Reproposition of numerosity as the SI base quantity whose unit is the mole

‘Amount of substance’ was introduced in the end of the 1950s as the physical quantity whose unit of measurement is the mole. Fundamental problems associated with this physical quantity have caused a never-ending discussion that continues to this day. One of the reasons for this is the fact that the expression ‘amount of substance’ is not a good choice, due to its generality and inclusion of the word ‘substance’. Considering that samples of matter commonly handled by chemists are extremely numerous in entities and that the quality of being numerous or many is referred to as numerosity (a concept related to numerical cognition), this concept is reproposed as a replacement for amount of substance. Then, taking into account ongoing discussions toward a redefinition of the mole, the following definition is proposed for this SI base unit: “the mole is the numerosity of a sample of entities numbering exactly 6.022 141 794 × 10²³”. The relationships between four extensive properties of matter (mass, volume, numerosity and number of entities) are detailed and the resulting intensive physical quantities (proportionality constants) are discussed. The concept numerosity is not the product of an invented synonym; furthermore, as a consequence of its generality, it can be used to express the quantity of entities in samples of matter, as well as of light, chemical reactions, etc. The acceptance that mole is the SI unit of numerosity might also solve most of the pedagogic problems associated heretofore with teaching of mole and amount of substance.     

Alternative interpretations of the mole and the ideal gas equation

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.     

Ordinal quantities in clinical laboratory sciences

From an ontological point of view, the concept ??property?? may be defined as ??that which when possessed by an object contributes to it being as it is??. Ordinal quantity is one of the types into which properties may be divided. Ordinal quantity is understood internationally as a ??quantity defined by a conventional measurement procedure, for which a total ordering relation can be established, according to magnitude, with other quantities of the same kind, but for which no algebraic operations among those quantities exist??. The term ordinal quantity may be preceded by an adjective (generic, subgeneric, specific, or individual) to clarify the relation object?Cproperty. Ordinal quantities may have values belonging to binary ordinal scales and polinay ordinal scales.     

Bayesian analysis for very-low-background counting of short-lived isotopes: Lowest minimum detectable quantity

Conventional statistical analyses of counting measurements with a paired-count blank and sample yield unacceptably-large estimates of uncertainty that reduce measurement sensitivity when applied to very-low-background detection systems. An alternative is presented here: Bayesian analysis using longer-duration background measurements, appropriate modeling of the background, and a binomial distribution of decay-induced counts valid even for short-lived isotopes. We develop the needed formulae and demonstrate how the decision level and sample measurement duration are optimized jointly to produce the lowest minimum detectable quantity subject to constraints of specified acceptable risks of false detection and false failure to detect. A frequentist’s interpretation is maintained by using equal-likelihood prior distributions.     

Some metrological aspects of ordinal measurements

Although some measurements can be made on any scale (including a continual scale), cost and speed considerations sometimes tip the scales toward using ordinal measurements. This paper presents a way to evaluate classical metrological characteristics, such as error, uncertainty and precision of single and repeated measurements based on the legitimate basic operations for ordinal data. The only legitimate measurement operations among ordinal variables are limited to equal or greater than/less than, the usual assessment measures such as average, standard deviation cannot be applied. Consequently, in order to receive reliable results and draw valid conclusions from ordinal measurements it is essential to develop and use only the appropriate methods.     

On the use of the ‘uncertainty budget’ to detect dominant terms in the evaluation of measurement uncertainty

In the evaluation of measurement uncertainty, the uncertainty budget is usually used to identify dominant terms that contribute to the uncertainty of the output estimate. Although a feature of the GUF method, it is also recommended as a qualitative tool in MCM by using ‘nonlinear’ equivalents of uncertainty contributions and sensitivity coefficients. In this paper, the use of ‘linear’ and ‘nonlinear’ parameters is discussed. It is shown that when and only when the standard uncertainty of the output estimate is nearly equal to the square root of the sum of the squares of the individual uncertainty contributions, will the latter be a reliable tool to detect the degree of contribution of each input quantity to the measurand uncertainty.     

The mole: definition versus practical use

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.     

Generic division of ‘quantity’ and related terms

In the slow evolution of the International vocabulary of metrology (VIM), the first concept of ‘quantity’ has now been divided generically into ‘ordinal quantity’ and a coordinate primitive without definition and term. An analysis of the concepts by their characteristics is made, and the nature of inheritance is discussed in response to a recent communication in this journal. A completion of the initiated generic division of ‘quantity’ is suggested, and a neoterm for the sister of ‘ordinal quantity’ is offered on the basis of two proposals.     

