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The kilogram is the unit of mass and was defined in 1889 by the international prototype of the kilogram. The mole is the unit of amount of substance and was defined in 1960 by the number of atoms in 0.012 kg of 12C. These definitions were revised in May 2019. The new definitions of the kilogram and the mole are based on the Planck constant h and the Avogadro constant NA, respectively. The values of h and NA used in the new definitions were determined by summarizing measurement results of the two physical constants by several national metrology institutes around the world. In this review, the history of the two units and measurement technologies used to derive the new definitions are described. The effect of the revision on the development of new measurement technologies is also introduced.

Redefinition of the basic units of the International System of Units (SI) — the kilogram, mole, ampere, and kelvin, — which are now expressed in terms of fundamental physical constants means a substantial revision of the system. In particular, the new definition of the mole fixing the value of the Avogadro constant sets a unit of the amount of substance, which is independent of the unit of mass. We consider some consequences of redefining (the mole and kilogram) and focus on the uncertainty of measuring the amount of substance and related quantities which are important for description of the mixture composition. The issue regarding the molar mass of the substance and associated uncertainty is considered in detail It is noted that calculation of the molar mass using relative atomic masses, involves the molar mass constant which is not equal exactly to 1 g/'mol in the new SI. This introduces an additional, though very small, uncertainty of less than 1 x 10-9in relative terms. The budget of uncertainty for the amount of substance determined through the mass measurements when the mass is measured with the highest accuracy is scrutinized. It is demonstrated that for substances of less than 99.98% purity, the uncertainty associated to the purity is comparable to that of relative atomic masses of the elements. For high-purity substances, the uncertainty in the relative atomic masses have the largest contribution to the budget. Anyhow, the uncertainty associated to the molar mass constant is three orders of magnitude less than the nearest contribution to the uncertainty attributed to weighing. In the case of derived quantities which are the ratio of two quantities of the same kind, the additional uncertainty does not arise at all. This is illustrated by the calculation of the mole fraction of a component in the gravimetrically prepared gas mixture.

New definitions of the units for amount of substance – the mole – and for mass – the kilogram – will presumably come into force on the World Metrology Day 2019. In the revised SI, the mole will be defined by a fixed value of the Avogadro constant and the kilogram by a fixed value of the Planck constant. The X-ray-crystal-density (XRCD) method has been used for the determination of these fundamental constants by counting the number of atoms in 28Si-enriched spheres. Thus, silicon spheres will – after the redefinition – be used to realize the definitions of the mole and the kilogram. This is possible by SI-traceable measurements of lattice parameter, isotopic composition, volume, and surface properties, yielding a relative standard uncertainty below 2⋅10−8. Whereas this high accuracy is only reached with isotopically enriched silicon, it is also planned to use natural silicon spheres on a slightly lower level of accuracy. The future definitions will allow also new realization methods using silicon, in particular for small mass values.

This discussion article begins by highlighting the benefits of the mole's incorporation within the international system of units (SI), in particular by bringing chemical measurement within formal metrology structures. The origins of the confusion that has consistently existed between amount of substance (the base quantity of which the mole is the SI base unit) and counting quantities are examined in detail and their differentiating characteristics fully elaborated on. The importance and benefits of distinguishing between these different quantities and the role that the Avogadro constant plays in doing this are highlighted. It is proposed that these issues are becoming increasingly important for two reasons. First, as chemistry and biology consider increasingly small size domains, measurements are being made of significantly reduced collections of entities. Second, the proposed re-definition of the mole makes the link between amount of substance and the number of elementary entities more transparent. Finally, proposals for new ways of expressing very low amounts of substance in terms of new prefixes based on the numerical value of the Avogadro constant are presented as a way to encourage the use of the mole, when appropriate, even for ultra-low level chemical measurement.

Wilhelm Ostwald was a notable holdout against the acceptance of the reality of atoms. He steadfastly maintained a positivist perspective, that the empirical facts of chemistry implied no underlying meaning about the nature of matter. The amount of substance definition of the mole aligned with this view. He was moved to accept the reality of atoms based on the results of experimental work on Brownian motion by Jean Perrin, that gave a name to, and a value for, Avogadro’s constant. Ostwald could have modified the definition of the mole, making use of the constant to incorporate the atomic nature of matter into the concept. If he had, difficulties with the definition that persist today might have been avoided.

