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Home , Amount of substance, Avogadro constant, Dalton (unit), Molar mass constant, Mole (unit)

IUPAC

Definition of the mol e

For Peer Review Only Journal: Pure and Applied

Manuscript ID PAC-REC-17-01-06

Manuscript Type: Recommendation

Date Submitted by the Author: 11-Jan-2017

Complete List of Authors: Marquardt, Roberto; Université Louis Pasteur, Laboratoire de Chimie Quantique Theorique Meija, Juris; National Research Council Canada, Science and Standards Mester, Zoltan; National Research Council of Canada, Institute for National Measurement Standards Towns, Marcy; Purdue University System, Department of Chemistry Weir, Ron; Royal Military College of Canada, Dep. of Chemistry & Chemical Engineering Davis, Richard Stohner, Jürgen; ZHAW Zürich Univ. for Applied Sciences, ICBC Institute for Chemistry and Biological Chemistry; ETH-Zürich,

Keywords: the , definition, , Avogadro number

Author-Supplied Keywords:

P.O. 13757, Research Triangle Park, NC (919) 485-8700 Page 1 of 5 IUPAC

Pure Appl. Chem. 201X; aop 1 2 3 Sponsoring bodies: IUPAC Physical and Biophysical Chemistry Division, IUPAC Inorganic Chemistry Division, IUPAC Analyt- 4 ical Chemistry Division, IUPAC Committee on Chemistry Education, and IUPAC Interdivisional Committee on Terminology, 5 Nomenclature and Symbols: see more details on page XXX. 6 IUPAC Provisional Recommendation 7 8 9 Roberto Marquardt, Juris Meija, Zoltán Mester, Marcy Towns, Ron Weir, Richard Davis, 10 and Jürgen Stohner* 11 12 Definition of the mole (IUPAC Provisional 13 14 For Peer Review Only 15 Recommendation 201X) 16 17 18 DOI: 10.1515/pac-201X-XXXX, Received ...; accepted ... 19 Abstract: In 2011 the General Conference on Weights and Measures (CGPM) noted the intention of the 20 21 International Committee of Weights and Measures (CIPM) to revise the entire International System of 22 Units (SI) by linking all seven base units to seven fundamental physical constants. Of particular interest 23 to , new definitions for the and the mole have been proposed. A recent IUPAC Technical 24 Report discussed these new definitions in relation to immediate consequences for the chemical community. 25 This IUPAC Recommendation on the preferred definition of the mole follows from this Technical Report. 26 It supports a definition of the mole based on a specified number of elementary entities in contrast to the 27 present 1971 definition. 28 29 Keywords: SI; the mole; definition; Avogadro number; Avogadro constant 30 31 32 1 Introduction 33 34 The 9th General Conference on Weights and Measures (CGPM) instructed the International Committee 35 for Weights and Measures (CIPM) in 1948 “to make recommendations for a single practical system of units 36 of measurement, suitable for adoption by all countries adhering to the Convention” [1]. In 1954 the 37 10th CGPM adopted a practical system of units of for international use. It contained six 38 base units: the metre, kilogram, , , (later renamed kelvin), and [2]. This 39 international system was named “Système International d’Unités” (engl. International System of units) and 40 41 abbreviated as SI by the 11th CGPM [3]. The seventh , the mole, was added to the SI in 1971 by 42 the 14th CGPM [4]. 43 The International Bureau of Weights and Measures (BIPM) publishes the SI Brochure with the purpose 44 “to define and promote the SI, which has been used around the world as the preferred language of science 45 46 Roberto Marquardt: Laboratoire de Chimie Quantique, Institut de Chimie, Université Louis Pasteur, 1 Rue Blaise , 47 F-67008 Strasbourg France 48 Juris Meija: National Research Council Canada, Measurement Science and Standards, 1200 Montreal Road M-12, Ottawa, 49 ON K1A 0R6 Canada 50 Zoltán Mester: National Research Council Canada, Measurement Science and Standards, 1200 Montreal Road M-12, Ot- 51 tawa, ON K1A 0R6 Canada 52 Marcy Towns: Purdue University, Department of Chemistry, 560 Oval Drive, West Lafayette, Indiana USA 53 Ron Weir: Royal Military College of Canada, Department of Chemistry & Chemical Engineering, P.O. Box 17000, Stn. 54 Forces, Kingston, ON K7K 7B4 Canada 55 Richard Davis: Bureau International des Poids et Mesures, Pavillon de Breteuil F-92312 Sèvres Cedex France 56 *Corresponding Author: Jürgen Stohner: ZHAW Zürich University of Applied Sciences, ICBT Institute for Chemistry & 57 Biotechnology, Einsiedlerstrasse 31, CH 8820 Wädenswil Switzerland , email: [email protected] and Guest scientist at: ETHZ 58 Swiss Federal Institute of Technology, Laboratory for Physical Chemistry, ETH Hönggerberg, Wolfgang-Pauli-Strasse 10, 59 CH-8092 Zürich, Switzerland, email: [email protected] 60 P.O. 13757, Research Triangle Park, NC (919) 485-8700 IUPAC Page 2 of 5

