Analytical Methods
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Revision of the International System of Units (Background paper) Cite this: Anal. Methods,2019,11,1577 Analytical Methods Committee AMCTB No 86
DOI: 10.1039/c9ay90028d
www.rsc.org/methods
The International System of Units (SI) is the The current International respect to ‘dening constants’; the only globally agreed practical system of ampere, the kelvin and the mole (Mills measurement units. Stemming from the System of Units (SI) and et al., 2006; I. A. Robinson and S. Metre Convention of 1875, which established the need for change Schlamminger, 2016). The metre was a permanent organisational structure for redened in 1983 with respect to the member governments to act in common Measurement units were originally speed of light, and the second has, since accord on all matters relating to units of dened by physical artefacts or properties 1967, depended on a material property – measurement, the SI was formalised in 1960 of specic materials. However such a spectroscopic transition of a caesium- and defined by the ‘SI Brochure’. The foun- physical artefacts have obvious draw- 133 atom. The candela, dependent on dation of the SI are the set of seven well backs in terms of their stability and the luminous efficacy technical constant defined base units: the metre, the kilogram, susceptibility to damage and decay. It is related to a spectral response of the the second, the ampere, the kelvin, the mole, preferable to have units dened in human eye, was not directly part of and the candela, from which all derived units terms of constants of nature – so called discussions to revise the SI. (such as metres per second) are formed. On ‘dening constants’–which can be In considering which constants could 16 November 2018 the 26th General Confer- assumed to be invariant and can provide have their numerical values† xed to Published on 13 March 2019. Downloaded 3/28/2019 5:35:31 PM. ence on Weights and Measures (CGPM) met, the greater accuracy demanded by today’s redene the kilogram it was important to at an open meeting at the Palais des Congr`es, technology. As a result all the original ensure the relationship between quanti- Versailles, to discuss and vote on the re- unique physical artefacts which dened ties remained unaltered regardless of the definition of four of the SI’s seven base units have now all been superseded, choice of unit denition. A key equation, units: the mole, the ampere, the kelvin, and apart from one, the kilogram. eqn (1), in these considerations, demon- the kilogram. This change, effective from The kilogram remained the only base strating how the Planck constant, h, and World Metrology Day (20 May) 2019, is unit de ned and realised as a single the Avogadro constant, NA, are closely perhaps the most fundamental change in the material artefact – the international linked, is given by rearranging the rela- SI since its inception. For the first time the SI prototype of the kilogram (IPK) – a plat- tionship that denes the Rydberg will be defined entirely in terms of funda- inum-iridium cylinder with a mass of constant (a physical constant relating to mental physical constants, instead of exactly 1 kg, by denition, to which all atomic spectra): requiring the maintenance of a physical mass measurements across the world are artefact. This technical brief explains why this ultimately traceable and have been since re-definition came about. No practical impli- 1889. For a long time metrologists have cations of the change are envisaged for been keen to redene the kilogram in † The value of a quantity, Q, is expressed as the analytical chemistry in the short term and terms of constants of nature. The devel- – product of a numerical value, {Q}, and a unit, [Q]. improvements in measurement may take opment of the Kibble balance a device Thus, Q ¼ {Q}[Q]. The speed of light is a constant of ’ some time to realise. invented by Dr Bryan Kibble (at the UK s nature with a value Qc which is xed, and is not for National Physical Laboratory) which us to choose. However, we are free to assign a xed allows mechanical and electrical force to numerical value to the speed of light {Qc}, which – thereby de nes the size of the unit [Qc] for speed, be accurately compared brought this in m s 1, since both of the other terms in the possibility into sharper focus and also equation are xed. This approach is analogous to prompted additional proposals to rede- all other unit denitions based on xed numerical ne three other base units of the SI with values of ‘dening constants’.