Following the revision of the International System of Units (SI), that takes effect on 20 May 2019, the unit mole is defined by using a fixed number of elementary entities. This number is the fixed numerical value of the Avogadro constant, which is the defining constant of the unit mole. This definition was made possible because the determination of the Avogadro constant had reached a level of relative uncertainty that allowed its value to be fixed and, at the same time, safeguard continuity of measurement results before and after the definition. The motivation for the revision of the SI and the mole in particular will be explained and the experimental work that allowed it is summarized.

The base quantity ‘amount of substance’ is poorly understood and the name and symbol usually avoided. This is because of its formal interpretation as the number of entities multiplied by the reciprocal of the mysterious Avogadro constant, N A. If X signifies the kind of entities involved, the number of entities in a sample, N(X), is easily comprehended, and if m av(X) is the sample-average entity mass, the total mass, m(X) = N(X)m av(X)—an aggregate of N(X) average entity masses—is also conceptually straightforward. However, the corresponding amount of substance, n(X) = N(X)(1/N A)—an aggregate of N(X) ‘reciprocal Avogadro constants’—is incomprehensible unless some physical meaning can be attached to 1/N A. By contrast, the base unit, mole, is thought of by chemists as an aggregate of a particular number of entities: mol = $$ {\mathcal N}_{\rm{Avo}} $$ ent, where $$ {\mathcal N}_{\rm{Avo}} $$ is the Avogadro number (equal to g/Da) and ent represents one entity. It makes sense, therefore, to interpret amount of substance as an aggregate of a general number of entities: n(X) = N(X) ent—an easily grasped concept. A ‘reciprocal Avogadro constant’ is thus seen to actually be exactly one entity. One mole then corresponds to setting N(X) = $$ {\mathcal N}_{\rm{Avo}} $$ , for which the total mass is the relative entity mass in grams—conforming to the original mole concept.

The amount of substance and its unit the mole is a basic concept in chemistry. However, previous research has shown that teaching and learning the concept are challenging tasks for both teachers and students. The purpose of this study was to pinpoint the problems which emerge in the teaching and learning process, and provide integrated suggestions for classroom instruction. By means of videotaping and interviews, the case studies explored how the mole is presented and conceptualized in two secondary classrooms in two different countries, Australia and Taiwan. Data analysis was based on a concept map and focused on how two key ideas were presented in the lessons and perceived by the students: (1) the definition of the mole, and (2) the concept of molar mass. The findings show that during the lessons on the mole, most of the time was spent on solving stoichiometric problems. Conceptually, the number aspect of the mole, that is, Avogadro's number, was emphasized; the concept of molar mass was introduced without meaningfully connecting it to the concept of relative atomic/molecular mass. Although the students were able to solve relevant problems, they could not coherently explain the relations among the concepts. Two critical components for a conceptual understanding of the mole emerged: (1) the number aspect of the mole needs to be justified by its mass aspect, and (2) the connection between molar mass and relative atomic/molecular mass needs to be explicitly explained. The two components provide one explanation for students' algorithmic learning and their confusion in learning about the mole, and serve as concrete suggestions for improving classroom instruction. The study once again manifested the significance of teaching for conceptual understanding in science education. It also exemplifies how a concept map of a specific scientific concept can also be a useful analytical tool in educational research. © 2015 Wiley Periodicals, Inc. J Res Sci Teach 53: 181–214, 2016.

Recent results of measurements of the Avogadro constant by the method of crystal silicon spheres in connection with the planned transition to a new definition of the basic SI unit, the mole, are discussed.

In their paper, Mohr and Phillips demonstrate that the SI's representation of 'plane angle' as dimensionless rather than as an independent dimensional quantity continues to create confusion. The authors also address perceived problems in terminology regarding numbers of items, such as discrete events or particles. However, their general philosophy of equating the dimensionless 'number of items' to '(number of items) × (item name)' leads to false conclusions, such as that the hertz is equal to 2π radians per second, and therefore not a coherent SI unit. In attempting to specify kinds of entities, the authors introduce descriptive labels into their supposed 'units,' resulting in confusion between number of entities and amount of substance. And, in discussing the mole and related fundamental constants, they incorrectly portray the Avogadro constant as a conversion factor, identically equal to 1, thereby corrupting the relationships between the Boltzmann constant and the universal gas constant, and between the elementary charge and the Faraday constant. In my comment, I explain and correct these and related errors.