2 Marquardt et al, Definition of the mole 1 2 3 and technology since its adoption in 1948” [5]. The SI is an evolving system which reflects current best 4 measurement practices. Thus, changing the definition of base units of measurement is not an unprecedented 5 nor unusual action. The evolving definition of the metre is an example of this. Early adoption of the metre as 6 the unit of by the French government resulted in its definition as the 1:10 000 000 part of the meridian 7 through Paris between the North Pole and the equator. A century later, the first meeting of the CGPM 8 in 1889 sanctioned a new platinum-iridium prototype metre bar which served as the official international 9 metre until 1960. The desire to adopt an indestructible standard and advances in interferometry led the 10 11th CGPM to further redefine the metre as “the length equal to 1650 763.73 wavelengths in of 11 12 the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton 86 ” 13 in 1960 [6]. With fixing the velocity of light to a constant value, the metre was last redefined by the 14 17th CGPMFor in 1983 Peer as “the length ofReview the path travelled by lightOnly in vacuum during a interval of 15 1/299 792 458 of a second” [7]. 16 The present SI has several important shortcomings (see [8] and references therein). Notably, the base 17 unit kilogram is based on an artifact, a platinum-iridium cylinder (the international prototype kilogram, 18 IPK) manufactured in 1879 and stored at the BIPM. There is an intrinsic uncertainty in the long-term 19 stability of the IPK. In principle, this instability also impacts other SI units that depend on the kilogram, 20 21 among which is the mole. 22 In 1999 the 21st CGPM recommended that “national laboratories continue their efforts to refine exper- 23 iments that link the unit of to fundamental or atomic constants with a view to a future redefinition 24 of the kilogram” [9]. Furthermore, in 2011 the CGPM noted the intention of the International Commit- 25 tee of Weights and Measures (CIPM) to revise the entire SI by linking all seven base units to seven 26 constants [10, 11]. 27 In a recent IUPAC Technical Report [8], a thorough analysis of the discussion on the impact of the 28 proposed new definitions of two key units for chemists was undertaken: the kilogram and the mole. The 29 present recommendation focuses on the unit mole. In Section 2 a brief summary of the discussion is recalled, 30 31 in Section 3 the recommended definition of the mole is formulated, and in Section 4 some additional remarks 32 and explanations are presented. 33 34 35 36 2 Discussion 37 38 Since the proposals for a new definition of the mole were put forward, a major division of opinions among 39 chemists was whether to retain the current definition based on the mass of -12 or to adopt a definition 40 that is based on a fixed value of the Avogadro constant. 41 The amount of chemical substances is traditionally measured by mass or . Since the introduction 42 of relative atomic (also called “atomic weights”) by (see for example [12]), chemists are able 43 to express their observations in a quantity that is proportional to the number of elementary entities. The 44 unit of the SI quantity “” in its present definition still relies on the mass of the 45 46 international prototype kilogram [4]: 47 “1. The mole is the amount of substance of a system which contains as many elementary entities as 48 there are in 0.012 kg of carbon 12; its symbol is “mol”. 49 2. When the mole is used, the elementary entities must be specified and may be atoms, , 50 , , other particles, or specified groups of such particles.” 51 52 Thus, the 1971 definition refers to well-defined number of atoms in a certain fixed mass of carbon-12. 53 With the recent advances in science and measurement practice, our ability to determine the value of the 54 55 Avogadro constant has now reached a level of relative uncertainty that allows a redefinition of the mole 56 in terms of the explicit number of elementary entities. While this conceptual change does not bring any 57 immediate practical benefits to our ability to better realize the mole, it realigns the definition of the mole 58 with the way most chemists understand it [8]. 59 60 P.O. 13757, Research Triangle Park, NC (919) 485-8700 Page 3 of 5 IUPAC