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Table 1 From 20 May 2019 the SI will be the system of units in which these defining constants have the exact numerical values shown, when expressed in the units given in the final column (Resolution 1 of the 26th CGPM, 2018)
Symbol Name Numerical value SI unit
Dn Cs Hyper ne transition frequency of Cs 9 192 631 770 Hz c The speed of light in vacuum 299 792 458 m s 1 h Planck constant 6.62607015 10 34 Js e Elementary charge 1.602176634 10 19 C k Boltzmann constant 1.380649 10 23 JK 1 23 1 NA Avogadro constant 6.02214076 10 mol 1 Kcd Luminous efficacy 683 lm W
2 h NAh ca and 2014) and by the behaviour of similar as there are atoms in 0.012 kilogram of ¼ ¼ ArðeÞ (1) mu Mu 2RN mass standards. These considerations carbon 12. Therefore currently we only resulted in international agreement that know implicitly how many elementary where, N is the Avogadro constant, h is A once three independent experiments (two entities this is by using a measure of an the Planck constant, m is the atomic u or more Kibble balances and the Avoga- exact mass of a known material as mass constant, M is the molar mass u dro experiment) provided consistent a surrogate. The new denition removes constant, c is the speed of light in results with an uncertainty of less than 5 this ambiguity, and reliance of the mole vacuum, a is the ne structure constant, parts in 108, a change would be bene- on the kilogram, by stating an exact RN is the Rydberg constant and A (e) is r cial. These conditions were met in time number of elementary entities explicitly: the relative atomic mass of the electron. for a resolution to be brought before the “The mole, symbol mol, is the SI unit The components of eqn (1) have either 26th CGPM to propose revision of the SI of amount of substance. One mole exact values or have uncertainties signif- according to xed numerical values of contains exactly 6.02214076 1023 icantly smaller than the uncertainties in h seven ‘dening constants’ including elementary entities. This number is the and N prior to SI revision. A redenition of the kilogram, the mole, xed numerical value of the Avogadro Considering that h is related to the ampere and the kelvin in terms constant, NA, when expressed in the unit macroscopic mass via the Kibble balance of a xed numerical value of the mol 1 and is called the Avogadro experiment, and N is related to macro- A Planck constant, Avogadro constant, the number. The amount of substance, scopic mass via the Avogadro elementary charge and the Boltzmann symbol n, of a system is a measure of the experiment‡ (Bartl, et al., 2017) it is constant, respectively. Whilst the deni- number of specied elementary entities. clearly possible to dene mass in terms of tions of the second, metre and ampere An elementary entity may be an atom, either of these constants. The corollary to
Published on 13 March 2019. Downloaded 3/28/2019 5:35:31 PM. will not change, they will be written in a molecule, an ion, an electron, any other this was that a new denition of the mole, adifferent form to make them consistent particle or specied group of particles.” based on a xed numerical value of N , A with the new denitions for the units that This denition is worded in the was also likely. will change. The resolution was unani- ‘explicit constant’ format that all SI base mously approved on 16 November 2018, units will adopt following the revision of Time for change with an effective date of 20 May 2019. The the SI. The implications of the change for delay between decision and imple- the mole, shown in Fig. 1, are that the At the point of redenition of any unit it mentation allows more widespread uncertainty previously associated with is essential that the size of the unit does communication of the change to stake- the Avogadro constant will disappear, not change, and furthermore that the 12 holders, especially in the electrical area and the molar mass of C and the molar new denition is an improvement on the where there will be a small step change in mass constant – previously known exactly old denition. In the case of the kilogram the size of the ampere (about 1 part in 10 – will acquire a relative standard uncer- (and therefore the mole) the limitation in million). The seven de ning constants of tainty equal to that of NAh at the time of the old denition was the dri in the 10 the SI from 20 May 2019 are shown in redenition, namely 4.5 10 , and mass of IPK over time. This cannot be Table 1. that in the