The core objective of a chemical composition measurement is to determine its true value. However, when measuring the composition of a macroscopic sample with a large number of atoms or molecules, realizing the true value of the measurand at both the macroscopic and microscopic levels remains an unsolved theoretical problem. We find that the true value of a sample composition exists in any subsample of a homogeneous molecular population of the sample. Here, we propose the Central Law of Measurement of the Amount of Substance: “The homogeneity of a sample molecular population represents the measurement accuracy of the sample composition in an analytical procedure”. The Central Law is based on a homogeneous molecular population axiom in which the molecular composition of a sample is identical for any homogeneous subsample. Furthermore, we point out that, at the microscopic scale, Avogadro’s law does not hold true.

Just as the gram is an Avogadro number of daltons, g = (g/Da) Da, the current definition of the mole can be interpreted as an Avogadro number of entities, as it is often thought of by chemists—and it should be explicitly redefined this way. By introducing a hitherto missing atomic-scale unit for the amount of any substance, the entity (symbol ent), analogous to the dalton for mass, we can then define the mole as: mol = (g/Da) ent—i.e., an Avogadro number of entities. It is argued that the name for the base quantity should be “chemical amount,” by analogy with “electric current.” Recent proposals and counterproposals for redefining the mole (and renaming “amount of substance”) are critically discussed in light of the above intuitively obvious definition.

The Avogadro constant, the number of entities in the amount of substance of one mole, links the atomic and the macroscopic properties of matter. Since the molar Planck constant is very well known via the measurement of the Rydberg constant, the Avogadro constant is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a new definition of the kilogram in terms of a fundamental constant. Here, we describe a new and unique approach for the determination of the Avogadro constant by “counting” the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. This approach has enabled us to apply isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.02214084(18) × 1023 mol−1, is now the most accurate input datum for a new definition of the kilogram.

The mole is a difficult concept. Surveys have shown that even many teachers do not have a proper understanding of it. To help to meet this problem, the SI/IUPAC formulation of the mole is carefully presented and explained. New SI proposals are also briefly discussed.

Amount of substance is one of the base quantities that form the International System of units. The quantity measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons and other particles. In order to count atoms with a relative uncertainty of better than 2 × 10−8, here we formulate the amount of substance measurement homogeneity principle. A consequence of this principle is that the accuracy of a measurement of amount of substance is limited by the homogeneity of the sample. We propose a criterion of sample preparation for the accurate determination of molar mass which is to ensure complete chemical conversions, no fractionation, homogeneity at the molecular level and less contamination. Based on this philosophy, a more accurate molar mass of natural single crystal silicon was achieved. We found that there was an isotope fractionation in the preparation process of the NaOH solution method. It led to an Avogadro constant value 1.0 × 10−6 lower. The corrected value is higher than previous data, and compatible with recent values of the Planck constant.

The Avogadro constant, the number of entities in an amount of substance of one mole, links the atomic and the macroscopic properties of matter. Since the molar Planck constant—the product of the Planck constant and the Avogadro constant—is very well known via the measurement of the Rydberg constant, the Avogadro constant is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a new definition of the kilogram in terms of a fundamental constant. Here, we describe a new and unique approach to determine the Avogadro constant from the number of atoms in 1 kg single-crystal spheres that are highly enriched with the 28 Si isotope. This approach has enabled us to apply isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, N A =6.022 140 82(18)×10 23 mol −1 , is now the most accurate input datum for a new definition of the kilogram.

The mole is the most recent addition to the set of base units that form the International System of Units, although its pre-cursor the ‘gram-molecule’, had been in use by both physicists and chemists for more than 120 years. A proposal has been published recently to establish a new definition for the mole based on a fixed value for the Avogadro constant. This would introduce consistent relative uncertainties for the molar and the atomic masses while making no change to the system of relative atomic masses (‘atomic weights’). Although the proposal would have little impact on the measurement uncertainty of practical work, it has stimulated considerable debate about the mole and the nature of the quantity amount of substance. In this paper, the rationale for the new definition is explained against the background of changes in the way the quantity amount of substance has been used, from its first use during the early development of thermodynamics through to the use of the ‘number of gram-molecules’ at the end of the nineteenth century.