Marquardt et al, Definition of the mole 3 1 2 3 3 The definition 4 5 The amount of substance, symbol n, is a measure of the number of specified elementary entities. An 6 7 elementary entity may be an atom, a , an , an , any other particle or specified group of 8 particles. 9 10 The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 23 11 6.022 140 8Y × 10 elementary entities. This number is called the Avogadro number. 12 13 The effect of the above definition of the mole is that it fixes the value of the Avogadro constant to be 23 −1 14 NA = 6.022 140 8Y ×For10 mol .Peer The symbol Y signifiesReview the yet undecided digitsOnly which will be set by the 15 CODATA Task Group on Fundamental Constants prior to the 26th CGPM in 2018. 16 The amount of B, n(B), is proportional to the number of entities of B, N(B), with 17 −1 18 n(B) = NA N(B) 19 20 The proportionality factor is a universal that is independent of the nature of the substance. 21 Its reciprocal, NA, is the Avogadro constant which is the same for all substances. The stipulated Avogadro 14 22 number, {NA} = 602 214 08Y × 10 , is an integer and will be the numerical value of the fixed Avogadro 23 −1 −1 23 constant, NA = 6.022 140 8Y × 10 mol . The Avogadro constant has the SI unit mol , because the 24 amount of substance n is a base quantity with the SI unit mol and because the number of entities, being 25 a number, is a quantity of dimension one. The amount of B, n(B), is also proportional to the mass of B, 26 m(B), with 27 −1 28 n(B) = M(B) m(B) 29 The proportionality factor is the reciprocal of the , M(B), which is a characteristic constant of 30 the substance B. 31 The 1971 definition of the mole implies that the Avogadro number is the ratio of the to the 32 33 dalton, with the value of the dalton expressed in gram. The historical continuity of the present definition 34 preserves this relation to within an uncertainty negligible for practical purposes. 35 36 37 38 4 Explanatory remarks 39 40 A better understanding of the above definition requires some explanation and guidance. Below are some 41 remarks that might help the reader to gain a better understanding of the above definition. 42 43 1. Although the full name of the quantity is the amount of substance, the word “substance” is a placeholder 44 and should be replaced with the name of the actual substance referred. Thus, for example, one speaks 45 of the amount of , and not the amount of substance of water. 46 2. The name “amount of substance” is not universally liked and this quantity is sometimes also called 47 “chemical amount” [13, 8]. A thorough examination of the potential alternative name for the quantity 48 49 amount of substance, n, has to be performed. 50 3. The 1971 definition of the mole applies only to an ensemble of unbound atoms at rest and at zero 51 kelvin . While this stipulation is often ignored, the new definition of the mole decouples 52 the mole from the kilogram and therefore the accompanying stipulation that the atoms must be in the 53 unbound state is no longer required. Thus, one can say that 0.012 kg of pure carbon-12 in the form of 54 graphite is not exactly 1 mol under either the 1971 definition or the new definition. 55 56 57 The molar mass of any entity B, M(B), may still be obtained from its relative (also called 58 “atomic weight”), A (B), from the equation 59 60 P.O. 13757, Research Triangle Park, NC (919) 485-8700 IUPAC Page 4 of 5

