times seconds (A s). The new definition, then, relates the unit of charge very directly to the charges of greatest relevance to chemists, namely, those of electrons, protons, and ions (integral multiples of e). Conceptually, the SI unit of charge is much simpler under the revision than before, when it was defined via a specified magnetic force exerted across a vacuum by ideal conductors carrying a standard current.11 C
DOI: 10.1021/acs.jchemed.8b00707 J. Chem. Educ. XXXX, XXX, XXX−XXX
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A shift of perspective is required to treat the newly fixed constants as fixed. For years, increasingly precise and sophisticated experiments have been made to determine the values of these constants. The best estimates of these and other constants were reported in peer-reviewed journals, expressed in terms of SI units as then defined including appropriate ranges of uncertainty, often in parts per 108 or better. The Committee on Data of the International Council for Science (CODATA)18 would periodically review measurements of constants and issue recommendations of their best estimates and uncertainties. The last such report before the revision of the SI19 was used to determine the values at which the newly fixed constants were fixed. With the revision of the SI, the best experimental estimates of the newly fixed constants become the exact values of those constants, values that define (indirectly) the units in which the constants are expressed. Now that the Avogadro constant is fixed, along with the proton charge and Boltzmann constant, so too are the molar analogues of the latter, namely, the Faraday constant and the molar gas constant:
The explicit-constant formulation of the SI is philosophically elegant. The revised system fixes values of some of the most fundamental constants in physics: the speed of light (c, previously fixed), the Planck constant (h), the proton charge (e), and the Boltzmann constant (k), and by fixing seven physical constants, the values of the base units of the SI are implied as corollaries. The elegance comes at a cost in transparency, though, and likely a cost in understanding for students. The revised SI remains an international system of units, but a system whose units are defined not explicitly but indirectly. Four points are worth making with respect to the observation that the definitions in the revised SI are more complex and opaque than those of the former system. First, pedagogical transparency was not a primary consideration in the revision of the SI: as official definitions, they are (rightfully) more concerned with precision than with pedagogy. Second, the indirectness of the definitions is independent of the fact that the revised SI is based entirely on true invariants of nature, as the case of the meter shows. The meter was previously defined in terms of the speed of light; however, the old definition explicitly defined the unit rather than the constant. Third the revised definition of the mole is an exception in that it is clearer than the old definition, and it includes explicit definitions of both the unit and its corresponding constant, NA. (That prompted grumbling from some metrologists for spoiling the elegance of the otherwise exclusively explicit-constant system.)14 Finally, ordinary laboratory procedures are unchanged: even though the kilogram, for example, is defined by the Planck constant, macroscopic mass measurements still involve balances calibrated to standards traceable to the defined unit; even though the kelvin is defined by the Boltzmann constant, laboratory temperature measurements continue to be made with tubes containing a liquid whose thermal expansion is well characterized or devices made from materials with wellcharacterized thermoelectric properties. Thus, for all practical purposes, the kilogram (or gram) in the teaching lab can be operationally defined by secondary standards or instruments traceably calibrated to the officially defined kilogram.
F = eNA
and
R = kNA
The shift of perspective is not entirely in one direction, though. Some quantities that were exact under the previous SI now have (small) experimental uncertainties associated with them. For chemists, the most important of these is the molarmass constant, Mu, a constant of which many chemistry students and probably many practicing chemists are unaware.20 Under the old SI, the numerical value of a molar mass in grams per mole was exactly equal to the numerical value of the corresponding atomic or molecular mass in unified atomic mass units. This relationship was exact because 12C was used to define both the SI unit the mole and the (non-SI) unified atomic mass unit, u (also known as mu or the dalton, Da). Now the molar mass of 12C is an experimental number, the rest mass of exactly 6.02214076 × 1023 atoms of 12C, whereas the atomic mass of 12C is still exactly 12 Da. The ratio10 of the molar mass of 12C in grams per mole to the atomic mass of 12C in daltons is very close to 1 (to within about 5 parts in 1010) but not exactly 1. (This high level of precision is not determined using a balance but rather a mass spectrometer.)