Computational study of pulsed neutron induced activation analysis of cargo

Pulsed neutron induced activation analysis is a nondestructive technique to detect threats hidden in bulk objects such as cargo pallets, trucks, etc. Isotopic content of cargo can be measured by counting photons emitted with characteristic energies as a result of neutron induced reactions within cargo’s materials. Neutron and gamma radiation transport in active interrogation system consisting of a 14-MeV neutron source, photon detector, and a cargo truck was analyzed with MCNPX code. Gamma ray signatures of cargo with hidden explosive threat were analyzed during the neutron pulse and between neutron pulses for varying system’s geometry and material composition of cargo.     

Failures of the global measurement system. Part 1: the case of chemistry

This discussion puts a case of advocatus diaboli: that the Treaty of the Metre, its associated administrative apparatus and the International System of measurement units (SI) has basically failed for chemical measurement and is largely irrelevant to modern analysis, much of practical measurement in modern economies and much of recent technology. The practical use of the chemical unit termed the mole, the introduction to the SI units of the thermodynamic mole and the invention of a new physical quantity called “amount of substance” are each reviewed with the conclusion that the current means of expressing the results of chemical measurements are unsatisfactory in both practice and theory and are imposing large and readily avoidable costs on all advanced economies.     

Measurement of small quantities: further observations on Bayesian methodology

This article discusses the measurement of the sum of small positive quantities each estimated in separate analyses. It extends criticism recently given of ‘objective Bayesian’ methodology (Accred Qual Assur 15:181–188, 2010) and identifies two troublesome effects: the inherent bias in an analysis for a single quantity is compounded when the measurand is the sum of such quantities, and the precaution of overestimating measurement variability can actually make the resulting interval of measurement uncertainty less reliable! Unacceptable results are obtained. A cause of this behavior is identified, and a distinction between ‘objective’ and ‘subjective’ Bayesian statistics is discussed.     

No prospect for change

A recent discussion by Martin Milton in the November issue of this journal was critical of many published objections to the proposed new International System (SI) measurement units (and in particular the definition of the mole) on the grounds that many objectors had proposed new terms in attempts to clarify thinking and that it is impractical to achieve consensus on such proposals. This discussion in response argues that those criticisms miss the point of the objectors’ arguments and are perhaps more appropriately directed at both the current and the new SI itself. A primary example of a neologism in the SI is the term “amount of substance.” The many substantive problems with the new SI remain unaddressed by its proponents. Many important consequences of exactly fixing multiple inter-dependent fundamental physical constants as the basis of the world’s measurements would appear not to have been considered by the global institutions responsible for the world’s measurement units.     

The prospect of the dalton in the new SI: an educator’s point of view

If the definitions of the kilogram and the mole, based on exact values of the Planck and Avogadro constants, respectively, are accepted within the framework of the new SI, then the current definition of the dalton cannot be retained. Acceptance implies redefinition of the dalton exactly in terms of the kilogram. The redefined, exact dalton is useless in mass spectrometry, and hence, a new quantity for the carbon-12 reference mass would have to be established—against the principle of Ockham’s razor. In order to remove the roots of this awkward concept, the kilogram based on the Planck constant, and the mole, consisting of a particular number of entities equal to the inexactly determined numerical value of gram-to-dalton mass ratio, should be included in the new SI system. Some controversies related to the concept of mole have been also briefly outlined.     

Effect of relative positions of substituents on the mechanism of oxidative coupling of isomeric naphthylaminosulfonic acids

We have investigated the electrochemical behavior of isomeric naphthylaminosulfonic acids in a 0.5 mole/liter sulfuric acid solution on a Pt electrode and the synthesis conditions for polymeric films based on these acids. We have established the electrochemical parameters and we propose a mechanism for anodic oxidation of naphthylaminosulfonic acids. L’viv Polytechnic State University, 12 S. Bandery St., 290646 L’vov-13, Ukraine. Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 33, No. 1, pp. 22–26, January–February, 1997.     