4 Marquardt et al, Definition of the mole 1 2 3 12 4 M(B) = Ar(B) M( C)/12 = Ar(B) Mu 5 12 where Mu is the , equal to M( C)/12. Because the molar mass of unbound carbon-12, 6 12 −1 −1 M( C), is no longer 12 g mol exactly, the molar mass constant, Mu, is no longer 1 g mol exactly. 7 9 8 The uncertainty of Mu, being smaller than 1 part in 10 , however, is of no practical relevance in chemistry. −1 9 Within this uncertainty, the value of Mu remains 1 g mol . The molar mass of any entity B is also related 10 to the mass of the elementary entity, m(B), by the equation 11 12 M(B) = NA m(B) = NA Ar(B) mu 13 12 14 where mForu is the atomic Peer mass constant Review equal to the atomic mass Only of carbon-12 divided by 12, ma( C)/12. 15 Both Mu and mu are related to the Avogadro constant through the equation Mu = NA mu. 16 17 18 19 5 Membership of sponsoring bodies 20 21 Membership of the IUPAC Physical and Biophysical Chemistry Division for the period 2014–2015 was as 22 follows: 23 President: R. Marquardt (France); Secretary: A. Friedler (Israel); Vice President: A. K. Wilson (USA); 24 Past President: K. Yamanouchi (Japan); Titular Members: K. Bartik (Belgium); A. R. Goodwin 25 (USA); A. E. Russell (UK); J. Stohner (Switzerland); Y. H. Taufiq-Yap (Malaysia); F. van Veggel (Canada); 26 Associate Members: A. Császár (Hungary); V. Yu. Kukushkin (Russia); A. W. Mombrú Rodriguez 27 28 (Uruguay); X. S. Zhao (China); K. Bhattacharyya (India); J. L. B. M. de Faria (Portugal); National 29 Representatives: J. Cejka (Czech Republic); S. Hannongbua (Thailand); M. Koper (The Netherlands); 30 J. E. G. Mdoe (Tanzania); V. Tomišić (Croatia); A. bin Hasan Susan (Bangladesh); S.-J. Kim (South 31 Korea); E. Klein (Bulgaria); M. Korenko (Slovakia); K. E. Laasonen (Finland); H. Corti (Argentina) 32 33 Membership of the IUPAC Inorganic Chemistry Division for the period 2014–2015 was as follows: 34 President: J. Reedijk (Netherlands); Secretary: M. Leskelä (Finland); Vice President: L. R. Öhrström 35 (Sweden); Past President: R. D. Loss (Australia); Titular Members: T. Ding (China); M. Drábik (Slo- 36 vakia); D. Rabinovich (USA); E. Tshuva (Israel); T. Walczyk (Singapore); M. Wieser (Canada); Associate 37 Members: J. Buchweishaija (Tanzania); J. García-Martínez (Spain); P. Karen (Norway); A. Kiliç (Turkey); 38 39 K. Sakai (Japan); R.N. Vannier (France); National Representatives: Y. Abdul Aziz (Malaysia); L. 40 Armelao (); A. Badshah (Pakistan); V. Chandrasekhar (India); J. Galamba Correia (Portugal); S. 41 Kalmykov (Russia); S. Mathur (Germany); L. Meesuk (Thailand); B. Prugove˘cki(Croatia); N. Trendafilova 42 (Bulgaria) 43 44 Membership of the IUPAC Analytical Chemistry Division for the period 2014–2015 was as follows: 45 President: D. Brynn Hibbert (Australia); Secretary: Z. Mester (Canada); Vice President: J. Labuda 46 (Slovakia); Past President: M. Filomena Camões (Portugal); Titular Members: C. Balarew (Bulgaria); 47 Y. Chen (China); A. Felinger (Hungary); H. Kim (South Korea); C. Magalhães (Portugal); H. M. M. Sirén 48 (Finland); Associate Members: R. Apak (Turkey); P. Bode (The Netherlands); D. Craston (UK); Y. Heng 49 50 Lee (Malaysia); T. Maryutina (Russia); N. Torto (South Africa); National Representatives: P. DeBièvre 51 (Belgium); M. N. Eberlin (Brazil); P. Novak (Croatia); L. Charles (France); D. Mandler (Israel); J. Hanif 52 (Pakistan); A. Fajgelj (Slovenia); O. Chande Othman (Tanzania); K. Grudpan (Thailand); D. G. Shaw 53 (USA) 54 55 Membership of the IUPAC Committee on Chemistry Education for the period 2014–2015 was as fol- 56 lows: 57 President: M.-H. Chiu (China); Secretary: J. Apotheker (The Netherlands); Titular Members: 58 N. H. K. Aremo (Finland); S. Boniface (New Zealand); M. Kamata (Japan); R. M. Naaman (Israel); 59 60 P.O. 13757, Research Triangle Park, NC (919) 485-8700 Page 5 of 5 IUPAC