The fundamental concept of the mole stems from the idea of the gram-atom (or gram-molecule): that an amount of one mole of a given substance has an associated mass, in grams, numerically exactly equal to the relative atomic (or molecular) mass of the substance. This means that the particular number of entities comprising one mole, Avogadro’s number, must be exactly equal to the gram-to-dalton mass ratio. Various interpretations of what a mole actually means and how this affects the ideal gas equation depend on how the amount of a given substance, n, is related to the corresponding number of entities, N. We look at three alternatives: (1) the conventional interpretation in which n is directly proportional to N, where the proportionality factor is the reciprocal of the (evidently poorly understood) Avogadro constant; (2) a more easily comprehended alternative in which n is equal to N entities; and (3) an interpretation in which n and N both represent the number of entities, but expressed in different ways. Regardless of these different interpretations, the form of the stoichiometric equations (relating N, n and the total sample mass) and the form of the relationship between the universal gas constant and the Boltzmann constant remain the same.

In this paper, it is argued that the SI system has not carefully enough taken into account the differences that exist between stoichiometry and physics, and because of this neglect forced the kind-of-quantity amount of substance into a false form. The mole is not a unit such as the metre, the kilogram, and the second. It is a “unit” only in the sense in which purely mathematical scaling factors can be called units.

There is a common misconception among educators, and even some metrologists, that the Avogadro constant NA is (or should be) a pure number, and not a constant of dimension N?1 (where N is the dimension amount of substance). Amount of substance is (and always has been) measured as a ratio of other physical quantities, and not in terms of a specified pure number of elementary entities. Hence the Avogadro constant has always been defined in terms of the unit of amount of substance, and not vice versa. The proposed redefinition of the mole in terms of a fixed value of the Avogadro constant is examined, and it is shown that such a redefinition would not bring any significant metrological benefit. It is contended that such a redefinition would only add to the confusion in this field, and so should be rejected.

Most base units in the SI relate to specific sensoric qualities our body is able to observe: space, heat, brightness, etc. The base unit ‘mole’ incorporates intellectual insight: the atomistic perception of the world. This perception is a quintessence of over 300 years of scientific research. The quintessence, from Dalton’s ‘The sceptical chymist’ to Perrin’s Nobel Prize in 1926 and Pauling’s ‘Nature of the Chemical Bond’ in 1939, results in the conclusion that the base unit of the SI quantity ‘amount of substance’ is not the mole but the dimensionless entity.

It is shown here that five base quantities (and the corresponding five base units) of nature are sufficient to define all derived quantities (and their units) and to describe all natural phenomena. The base quantities (and their base units) are: length (m), mass (kg), time (s), temperature (K) and electric charge (C). The amount of substance (mole) is not taken as a base quantity of nature and the Avogadro constant is not considered as a fundamental constant of nature, as they are both based on an arbitrary definition (due to the arbitrary value of 0.012 kg for the mass of 1 mole of C-12 isotope). Therefore, the amount of substance (mole) is moved from the list of base quantities to the category of the supplementary units (to be re-created after its abrogation in 1995). Based on its definition, the luminous intensity (cd) is not a base quantity (unit), therefore it is moved to the list of derived quantities (units). The ampere and coulomb are exchanged by places in the list of base and derived units, as ampere is a speed of coulombs (but SI defines meter, not its speed as a base unit). The five base quantities are re-defined in this paper by connecting them to five fundamental constants of nature (the most accurately known frequency of the hydrogen atom, the speed of light, the Planck constant, the Boltzmann constant and the elementary charge) with their numerical values fixed in accordance with their CODATA 2006 values (to be improved by further experiments).

Proposals on the floor at CIPM are aiming at defining basic units by stipulating a consensus value for a number of fundamental constants. The paper indicates the author’s viewpoint about a number of issues that, in his view, should be better understood before such a choice becomes indisputable. They include the count nature of the Avogadro number; the correct expression of its stipulated numerical value; the check for the consistency of the SI system; the shift to the unit of the experimental uncertainty; the loss of the concept of base unit; the possibility of checking the correctness of the future standards; implications for the future reductions in uncertainty; the meaning of ‘fundamental’ related to the constants; and some lexical problems.