future their values will be measured directly since the mass of the determined experimentally. IPK is always 1 kg by denition! However There are some immediate notional it may be estimated by comparison over ff The e ects of benets of the redenition of the mole: time against its copies (IPK has only been redefinition for the mole The reliance of the mole on the removed from the safe in which it is kept kilogram is removed; on three occasions since 1889: 1946, 1991 and chemical The relative uncertainty of the measurement atomic mass and molar mass scales are ‡ Sometimes called the X-ray crystal density (XRCD) equalised; experiment – an international consortium to count The current de nition refers to the mole atoms in a near perfect silicon sphere. containing as many elementary entities
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the unit of mass, Metrologia, 2016, 53, A46–A74. I. M. Mills, P. J. Mohr, T. J. Quinn, B. N. Taylor and E. R. Williams, Redef- inition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005), Metrologia, 2006, 43,227– 246. G.Bartl,P.Becker,B.Beckhoff,H. Fig. 1 Diagrammatic relationship between the quantities: atomic mass constant, mu; molar 12 12 12 12 Bettin,E.Beyer,M.Borys,I.Busch,L. mass constant, Mu; relative atomic mass of C, Ar( C); molar mass of C, M( C); mass of one 12 12 ’ atom of C, m( C); and the Avogadro constant, NA, before and after the SI revision. The Cibik, G. D Agostino,E.Darlatt,M.Di 12 12 direction of the arrow indicates multiplications (for instance, mu Ar( C) ¼ m( C)). Those Luzio, K. Fujii, H. Fujimoto, K. quantities with a fixed numerical value and zero uncertainty are shown with a box around them Fujita,M.Kolbe,M.Krumrey,N.Kur- (for instance, A (12C) h 12 will be unchanged by the revision of the SI). Adapted from M. J. T. r amoto, E. Massa, M. Mecke, S. Milton and I. M. Mills, 2009. Mizushima, M. Muller,¨ T. Narukawa, A. Nicolaus, A. Pramann, D. Rauch, O. The mole is no longer dependent on paving the way for more accurate chem- Rienitz, C. P. Sasso, A. Stopic, R. Stosch, a material property and is more universal ical measurement in future, particularly A. Waseda, S. Wundrack, L. Zhang and in its applicability; at ultra-low amounts of substance. X. W. Zhang, A new 28Si single crystal: It reects the way most chemists counting the atoms for the new kilo- already consider the mole; Wider benefits of revision gram denition, Metrologia, 2017, 54, The new denition may prove easier 693–715. to teach; of the SI Resolution 1 of the 26th CGPM, st It is a better t with 21 century 2018, https://www.bipm.org/en/CGPM/ Aside from removing the last unique technologies and keeps chemical db/26/1/. physical artefact from the SI, the new metrology aligned with the rest of the SI. M. J. T. Milton and I. M. Mills, Amount denitions in terms of xed numerical Relative atomic masses and relative of substance and the proposed redeni- values of dening constants are more molecular masses are ratios, not depen- tion of the mole, Metrologia, 2009, 46, dent on the current denition of the universal in their applicability and more – 332 338. kilogram, and will be unaffected by the consistent with twenty rst century tech- Dr Richard J. C. Brown (National proposed new denitions of the kilogram nologies. The way to realise a unit is no Physical Laboratory). and the mole. longer implicitly or explicitly suggested This Technical Brief was prepared on Published on 13 March 2019. Downloaded 3/28/2019 5:35:31 PM. The relative uncertainties associated by its de nition. This separation future- behalf of the AMC, and was approved by with the quantities involved in the mole proofs the unit de nitions, ensuring the AMC on 28 January 2019. redenition are still several orders of that unit realisations will be able to magnitude smaller than those associated bene t from all relevant future advances with the practical realisation of chemical in technology and lays the foundations quantities, which mostly occurs by for more accurate measurements for all weighing materials of known purity. As stakeholders for decades to come. a result no practical implications of the change are envisaged for analytical Further reading chemistry in the short term and improvements may take some time to I. A. Robinson and S. Schlamminger, The realise. However, the change is overall of watt or Kibble balance: a technique for benet for chemistry in the longer term, implementing the new SI denition of
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