Analytical Methods Committee AMCTB No 86
First published on 13th March 2019
The International System of Units (SI) is the only globally agreed practical system of measurement units. Stemming from the Metre Convention of 1875, which established a permanent organisational structure for member governments to act in common accord on all matters relating to units of measurement, the SI was formalised in 1960 and defined by the ‘SI Brochure’. The foundation of the SI are the set of seven well defined base units: the metre, the kilogram, the second, the ampere, the kelvin, the mole, and the candela, from which all derived units (such as metres per second) are formed. On 16 November 2018 the 26^{th} General Conference on Weights and Measures (CGPM) met, at an open meeting at the Palais des Congrès, Versailles, to discuss and vote on the re-definition of four of the SI’s seven base units: the mole, the ampere, the kelvin, and the kilogram. This change, effective from World Metrology Day (20 May) 2019, is perhaps the most fundamental change in the SI since its inception. For the first time the SI will be defined entirely in terms of fundamental physical constants, instead of requiring the maintenance of a physical artefact. This technical brief explains why this re-definition came about. No practical implications of the change are envisaged for analytical chemistry in the short term and improvements in measurement may take some time to realise.
The kilogram remained the only base unit defined and realised as a single material artefact – the international prototype of the kilogram (IPK) – a platinum-iridium cylinder with a mass of exactly 1 kg, by definition, to which all mass measurements across the world are ultimately traceable and have been since 1889. For a long time metrologists have been keen to redefine the kilogram in terms of constants of nature. The development of the Kibble balance – a device invented by Dr Bryan Kibble (at the UK’s National Physical Laboratory) which allows mechanical and electrical force to be accurately compared – brought this possibility into sharper focus and also prompted additional proposals to redefine three other base units of the SI with respect to ‘defining constants’; the ampere, the kelvin and the mole (Mills et al., 2006; I. A. Robinson and S. Schlamminger, 2016). The metre was redefined in 1983 with respect to the speed of light, and the second has, since 1967, depended on a material property – a spectroscopic transition of a caesium-133 atom. The candela, dependent on the luminous efficacy technical constant related to a spectral response of the human eye, was not directly part of discussions to revise the SI.
In considering which constants could have their numerical values† fixed to redefine the kilogram it was important to ensure the relationship between quantities remained unaltered regardless of the choice of unit definition. A key equation, eqn (1), in these considerations, demonstrating how the Planck constant, h, and the Avogadro constant, N_{A}, are closely linked, is given by rearranging the relationship that defines the Rydberg constant (a physical constant relating to atomic spectra):
(1) |
Considering that h is related to macroscopic mass via the Kibble balance experiment, and N_{A} is related to macroscopic mass via the Avogadro experiment‡(Bartl, et al., 2017) it is clearly possible to define mass in terms of either of these constants. The corollary to this was that a new definition of the mole, based on a fixed numerical value of N_{A}, was also likely.
Symbol | Name | Numerical value | SI unit |
---|---|---|---|
Δν_{Cs} | Hyperfine transition frequency of Cs | 9192631770 | Hz |
c | The speed of light in vacuum | 299792458 | m s^{−1} |
h | Planck constant | 6.62607015 × 10^{−34} | J s |
e | Elementary charge | 1.602176634 × 10^{−19} | C |
k | Boltzmann constant | 1.380649 × 10^{−23} | J K^{−1} |
N _{A} | Avogadro constant | 6.02214076 × 10^{23} | mol^{−1} |
K _{cd} | Luminous efficacy | 683 | lm W^{−1} |
“The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.02214076 × 10^{23} elementary entities. This number is the fixed numerical value of the Avogadro constant, N_{A}, when expressed in the unit 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.”
This definition is worded in the ‘explicit constant’ format that all SI base units will adopt following the revision of the SI. The implications of the change for the mole, shown in Fig. 1, are that the uncertainty previously associated with the Avogadro constant will disappear, and the molar mass of ^{12}C and the molar mass constant – previously known exactly – will acquire a relative standard uncertainty equal to that of N_{A}h at the time of redefinition, namely 4.5 × 10^{−10}, and that in the future their values will be determined experimentally.
There are some immediate notional benefits of the redefinition of the mole:
• The reliance of the mole on the kilogram is removed;
• The relative uncertainty of the atomic mass and molar mass scales are equalised;
• The mole is no longer dependent on a material property and is more universal in its applicability;
• It reflects the way most chemists already consider the mole;
• The new definition may prove easier to teach;
• It is a better fit with 21^{st} century technologies and keeps chemical metrology aligned with the rest of the SI.
Relative atomic masses and relative molecular masses are ratios, not dependent on the current definition of the kilogram, and will be unaffected by the proposed new definitions of the kilogram and the mole.
The relative uncertainties associated with the quantities involved in the mole redefinition are still several orders of magnitude smaller than those associated with the practical realisation of chemical quantities, which mostly occurs by weighing materials of known purity. As a result no practical implications of the change are envisaged for analytical chemistry in the short term and improvements may take some time to realise. However, the change is overall of benefit for chemistry in the longer term, paving the way for more accurate chemical measurement in future, particularly at ultra-low amounts of substance.
I. M. Mills, P. J. Mohr, T. J. Quinn, B. N. Taylor and E. R. Williams, Redefinition 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. Bettin, E. Beyer, M. Borys, I. Busch, L. Cibik, G. D’Agostino, E. Darlatt, M. Di Luzio, K. Fujii, H. Fujimoto, K. Fujita, M. Kolbe, M. Krumrey, N. Kuramoto, E. Massa, M. Mecke, S. Mizushima, M. Müller, T. Narukawa, A. Nicolaus, A. Pramann, D. Rauch, O. Rienitz, C. P. Sasso, A. Stopic, R. Stosch, A. Waseda, S. Wundrack, L. Zhang and X. W. Zhang, A new ^{28}Si single crystal: counting the atoms for the new kilogram definition, Metrologia, 2017, 54, 693–715.
Resolution 1 of the 26th CGPM, 2018, https://www.bipm.org/en/CGPM/db/26/1/.
M. J. T. Milton and I. M. Mills, Amount of substance and the proposed redefinition of the mole, Metrologia, 2009, 46, 332–338.
Dr Richard J. C. Brown (National Physical Laboratory).
This Technical Brief was prepared on behalf of the AMC, and was approved by the AMC on 28 January 2019.
Footnotes |
† The value of a quantity, Q, is expressed as the product of a numerical value, {Q}, and a unit, [Q]. Thus, Q = {Q}[Q]. The speed of light is a constant of nature with a value Q_{c} which is fixed, and is not for us to choose. However, we are free to assign a fixed numerical value to the speed of light {Q_{c}}, which thereby defines the size of the unit [Q_{c}] for speed, in m s^{−1}, since both of the other terms in the equation are fixed. This approach is analogous to all other unit definitions based on fixed numerical values of ‘defining constants’. |
‡ Sometimes called the X-ray crystal density (XRCD) experiment – an international consortium to count atoms in a near perfect silicon sphere. |
This journal is © The Royal Society of Chemistry 2019 |