Monte Carlo efficiency calibration of a neutron generator-based total-body irradiator

Many body composition measurement systems are calibrated against a single-sized reference phantom. Prompt-gamma neutron activation (PGNA) provides the only direct measure of total body nitrogen (TBN), an index of the body’s lean tissue mass. In PGNA systems, body size influences neutron flux attenuation, induced gamma signal distribution, and counting efficiency. Thus, calibration based on a single-sized phantom could result in inaccurate TBN values. We used Monte Carlo simulations (MCNP-5; Los Alamos National Laboratory) in order to map a system’s response to the range of body weights (65–160 kg) and body fat distributions (25–60%) in obese humans. Calibration curves were constructed to derive body-size correction factors relative to a standard reference phantom, providing customized adjustments to account for differences in body habitus of obese adults. The use of MCNP-generated calibration curves should allow for a better estimate of the true changes in lean tissue mass that many occur during intervention programs focused only on weight loss.     

Between-examiner reproducibility in manual differential leukocyte counting

In manual–visual differential leukocyte counts, the counting itself may be different depending on the examiner. We estimated the between-examiner (B-E) reproducibility in differential leukocyte counting. During 2 months, daily, after performing manual–visual differential leukocyte counts, two slides with blood films were retained. Next day these two blood films were re-examined by different examiners. For each type of leukocyte the B-E reproducibility was estimated from the 58 pairs of data obtained by four technicians. The B-E coefficient of variation for each type of leukocyte was: basophilocytes, 263.2%; eosinophilocytes, 68.8%; lymphocytes, 32.5%; metamyelocytes, 69.6%; monocytes, 55.0%; myelocytes, 132.5%; and neutrophilocytes, 6.6%. For each type of leukocyte the coefficient of variation is the sought estimate of the average reproducibility due to the “human factor” as a whole, without regard to any examiner in particular. Knowledge of this component of day-to-day imprecision, and its follow-up, may be used to decide corrective actions (training of the examiner, etc.) and to set critical differences to interpret the significance of changes in serial results.     

Comparative DSC study on thermal decomposition of iron sulphates

The objects for the studies of this paper are iron sulfates where the iron has second or third valences and where coordination between iron, sulfur and oxygen is different. DSC technique is used to investigate thermal stability and enthalpy changes when iron compounds are treated in different gas medium. The main objective is to compare thermal stability and enthalpy of iron oxy-sulphate, often detected as an intermediate, with commonly known iron sulphates. DSC curves of samples with equal mass under different gas medium, determining different partial pressure of oxygen in the gas phase, are the base for comparative study of the sample’s thermal properties. Obtained different values of the enthalpy and mass losses and kinetic parameters demonstrate that the stability of oxy-sulphate strongly depended on the value of oxygen partial pressure in the gas phase. The new evidences from the experimental study help to propose the mechanism of the decomposition and to compare some of the iron sulphates properties.     

Some metrological aspects of the comparison between two ordinal measuring systems

The usage of ordinal scales (sometimes called ‘semi-quantitative’ scales) for performing measurements in the area of applied chemical metrology and quality assurance is widespread. This paper presents a method for handling actions such as calibration, measuring systems’ capabilities comparison and reproducibility evaluation as a comparison between two measuring systems (MSs) referring to a known/unknown reference standard. The strength of the agreement between these MSs is evaluated through two known versions of Cohen’s kappa statistics (the traditional one and the modified one). The effectiveness of these statistics from the metrological point of view is examined, and the preferability of the modified kappa statistics is demonstrated via an example.     

LIBS for landmine detection and discrimination

The concept of utilizing laser-induced breakdown spectroscopy (LIBS) technology for landmine detection and discrimination has been evaluated using both laboratory LIBS and a prototype man-portable LIBS systems. LIBS spectra were collected for a suite of landmine casings, non-mine plastic materials, and ‘clutter-type’ objects likely to be present in the soil of a conflict area or a former conflict area. Landmine casings examined included a broad selection of anti-personnel and anti-tank mines from different countries of manufacture. Other materials analyzed included rocks and soil, metal objects, cellulose materials, and different types of plastics. Two ‘blind’ laboratory tests were conducted in which 100 broadband LIBS spectra were obtained for a mixed suite of landmine casings and clutter objects and compared with a previously-assembled spectral reference library. Using a linear correlation approach, ‘mine/no mine’ determinations were correctly made for more than 90% of the samples in both tests. A similar test using a prototype man-portable LIBS system yielded an analogous result, validating the concept of using LIBS for landmine detection and discrimination.     

The mole is an Avogadro number of entities,the macroscopic unit for chemical amount

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.