Marquardt et al, Definition of the mole 5 1 2 3 M. Sözbilir (Turkey); M. Towns (USA); National Representatives: A. H. Wright (Australia); M. 4 M. Rahman (Bangladesh); L. Brandt (Belgium); B. Toshev (Bulgaria); L. L. Santibañez (Chile); Z. 5 Shuai (China); T. Solomon (Ethiopia); C. S. Reiners (Germany); M. Riedel (Hungary); U. Maitra (In- 6 dia); P. E. Childs (Ireland); L. Cardellini (Italy); A. A. Al-Najjar (Kuwait); T.-K. Soon (Malaysia); R. 7 Adhikari (Nepal); F. Mahmood (Pakistan); A. Pokrovsky (Russia); M. Elmgren (Sweden); P. Boesch 8 (Switzerland); S. Tantayanon (Thailand); M. Z. Hoffman (USA); T. Overton (UK); Division Repre- 9 sentatives: A. Russell (UK); J. García-Martïnez (Spain); M. J. Garson (Australia); W. Mormann (Ger- 10 many); Y. Chen (China); M. Dassenakis (Greece); J. H. Duffus (UK); R. M. Hartshorn (New Zealand) 11 12 13 Membership of the IUPAC Interdivisional Committee on Terminology, Nomenclature and Symbols for the 14 period 2014–2015 wasFor as follows: Chair:PeerR. Weir (Canada);ReviewSecretary: J. StohnerOnly (Switzerland); Titu- 15 lar Members: J. Frey (UK); J. Meija (Canada); G. P. Moss (UK); Associate Members: R. Cornelis 16 (Belgium); M. Drábik (Slovakia); J. Kaiser (UK); Division Representatives: M. Drábik (Slovakia); 17 M. Brimble (New Zealand); P. S. Fedotov (Russia); A. Goodwin (USA); D. B. Hibbert (Australia); Y. 18 Martin (USA); G. Moad (Australia); A. Rauter (Portugal); Representatives of Other Organizations: 19 A. Authier (France), International Union of Crystallography; I. Elmadfa (Austria), International Union 20 21 of Nutritional Sciences; S. N. Lea (UK), International Union of Pure and Applied ; D. Schom- 22 burg (Germany), International Union of Biochemistry and Molecular Biology; M. Spedding (France), 23 International Union of Pharmacology; R. Wielgosz (France), Bureau International des Poids et Mesures 24 25 26 27 References 28 29 [1] CGPM (1949): Comptes Rendus de la neuvième Conférence Générale des Poids et Mesures (1948). Résolution 6, 30 BIPM, URL http://www.bipm.org/en/CGPM/db/9/6/. 31 [2] CGPM (1955): Comptes Rendus des séances de la dixième Conférence Générale des Poids et Mesures (1954). Résolu- 32 tion 6, BIPM, URL http://www.bipm.org/en/CGPM/db/10/6/. 33 [3] CGPM (1961): Comptes Rendus des séances de la onzième Conférence Générale des Poids et Mesures (1960). Résolu- tion 12, BIPM, URL http://www.bipm.org/en/CGPM/db/11/12/. 34 [4] CGPM (1972): Comptes Rendus des séances de la quatorzième Conférence Générale des Poids et Mesures (1971). 35 Résolution 3, BIPM, URL http://www.bipm.org/en/CGPM/db/14/3/. 36 [5] BIPM (2006): Le Système international d’unités/The International System of Units (Brochure sur le SI/SI brochure), 37 2006, BIPM, 8 edition. 38 [6] CGPM (1961): Comptes Rendus des séances de la onzième Conférence Générale des Poids et Mesures (1960). Résolu- 39 tion 6, BIPM, URL http://www.bipm.org/en/CGPM/db/11/6/. 40 [7] CGPM (1984): Comptes Rendus des séances de la 17e Conférence Générale des Poids et Mesures (1983). Résolution 41 1, BIPM, URL http://www.bipm.org/en/CGPM/db/17/1/. 42 [8] Marquardt, R., J. Meija, Z. Mester, M. Towns, R. Weir, R. Davis, and J. Stohner (2017): “A critical review of the 43 proposed definitions of fundamental chemical quantities and their impact on chemical communities (IUPAC Technical 44 Report),” Pure Appl. Chem., XX, XX–XX. 45 [9] CGPM (2001): Proceedings of the 21st meeting of the General Conference on Weights and Measures (1999). Resolu- 46 tion 7, BIPM, URL http://www.bipm.org/en/CGPM/db/21/7/. 47 [10] CGPM (2013): Proceedings of the 24th meeting of the General Conference on Weights and Measures (2011). Resolu- 48 tion 1, BIPM, URL http://www.bipm.org/en/CGPM/db/24/1/. 49 [11] CGPM (2015): Proceedings of the 25th meeting of the General Conference on Weights and Measures (2014). Resolu- tion 1, BIPM, URL http://www.bipm.org/en/CGPM/db/25/1/. 50 [12] Petley, B. W. (1989): “The Atomic Mass Unit,” IEEE Trans Instr Meas, 38, 175–179. 51 [13] Cohen, E. R., T. Cvitaš, J. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, 52 J. Stohner, H. L. Strauss, M. Takami, and A. J. Thor (2011): Quantities, Units and Symbols in Physical Chemistry, 53 Cambridge: IUPAC & The Royal Society of Chemistry, 3rd printing, 3rd edition. 54 55 56 57 58 59 60 P.O. 13757, Research Triangle Park, NC (919) 485-8700