There has been considerable discussion about the merits of redefining four of the base units of the SI, including the mole. In this paper, the options for implementing a new definition for the mole based on a fixed value for the Avogadro constant are discussed. They are placed in the context of the macroscopic nature of the quantity amount of substance and the opportunity to introduce a system for molar and atomic masses with unchanged values and consistent relative uncertainties.

The atomic-scale unit, entity (ent), is defined as the number-specific amount of substance, n/N, the amount of substance of a single entity. This unit is an invariant physical quantity (the reciprocal of the Avogadro constant) that serves as the basis for redefining the SI base unit for amount of substance in a direct and easily understood manner. It is argued here that the kilomole should be the base unit in order to avoid factors of 10−3 or 103 appearing in relationships involving both mass and amount of substance expressed in base units. Since, in a compatible formulation, the amount-specific number of entities, N/n (= NA), is equal to Mu/Da, exactly, where Mu = kg kmol−1 = g mol−1 = Da ent−1, exactly, then NA = (kg/Da) kmol−1 = (g/Da) mol−1 = 1 ent−1, exactly. The kilomole can thus be defined very simply as: , exactly, where , the exact kilomole-to-entity amount ratio, is identical to the kilogram-to-dalton mass ratio: . The Avogadro constant, , does not appear explicitly in the defining equation, its reciprocal having been replaced by one entity. Like the dalton, the entity would be categorized as a unit in use with SI.

There is a common misconception that the Avogadro constant is one of the fundamental constants of nature, in the same category as the speed of light, the Planck constant and the invariant masses of atomic-scale particles. Although the absolute mass of any specified atomic-scale entity is an invariant universal constant of nature, the Avogadro constant relating this to a macroscopic quantity is not. Rather, it is a man-made construct, designed by convention to define a convenient unit relating the atomic and macroscopic scales. The misportrayal seems to stem from the widespread use of the term 'fixed-Avogadro-constant' for describing a redefinition of the kilogram that is, in fact, based on a fixed atomic-scale particle mass. This paper endeavours to clarify the role of the Avogadro constant in current definitions of SI units for mass and amount of substance as well as recently proposed redefinitions of these units—in particular, those based on fixing the numerical values of the Planck and Avogadro constants, respectively. Precise definitions lead naturally to a rational, straightforward and intuitively obvious construction of appropriate (exactly defined) atomic-scale units for these quantities. And this, in turn, suggests a direct and easily comprehended two-part statement of the fixed-Planck-constant kilogram definition involving a well-understood and physically meaningful de Broglie–Compton frequency.

The International System of Units (SI) is founded on seven base units, the metre, kilogram, second, ampere, kelvin, mole and candela corresponding to the seven base quantities of length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity. At its 94th meeting in October 2005, the International Committee for Weights and Measures (CIPM) adopted a recommendation on preparative steps towards redefining the kilogram, ampere, kelvin and mole so that these units are linked to exactly known values of fundamental constants. We propose here that these four base units should be given new definitions linking them to exactly defined values of the Planck constant h, elementary charge e, Boltzmann constant k and Avogadro constant NA, respectively. This would mean that six of the seven base units of the SI would be defined in terms of true invariants of nature. In addition, not only would these four fundamental constants have exactly defined values but also the uncertainties of many of the other fundamental constants of physics would be either eliminated or appreciably reduced. In this paper we present the background and discuss the merits of these proposed changes, and we also present possible wordings for the four new definitions. We also suggest a novel way to define the entire SI explicitly using such definitions without making any distinction between base units and derived units. We list a number of key points that should be addressed when the new definitions are adopted by the General Conference on Weights and Measures (CGPM), possibly by the 24th CGPM in 2011, and we discuss the implications of these changes for other aspects of metrology.