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FINE PRINT: WHAT IS EXACT AND WHAT IS EXPERIMENTAL The revised SI newly fixes the values of four constants, namely, h, NA, e, and k, and retains previously fixed values for three more, c, ΔνCs, and Kcd. “Fixing” means specifying values exactly and permanently. That is to say the numerical values of these constants, expressed in the specified units, are exact quantities with no uncertainty; they are no longer experimental quantities. Treating NA, for example, as an exact quantity rather than an experimental one is a philosophical change, albeit one that has no practical effect in calculations involving numbers that have typical experimental uncertainties. In usual chemistry calculations, the uncertainty of the data (masses, volumes, concentrations, etc.) is much greater than that of the constants involved in the calculation. Put another way, when NA was known to eight significant figures, then NA was not the limiting factor in the precision of a computed quantity based on data known to three or even six significant figures, and now that NA is an exact number, it still does not limit the precision of such calculations.
CONCLUSIONS The revision of the SI recently approved by the CGPM causes no changes in the names of units or physical quantities used in the teaching of chemistry, no changes in the values of units or related constants to within the precision typically relevant for high-school or undergraduate education, and no changes in practical procedures of measurement in the teaching laboratory. The revision provides a definition of the mole closer to the understanding of many chemists and to textbook language than the previous definition. The base unit ampere (and by implication the derived unit coulomb) also has a new definition that is conceptually more direct than it used to be. For the other base units, the revision presents both challenges and opportunities for the teaching of chemistry. Among the challenges are the definitions themselves, definitions that are more indirect and abstract and therefore more challenging to teach and to learn, particularly at the introductory level. Among the opportunities is the act of revision itself, an effort deemed worth a large investment in time and effort by scientists the world over: the act of revision provides an D
DOI: 10.1021/acs.jchemed.8b00707 J. Chem. Educ. XXXX, XXX, XXX−XXX
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Fundamental Chemical Quantities and Their Impact on Chemical Communities (IUPAC Technical Report). Pure Appl. Chem. 2017, 89 (7), 951−981 and references therein. This extensive and informative review article (over 100 references) is available for free online DOI: 10.1515/pac-2016-0808. (11) BIPM. The International System of Units (SI), 8th ed.; BIPM, 2006, revised 2014. https://www.bipm.org/utils/common/pdf/si_ brochure_8_en.pdf (accessed July 28, 2018). (12) Giunta, C. J. The Mole and Amount of Substance in Chemistry and Education: Beyond Official Definitions. J. Chem. Educ. 2015, 92, 1593−1597. (13) In particular, the authors of ref 10 constituted the members of an IUPAC task group who proposed to consult the international chemical community as well as the chemical literature in order to formulate recommendations on the revision of the SI and of the mole in particular. A description of the project and progress reports can be found at IUPAC. Project Details: a Critical Review of the Proposed Definitions of Fundamental Chemical Quantities and Their Impact on Chemical Communities. https://iupac.org/projects/project-details/ ?project_nr=2013-048-1-100 (accessed Dec 4, 2018). (14) Consultative Committee for Units (CCU). Report of the 23rd meeting (5−6 September 2017) to the International Committee for Weights and Measures; BIPM, 2017. https://www.bipm.org/utils/ common/pdf/CC/CCU/CCU23.pdf (accessed July 28, 2018). (15) See, for example, Giunta, C. J. What’s in a Name? Amount of Substance, Chemical Amount, and Stoichiometric Amount. J. Chem. Educ. 2016, 93, 583−586 and references therein . (16) It is worth noting, particularly when explicit-constant vs explicit-unit definitions are discussed, that the SI brochure published by BIPM (ref 4) includes explicit-unit equations like this as part of the explanations of the definitions. (17) See, for example, Karol, P. J. Weighing the Kilogram. Am. Sci. 2014, 102, 426−429. (18) CODATA: The Committee on Data of the International Council for Science. http://www.codata.org (accessed July 29, 2018). (19) Mohr, P. J.; Newell, D. B.; Taylor, B. N.; Tiesinga, E. Data and Analysis for the CODATA 2017 Special Fundamental Constants Adjustment. Metrologia 2018, 55, 125−146. (20) Taylor, B. N. Molar Mass and Related Quantities in the New SI. Metrologia 2009, 46, L16−L19.
