The New SI

Metrology, the science of measurement, is part of the essential but largely hidden infrastructure of the modern world. We need it for high-technology manufacturing, human health and safety, the protection of the environment, global climate studies, information transfer and the basic science that underpins all these. Highly accurate measurements are no longer the preserve of only the physical sciences and engineering. The International System of Units, the SI (Système International d’unités), provides the internationally agreed means by which we make such measurements.

At a meeting of the General Conference on Weights and Measures (CGPM) held in Paris on 16 November 2018 a new and revised SI was approved, adapted for the 21st century.* These changes will be implemented on 20 May 2019, the next “World Metrology Day” and the day anniversary on which the Convention of the Metre was first signed in 1875. Of particular interest to chemists are the changes in the definition of the SI units kilogram and mole.

* See We Did It! Redefinition of SI adopted, video release by The BIPM, 20 Nov 2018

In this context the well-known opening sentence of Jane Austen’s novel Pride and Prejudice may be adapted to read: “It is a truth universally acknowledged that a single man in possession of a good fortune, must be in want of a good set of units.” In the last four words of this sentence Jane Austen wrote “must be in want of a wife,” but we have substituted “in want of a good set of units.” Perhaps we need both!

The following is a brief summary of the changes that are being adopted in this new SI.

1. Each of the seven base units of the SI (second, metre, kilogram, ampere, kelvin, mole, and candela) is defined by an agreed reference that has to be readily available and easily realized experimentally by anyone anywhere at any time with sufficient precision (sufficiently low uncertainty) for our needs. Four of the seven base units, the kilogram, ampere, kelvin and mole, have revised definitions in the new SI as described below. The definitions of the second, metre and candela remain unchanged.

2. All of the new definitions will in future be expressed in terms of seven ‘defining constants’ which are believed to fulfil these requirements and are summarized below. The numerical values of these seven constants when expressed in SI units provides the definition of all SI units, both base and derived units.

3. The revised definition of the kilogram is chosen to fix the numerical value of the Planck constant h, that of the ampere to fix the numerical value of the elementary charge e, that of the kelvin to fix the numerical value of the Boltzmann constant k (k_B), and that of the mole to fix the numerical value of the Avogadro constant N_A (L), all these numerical values being expressed in terms of the corresponding SI unit. The definitions of the remaining three base units, the second, the metre, and the candela fix the numerical value of the caesium hyperfine splitting Δν_Cs, the speed of light in vacuum c, and the luminous intensity of the specified source I_v, just as they do at present.

4. The values of the seven defining constants listed in Table 1 below are chosen to be consistent with the best experimental values at the time of adopting the new definitions, to preserve continuity.

5. To summarize, the International System of Units, the SI, is the system of units in which:

where the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz, J, C, lm, and W, respectively, are related to the units second, metre, kilogram, ampere, kelvin, mole, and candela, with unit symbols s, m, kg, A, K, mol, and cd, respectively, according to Hz = s^–1, J = m² kg s^–2, C = A s, lm = cd sr, and W = m² kg s^–3.

The numerical values of the seven defining constants have zero uncertainty. They are summarized in Table 2 below. Definitions based on defining constants are called explicit-constant definitions; they are based on the fundamental constants of nature, in contrast to explicit-unit definitions which are based on particular experimental procedures.

For chemists, the definition of the mole has an important conceptual consequence. It is namely equivalent to stating that “One mole contains exactly 6.022 140 76 × 10²³ elementary entities,” quite in the spirit of William Shakespeare in As You Like It: “It is as easy to count atomies as to resolve the propositions of a lover.” In addition, the exact and fixed number of elementary entities defining a mole finally receives the name that has been used for it for decades without proper definition: the Avogadro number.

In general, the changes associated with the new SI will lead to reduced uncertainties in our knowledge of most of the fundamental constants of physics and chemistry in the new SI.

The changes in the new SI will strengthen the philosophical foundation of our system of units in relation to our present understanding of theoretical and quantum physics. However, they will not affect the daily work in the laboratory in any sizeable manner.

What are the direct consequences of these changes to a chemist working in the laboratory? For example, the equation

C₂H₄O = CH₄ + CO

has the meaning that one mole of oxirane (C₂H₄O) decomposes to yield one mole of methane (CH₄) and one mole of carbon monoxide (CO). The new definition of the mole will not change this meaning. A chemist in the laboratory will continue to determine the amount of a chemical entity B, n(B), by weighing the corresponding mass m(B) and setting n(B) = m(B)/M(B), where M(B) is the molar mass of B. He/she will continue to state that 44.053 g of oxirane decomposes to yield 16.043 g methane and 28.010 g carbon monoxide. Truly, the molar mass M(B) = M_r(B) M_u will acquire an uncertainty component of less than 1 part in 10⁹ due to the new uncertainty of the molar mass constant M_u = M(¹²C)/12 (see Table 2; the relative molar mass M_r(B) of any atom B is unchanged in the new SI). However, balances in chemistry laboratories will continue to yield masses (e.g. in the SI unit kg) with uncertainties that far exceed the uncertainty of the molar mass of any given chemical entity by orders of magnitude, so that the change in the new definition of the mole will never influence the result of the determinations of amount of substance in practice.

* This story was first published in Chemistry International in January 2019 (CI 41(1), pp. 32-35; https://doi.org/10.1515/ci-2019-0108)

Ian Mills <[email protected]> is emeritus professor of chemistry at the University of Reading, UK and an elected Fellow of the Royal Society. He was the President of Consultative Committee on Units of the International Bureau of Weights and Measures (BIPM) and retired from this role in 2013 after 18 years of service. In IUPAC, he served as chair of the Commission on Physicochemical Symbols, Terminology, and Units (Commission I.1), and also as chair of the Interdivisional Committee on Nomenclature and Symbols (IDCNS, preceding the current ICTNS) until 1999.

Roberto Marquardt <[email protected]> was President of the Physical and Biophysical Chemistry Division of IUPAC in 2014-15.

Title image from Light show dedicated to the redefinition of the SI at Sevres, The BIPM 7 Jan 2019

The theme for World Metrology Day 2019 is The International System of Units – Fundamentally better. This theme was chosen because on 16 November 2018, the General Conference on Weights and Measures agreed perhaps one of the most significant revisions to the International System of Units (the SI) since its inception. Research into new measurement methods, including those using quantum phenomena, underpin the change, which comes into force on 20 May 2019. The SI is now based on a set of definitions each linked to the laws of physics and have the advantage of being able to embrace further improvements in measurement science and technology to meet the needs of future users for many years to come. <http://www.worldmetrologyday.org>

View video produced by the National Institute of Standards and Technology, published by The BIPM on Nov 5, 2018