Two synthetic isotope mixtures for the calibration of sulfur isotope amount ratio measurements were gravimetrically prepared from high purity Ag2S materials enriched in 32S, 33S, and 34S. The mixtures were made so as to closely resemble the (natural) isotopic composition of the materials to be “calibrated”. This allowed a totally independent evaluation, on the same samples, of the relative combined uncertainty of: (a) the procedure to perform direct measurements of the amount of substance ratios of gas isotopes in the redetermination of the Avogadro constant and (b) the gravimetric preparation procedure. The result of both procedures, mass spectrometry and gravimetry, agree to a relative uncertainty of 3 × 10−4 for sulfur amount ratio measurements of the major abundant isotopes. Thus it seems that a direct measurement of isotopic gas mixtures (e.g. of natural isotopic composition) is now possible for sulfur—and probably also for other gaseous isotopes—without necessarily having to rely on “calibration” by means of values provided by measurements of gravimetrically prepared isotope mixtures. However, synthetic mixtures may be needed for validation and verification purposes, in particular for quality assurance.

One of the routes to re-determine the Avogadro constant requires ultra-high accuracy isotopic measurements of amount ratios of Si isotopes to 10 -5 reproducibilities on the ratio measurements and calibrating the results by synthetic isotope mixtures prepared to 2 10 -5 relative combined uncertainty. The route to these results is described. followed by a description of the improvement of out knowledge of the Avogadro constant N A through these measurements. The same route has recently been opened for other gases and has opened the way to the establishment of Primary Standards of Measurements' for gas isotopic measurements. It is described how these highly accurate measurements of ratios of amount of substance have considerably contributed to clearer thinking about concepts for measurements of amount of substance. The acquired expertise in measurement instrumentation and measurement procedures can now be extended to a more general use in measurements of isotope amount ratio (i.e. in other elements). It can also be combined with isotope dilution. This latter combination opens up a new route towards a realization of traceability of an amount-of-substance measurement to the SI and to the (measurement procedure and instrumentation leading to) Avogadro constant.

Procedures developed for accurate measurement of amount of substance ratios for gas isotopes, as used to improve our knowledge of the Avogadro constant and checked for quantitative conformity against kinetic gas theory, were used to measure synthetic mixtures of enriched xenon gas isotopes, prepared by (micro)-gravimetry as is usual in the preparation of synthetic gas compound mixtures. This allowed a totally independent evaluation, on the same samples, of the relative combined standard uncertainty of (a) the procedure to perform direct measurements of amount of substance ratios of gas isotopes in the redetermination of the Avogadro constant and (b) the gravimetric preparation procedure. The results of both procedures, mass spectrometry and gravimetry, agree to a relative uncertainty of 2 × 10-3 for amount measurements of the major abundant isotopes. Thus it seems that a direct measurement of isotopic gas mixtures (e.g. of natural isotopic composition) is now possible for xenon isotopes- and probably also for other gaseous isotopes- without necessarily having to rely on ''calibration'' by means of values provided by measurements of gravimetrically prepared isotope mixtures. However, synthetic mixtures may be needed for validation and verification purposes, in particular for quality assurance (QA).

Metrology is the science of measurement and its application. Whenever one performs a measurement one compares the measurand to an appropriate unit. The number of these units has changed since the metre convention in 1875 to 1960 when the 11th CGPM (Conference Generale des Poids et Mesures) decided the actual SI (Systeme International d’Unites). Currently the SI is based on seven units – kilogram for mass, second for time, metre for length, ampere for electric current, Kelvin for thermodynamic temperature, candela for luminous intensity and – since 1971 – mol for amount of substance. Their definition also sometimes changes, due to demands on the unit or the advent of new methods for a possible better realisation. The metre, for instance, was incipiently defined as a part of a meridian of the earth. This definition was impractical to realise, so for the realisation the length between the ends of a platinum bar was used. To overcome the difficulties of the handling and measurement of this length standard, the definition was again revised to the distance between two marks on a new, x-shaped Pt-Ir rod. Although the measurement capabilities grew and even though interferometry was discovered early, the next redefinition took two ages. Eventually, in 1960 the metre was defined by a multiple of the wavelength of the radiation of 86krypton. And since 1983, for the present finally, the metre is defined by a time-of-flight definition: one metre is the distance which light travels in 1/299792458 seconds where this special number is given by the fixed value of the speed of light.