occasion to delve into the nature of units and experimental uncertainty.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Carmen J. Giunta: 0000-0002-2414-6544 Notes
The author declares no competing financial interest.
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ACKNOWLEDGMENTS I wish to thank the ACS Committee on Nomenclature, Terminology, and Symbols for the opportunity to explore the implications of the revised SI for chemistry education at its symposium at the 248th National Meeting (San Francisco, CA, 2014) and at committee meetings over recent years. Several committee members provided insightful comments that improved this commentary.
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REFERENCES
(1) International Bureau of Weights and Measures (Bureau International de Poids et Mesures, BIPM). Resolutions adopted/ Résolutions adoptées 26e CGPM Versailles 13−16 novembre 2018; BIPM, 2018. https://www.bipm.org/utils/common/pdf/CGPM2018/26th-CGPM-Resolutions.pdf (accessed Dec 4, 2018). (2) The phrase “New SI” was commonly applied to the projected revision over much of the past decade, both within the metrology community and in reports in scientific periodicals. Within the last year or so, however, BIPM has all but discontinued its use of the phrase. (3) Luminous efficacy is a quantity that depends on both the standardized response of the light receptors in human vision and the radiant power of a light source. In particular, it is the ratio of luminous intensity (specifically, response to visible light) to radiated power (i.e., output of electromagnetic radiation over all spectral bands). The candela is defined in terms of monochromatic radiation (540 THz or 555 nm) that produces maximal response by human cone receptors. (4) BIPM. The International System of Units (SI), 9th ed., draft; BIPM, 2018. https://www.bipm.org/utils/en/pdf/si-revisedbrochure/Draft-SI-Brochure-2018.pdf (accessed July 28, 2018). (5) Mills, I. M.; Mohr, P. J.; Quinn, T. J.; Taylor, B. N.; Williams, E. R. Redefinition of the Kilogram: a Decision whose Time has Come. Metrologia 2005, 42, 71−80. (6) Consultative Committee for Units (CCU). Report of the 17th meeting (29 June − 1 July 2005) to the International Committee for Weights and Measures; BIPM, 2005. https://www.bipm.org/utils/ common/pdf/CC/CCU/CCU17.pdf (accessed July 28, 2018). (7) Maxwell, J. C. Address to the Mathematics and Physics Section. In Report of the Fortieth Meeting of the British Association for the Advancement of Science; Murray: London, 1871; pp 1−9. Maxwell states, “If, then, we wish to obtain standards of length, time, and mass which shall be absolutely permanent, we must seek them not in the dimensions, or the motion, or the mass of our planet, but in the wavelength, the period of vibration, and the absolute mass of these imperishable and unalterable and perfectly similar molecules.” (8) Girard, G. The Third Periodic Verification of National Prototypes of the Kilogram (1988−1992). Metrologia 1994, 31, 317−336. (9) Stock, M.; Barat, P.; Davis, R. S.; Picard, A.; Milton, M. J. T. Calibration Campaign against the International Prototype of the Kilogram in Anticipation of the Redefinition of the Kilogram Part I: Comparison of the International Prototype with its Official Copies. Metrologia 2015, 52, 310−316, DOI: 10.1088/0026-1394/52/2/310. (10) Marquardt, R.; Meija, J.; Mester, Z.; Towns, M.; Weir, R.; Davis, R.; Stohner, J. A Critical Review of the Proposed Definitions of E
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