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No Rationale for a Redefinition of the Mole

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No Rationale for a Redefinition of the Mole 616 CHIMIA 2009, 63, No. 10 METROLOGY IN CHEMISTRY doi:10.2533/chimia.2009.616 Chimia 63 (2009) 616–618 © Schweizerische Chemische Gesellschaft No Rationale for a Redefinition of the Mole Hanspeter Andres*, Hans-Peter Haerri, Bernhard Niederhauser, Samuel Wunderli, and Ulrich Feller Abstract: In the wake of the redefinition of the kilogram, the last unit of the International System of Units (SI) that is still based on a man-made artefact, discussions were launched on the necessity of redefining other units, amongst other the unit mole. Since 1971 the mole is defined as the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. The symbol of the unit is ‘mol’. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. The definition is based on the pre-existing choice to set the relative atomic mass of carbon 12 equal to 12 exactly. In the proposed new definition the mole is the amount of substance containing exactly 6.022 141 79 × 1023 atoms or molecules, ions, electrons, other particles, or specified groups of such particles, i.e. the Avogardo constant would have a fixed value without an uncertainty.This contri- bution critically examines the submitted arguments to justify the proposed redefinition of the unit mole by 2011 for their persuasive power to change a scientific and cultural good such as a unit of measurement. As shown, there are no convincing scientific arguments for a redefinition of the mole that stand a closer examination. The current definition is well understood, established in science and technology for almost 50 years and is still up to date. Keywords: Avogadro’s constant . Base unit . International System of Units . Mole . Redefinition 1. Introduction Mills and coworkers have brought for- Units of measurements are scien- ward a series of arguments to justify a re- tific and cultural goods that must not be The continuous improvement of the units definition of the mole, e.g.[2,5,11,12] changed without convincing arguments. of measurement is a task that evolves in – quantum metrology; In the following chapters we subject the parallel with the evolution of science and – lack of comprehensibility of the current arguments cited above to closer examina- technology. The early man-made units definition; tion. have been replaced in the course of time – the desire to establish base units on true one by one by more stable units that are invariants of nature, i.e. on fundamen- preferentially based on constants given by tal constants; 2. Is There any Misunderstanding in nature. The last unit of the International – dependence of the mole on the kilo- the Concepts? System of Units (SI) that is still based gram. on a man-made artefact is the unit of the In ref. [11] we read: “This follows from The argument ‘quantum metrology’ is mass, the kilogram. There is no dispute our desire to define each of the base units not applicable to the mole and needs no that this 19th century artefact of the SI in relation to one of the fundamental con- further discussion. What about the com- should be removed. The work on that is stants of physics, or the properties of a prehensibility of the terms ‘amount of sub- ongoing. In the wake of the redefinition of simple atom, because we believe these to stance’ and mole? The current definition the kilogram discussions on the necessity be the most stable and reliable constants of the unit mole is given in the Table.[13] of a redefinition of other units have been of nature available. Specifically, new defi- The quantity ‘amount of substance’ and launched, amongst others a possible new nitions are being considered for the kilo- its unit mole are concepts that have a long definition of the mole.[1–12] The proposed gram, ampere, Kelvin, and mole. This is the tradition. Scientists like Dalton, Avogadro new definition is based on a fixed value for subject known as quantum metrology, and and others established these concepts in the Avogadro’s constant. the proposals are discussed in detail else- the nineteenth century. It is therefore where.” and eventually “It is something surprising that in publications and pres- of a paradox that such concepts as the entations promoting a redefinition of the quantity ‘amount of substance’and its unit mole it is repeatedly claimed that there ‘mole’, so widely used by practical chem- should be a misunderstanding in the con- ists, are also the subjects of widespread cepts.[5,11] misunderstanding.” The evoked ‘problem’ in the compre- In ref. [12] the authors quote: “As dis- hensibility of the quantity ‘amount of sub- cussed below, it is now being proposed that stance’ is in fact a very simple problem: the link between the quantity amount of When the amount of apples has to be speci- substance and the underlying concept of a fied, two pieces of information have to be number of entities should be strengthened given: *Correspondence: Dr. H. Andres by the introduction of a definition for the 1. What is the substance under consider- Federal Office of Metrology METAS Section Analytical Chemistry unit of amount of substance framed direct- ation? apples; e.g. Golden delicious. Lindenweg 50 ly in terms of a fixed number of entities. 2. How many apples are there? number CH-3003 Bern-Wabern This would break the direct link that exists (of apples). Tel.: +41 31 32 33 370 at present between the unit of amount of That’s all. The same concept is valid in Fax: + 41 31 32 33 210 E-mail: [email protected] substance and the unit of mass.” chemistry: METROLOGY IN CHEMISTRY CHIMIA 2009, 63, No. 10 617 Table. Current definitions of the units mole and second. 3. Is Avogadro’s Constant a Term Definition ‘True Invariant of Nature,’ i.e. a Fundamental Constant? mole 1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol Avogadro’s constant is an arbitrary is ‘mol’. number that has nothing to do with a ‘true 2. When the mole is used, the elementary entities must be specified and may be invariant of nature’ or a fundamental con- atoms, molecules, ions, electrons, other particles, or specified groups of such stant. A fundamental constant in physics is particles. understood as a constant that is given by It follows that the molar mass of carbon 12 is exactly 12 grams per mole, M(12C) = nature and which is free of any human con- 12 g/mol. structs, e.g. Planck’s constant, the speed of light, the electronic charge or the rest mass second The second is the duration of 9 192 631 770 periods of the radiation corresponding of a fundamental particle. These constants to the transition between the two hyperfine levels of the ground state of the caesium are given by nature and can be measured. 133 atom. It follows that the hyperfine splitting in the ground state of the caesium The Avogadro constant N is nowhere pro- 133 A 133 atom is exactly 9 192 631 770 hertz, ν(hfs Cs) = 9 192 631 770 Hz. vided by nature, we have to prepare this number by using a balance. The mole defi- nition tells us how we have to proceed. 1. What is the substance under consid- That the Avogadro number cannot be For a comprehensive explanation of eration? chemical substance; e.g. ‘counted’ in a normal way, but can be re- Avogadro’s constant the reader is referred methane. alised by weighing poses no problem in to the cited introductory textbooks.[14,15] 2. How many atoms or molecules are comprehension (see Figure). It is a com- The status of the Avogadro constant is there? number (of atoms or mol- mon procedure in trade and industry to comparable with the number of periods ecules). count large numbers of identical, small used for the definition of the second, s. The In principle the only relevant difference items using balances. For instance, coins current definition of unit ‘second’ is given between apples and atoms or molecules are routinely counted by precision balanc- in the Table.[13] This number tells us how with respect to the quantity ‘amount of’ is es, and people understand the difference many exactly fixed periods of the caesium their size; but that hardly hampers the com- between ‘number of coins’ and mass well. radiation we have to sum up to get a sec- prehensibility: When we speak of apples, it That among scientists and technicians ‘the ond. In mass measurement of substances may be adequate to state their numbers in name mole has been – and still is – the the Avogadro constant tells us how many units of one. If there’s a grocer trading with cause of some confusion’ we consider as atoms or molecules are contained in a mass a lot of eggs, it may be adequate for him an assertion that is in contradiction to the with a value near the exactly fixed mass of to trade them in units of dozen. And since rich textbook literature.[11] the prototype of the kilogram. atoms or molecules are very small, it is ad- Summarising: equate to express their numbers in a much 1. The concepts of the quantity ‘amount of larger counting unit, namely in N , the substance’ and its unit mole are easily A 4.
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