Entitic quantities are quantities, such as entitic number (or number of entities) Ne(B), , entitic mass me(B) or entitic volume Ve(B), relating to a specified ''generalized molecule'' or entity B, such as H (meaning a single atom of hydrogen) or H2O or {(1 - x)H20 + xCH3OH}. Molar quantities are the quotients of an extensive quantity and amount of substance nB, such as molar number Nm {or Avogadro constant L = Ne(B)/n(B)}, molar mass mm(B) {or M(B)}, or molar volume Vm(B), also of an entity B. It is shown that there is no imperative need to retain quantities like amount of substance n, or the Avogadro constant L, or the molar gas constant R, or the SI unit: mole. All of these could be discarded from the equations of physical science, though whether it would be useful to discard them is of course open to question.

The Planck constant, the Avogadro constant and the molar mass of carbon-12 satisfy a compatibility condition: the product of the first two quantities is proportional to the third. Independently fixing any two of these quantities at exact values creates invariant redefinitions of the SI base units for both mass and amount of substance. The third quantity is then determined by the compatibility condition. Of the three possible alternatives, the strategy of fixing the Planck constant to give an invariant redefinition of the base unit for mass together with fixing the Avogadro constant to give an invariant redefinition of the base unit for amount of substance, while necessarily relaxing the exactness constraint on the molar mass of carbon-12, has a number of positive attributes that would seem to make it worth considering along with the other two strategies that each fix the molar mass of carbon-12.

Numerous articles have been published that address problems encountered in teaching basic concepts of chemistry such as the atomic mass unit, Avogadro's number, and the mole. The origin of these problems is found in the concept definitions. If these definitions are adjusted for teaching purposes, understanding could be improved. In the present article, the definitions are discussed, and the following adjustments are suggested: (i) the feature that classifies carbon-12 for the definition as the standard be its abundance, (ii) Avogadro's number should refer directly to the standard nuclide sample, (iii) the definition of the mole be based on Avogadro's number, and (iv) the term amount of substance be replaced by the collection or quantity of microentities. It is also proposed that the definition of the mole is first presented for nuclides and then generalized for poly-isotopic elements and chemical compounds. A possible redefinition of kilogram as a multiple of the standard nuclide mass is also briefly discussed.

The potential role of isotope dilution (ID) in the future organization of traceability and therefore comparability of chemical measurements (amount measurements in SI terms) is described. Essential is that ID (e.g. in isotope dilution mass spectrometry IDMS), directly measuring in our SI unit for amount of substance (the mole), gives matrix-independent results and reduces a complicated chemical measurement to a simple physical measurement. It is possible to borrow from the ultra-high accuracy isotopic measurement techniques needed in the continuous improvement of the Avogadro constant in order to make high accuracy measurements of the amount of substance: both fields have in common the determination of isotope abundance ratios with small but well known total uncertainties (conditions for so-called “absolute” measurements). In addition, the use of such ratio measurements in an isotope dilution procedure for amount measurements seems to constitute a form of direct traceability of amount measurements to the “Avogadro measurement procedure” and therefore to the closest realisation of the mole so far. All of this will have far-reaching consequences: Will enriched isotopes be available in a systematic, continuous, affordable supply to ensure the possibility of isotope dilution in the future? Will simpler and, above all, cheaper isotope mass spectrometers be available for the key laboratories of future measurement networks needed in the organization of the traceability of chemical measurements? Will the difference between “chemical” and “physical” measurements not gradually fade away in the organization of traceability of amount measurements? Is further development and application of IDMS — but also of ID using other isotope-specific measurement techniques — not needed for all elements?

This discussion paper, circulated in advance of the 17th meeting of the Consultative Committee for Amount of Substance, addresses the proposed redefinition of the mole in terms of a fixed numerical value for the Avogadro constant. It gives ten reasons why the Avogadro constant should not be given a fixed numerical value in the International System of Units, noting that there would be no metrological benefit from such a change, and that the proposed redefinition would be more conceptually complex that the current one and divorced from practical measurement and historical background. As the conditions for redefinition of the kilogram have not been met, and no mise en pratique has been produced for the proposed new definition, the paper concludes that the proposal should be rejected.

The International System of Units (SI) is founded on the seven base units metre, kilogram, second, ampere, kelvin, mole and candela corresponding to the seven base quantities length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity. At the 23rd General Conference on Weights and Measures held in Paris in November 2007, Member States of the Metre Convention adopted Resolution 12 in which they recommended (among other things) that National Metrology Institutes and the BIPM ? pursue the relevant experiments so that the International Committee can come to a view on whether it may be possible to redefine the kilogram, the ampere, the kelvin, and the mole using fixed values of the fundamental constants at the time of the 24th General Conference (2011), ? initiate awareness campaigns to alert user communities to the possibility of redefinitions and that the technical and legislative implications of such redefinitions and their practical realizations be carefully discussed and considered. The proposal for such redefinitions, while long envisaged in general terms beginning with Maxwell in 1870, is based in detail on two recent papers by Mills, Mohr, Quinn Taylor and Williams (Metrologia 42 (2005) 227-246 and 43 (2006) 227-246). In these papers we proposed redefining the kilogram, ampere, kelvin and mole so that these units are explicitly linked to exactly known values of the Planck constant h, elementary charge e, Boltzmann constant k and Avogadro constant N A , respectively.

The problems created for chemical measurement by the 1971 inclusion of the thermodynamic ‘mole’ in the Systeme International (SI) measurement units are a salutary lesson to all other measurement disciplines seeking inclusion in the SI. Do not do it! By all means make units useable with the SI but do not surrender basic principles. Chemical measurement has a serious semantic problem. Most analysts, not unreasonably, regard the SI as fundamentally irrelevant as far as the thermodynamic ‘mole’ is concerned and continue to use the earlier chemical mole, understood as an Avogadro number of specified things. However, the users of their measurements do not have this understanding. They examine the SI Brochure [1] to find to their surprise that a ‘mole’ is something quite different, having to do with a thermodynamic quantity puzzlingly named ‘amount of substance’. The next edition of the brochure [2] will make the difference even starker and more inexplicable. The longstanding ambiguity of two ‘moles’ cannot continue into the twenty-first century. Analysts need to consider their options. The term ‘mole’ is unsuitable for clear communication; it has two incompatible meanings. Chemists themselves need to clear up this confusion for it is clear that the SI will not. The solution is simple for metrology in chemistry. All we need is a new name for an Avogadro number of things that cannot be confused with the thermodynamic ‘mole’ and to make it crystal clear that the quantity we measure is a number of things and not the inexplicable thermodynamic construct termed ‘amount of substance’. The new name is obvious. It is an Avogadro number of things, although the obvious common abbreviation will be the avo. It’s equally obvious symbol is Av, following wellaccepted conventions for honouring appropriate scientists, in this case Amedeo Avogadro (1776–1856). The avo is a unit that can be used with the SI but it is not of the SI. It is SI compatible. It is not a base unit. The base unit for its corresponding quantity is one specified thing. Leonard calls it the entity (symbol ent) [3]. As Leonard shows, there are many ways in practice to construct a system of measurement units, with a variety of advantages, disadvantages, and risks. There are a few essential requirements of any practical system of measurement units. The first and highest priorities are that it be simple, concise, clear, and most essential of all, comprehensible to all users. This includes especially the audience to which the measurement results are communicated. A number of things is the simplest and most comprehensible quantity there is. That cannot be said of ‘amount of substance’. The next priority is that it be well anchored. Anchoring chemical measurements in an Avogadro number of things is simple in concept and straightforward, dependent vitally on the specific measurement problem at hand. Its ultimate anchor is the notion of one thing. After four decades, we still do not know how to anchor an ‘amount of substance’ for we still do not know in clear and concise terms what it is. The next priority, and one implied by the previous, is to strive for maximum independence of the base units and quantities. This may be a counsel of perfection, but it is something to strive for. However, there is at least one measurement unit that is independent of all others. It is one thing (or entity). One thing is what it is, quite irrespective of what other measurement units one may choose. If one G. Price (&) PO box 57, Menai, NSW 2234, Australia e-mail: gzprice@ozemail.com.au

New isotope abundance and relative atomic mass (atomic weight) values — with low, hitherto unattained uncertainty—are reported for two previously described silicon reference materials using a well-known method with an improved isotope-ratio mass spectrometer. These new values are directly traceable to the SI, more specifically to the unit for amount of substance, the mole, and independent of the SI unit of mass and of the Avogadro constant. Besides the residual mass-spectrometric uncertainties, these new values depend in effect only on a recently published direct comparison of the cyclotron frequency in a Penning trap of ^"Si'* with that of