Why is ‘amount of substance’ so poorly understood? The mysterious Avogadro constant is the culprit!

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.     

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.     

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.     

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.     

The kinetics of the decarboxylation of n-butylmalonic acid in alkanols and amines

Rate constants and activation parameters are reported for the decarboxylation of n-butylmalonic acid in four normal alkanols (hexanol? 1, octanol? 1, decanol? 1, and dodecanol? 1) and in five amines (aniline, N-methylaniline, N-ethylaniline, N-n-propylaniline, and N-n-butylaniline). Both ΔH? and ΔS? of the reaction in both homologous series decrease regularly with increasing length of the hydrocarbon chain of solvent. If we compare data for the reaction in alkanol–amine pairs containing the same total number of carbon atoms in the molecule, we find that the ΔH? values are identical, but that the value of ΔS? is 0.8 eu/mole higher for the reaction in the amines as compared with the alcohol. The rate constant, at all temperatures, is 1.5 times as large in the amine as it is in the corresponding alcohol. Empirical equations are deduced relating the parameters ΔH? ΔS? ΔG? and k of the reaction to the parameters n and T, where n is the total number of carbon atoms in the solvent molecule and T is the absolute temperature. The results reported herein are compared with previously reported data for malonic acid.     

Mass transfer in the gas phase during top-blowing with plasma jets

Deoxidation of copper melts by hydrogen has been investigated experimentally by top-blowing with argon-hydrogen plasma jets. The course of the deoxidation process has been described mathematically using kinetic laws. The overall divided course of the process can be examined in live partial steps, which are hydrogen transport within the gas phase, hydrogen transport within the melt, oxygen transport within the melt, reaction between hydrogen and oxygen, and H₂O transport within the gas phase. Based on these five elementary processes, an equation for the velocity of deoxidation has been derived. The values of the rate of deoxidation resulting from this equation, in combination with the mass-transter coefficients valid for this process, have been compared to the experimental data. The results of this study verify those of former investigations on vaporization of elements out of copper melts. The mass-transfer coefficients are the same, when the local activity differences are used as the driving force for mass transport in a system. This means that the surface-renewal theory is valid, when mass-transfer coefficients are defined in this way. This is the case, at least, when metallic melts are subjected to top-blowing by plasma jets.Nomenclature a activity (a _i =x _{i i} ) - A _c (m²) effective mass-transfer area - D(m) characteristic length, such as diameter - D _r(m²/s) diffusion coefficient - H(Cu) oxygen dissolved in copper - k _g (mol/m²s) mass-transfer coefficient in the gas phase [k _g (i) mass-transfer coefficient for speciesi] - k _N (mol/m²s) mass-transfer coefficient in the melt phase - K _i = (x _i /y _i )_eq equilibrium coefficient (distribution coefficient) - n _N (mol) mole number of the melt phase - n _G (mol) mole number of the gas phase - n _i (mol/s) mole flow of speciesi - O(Cu) oxygen dissolved in copper - p(N) momentum flow - t(s) time - T (°C or K) temperature;T _G : in the gas,T _s : in the melt,T ^f : at the phase interface - x _i (mol/mol) concentration in the melt - y _i , (mol/mol) concentration in the gas phase - activity coefficient     

Low resolution and high resolution MS for studies on the metabolism and toxicological detection of the new psychoactive substance methoxypiperamide (MeOP)

In 2013, the new psychoactive substance methoxypiperamide (MeOP) was first reported to the European Monitoring Centre for Drug and Drug Addiction. Its structural similarity to already controlled piperazine designer drugs might have contributed to the decision to offer MeOP for online purchase. The aims of this work were to identify the phase I/II metabolites of MeOP in rat urine and the human cytochrome P450 (CYP) isoenzymes responsible for the initial metabolic steps. Finally, the detectability of MeOP in rat urine by gas chromatography–mass spectrometry (GC‐MS) and liquid chromatography coupled with multistage mass spectrometry (LC‐MSⁿ) standard urine screening approaches (SUSAs) was evaluated. After sample preparation by cleavage of conjugates followed by extraction for elucidating phase I metabolites, the analytes were separated and identified by GC‐MS as well as liquid chromatography‐high resolution‐tandem mass spectrometry (LC‐HR‐MS/MS). For detection of phase II metabolites, the analytes were separated and identified after urine precipitation followed by LC‐HR‐MS/MS. The following metabolic steps could be postulated: hydrolysis of the amide, N‐oxide formation, N‐ and/or O‐demethylation, oxidation of the piperazine ring to the corresponding keto‐piperazine, piperazine ring opening followed by oxidation of a methylene group to the corresponding imide, and hydroxylation of the phenyl group. Furthermore, N‐acetylation, glucuronidation and sulfation were observed. Using human CYPs, CYP1A2, CYP2C19, CYP2D6, and/or CYP3A4 were found to catalyze N‐oxide formation and N‐, O‐demethylation and/or oxidation. Mostly MeOP and N‐oxide‐MeOP but to a minor degree also other metabolites could be detected in the GC‐MS and LC‐MSⁿ SUSAs. Copyright © 2015 John Wiley & Sons, Ltd.     

On what terms and why the thermodynamic properties of polymer solutions depend on chain length up to the melt

Theoretical considerations based on chain connectivity and conformational variability of polymers have led to an uncomplicated relation for the dependence of the Flory–Huggins interaction parameter (χ) on the volume fraction of the polymer (?) and on its number of segments (N). The validity of this expression was tested extensively with vapor‐pressure measurements and inverse gas chromatography (complemented by osmotic and light scattering data from the literature) for solutions of poly(dimethylsiloxane) in thermodynamically vastly different solvents such as n‐octane (n‐C₈), toluene (TL), and methylethylketone (MEK) over the entire range of composition for at least six different molecular masses of the polymer. The new approach is capable of modeling the measured χ (?, N), regardless of the thermodynamic quality of the solvent, in contrast to traditional expressions, which are often restricted to good solvents but fail for bad mixtures and vice versa. At constant polymer concentration, the χ values were lowest for n‐C₈ (best solvent) and highest for MEK (Θ solvent); the data for TL fell between them. The influences of N depended strongly on the thermodynamic quality of the solvent and were not restricted to dilute solutions. For good solvents, χ increased with rising N. The effect was most pronounced for n‐C₈, where the different curves for χ (?) fanned out considerably. The influences of N were less distinct for TL, and for MEK they vanished at the (endothermal) θ temperature. For worse than θ conditions, the χ values of the long chains were less than that of the short ones. This change in the sign of N agreed with this concept of conformational relaxation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1601–1609, 2004     

The avo (Av), gali (G), entity (ent) and exact dalton

The Avogadro constant is generally considered to be the relevant physical invariant for stoichiometry, intimately associated with the SI base unit for the amount of a specified substance. Unfortunately, it has dimensions of reciprocal amount rather than of amount itself, and this appears to be the source of the widespread confusion permeating this subject. It would make sense, instead, to use its reciprocal—an amount consisting of a single representative entity—as the fundamental invariant for amount. Major simplifications in comprehension then result. In particular, the mole would be redefined in a straightforward way as a designated exact number of elementary entities, making stoichiometric calculations much more easily comprehended. Unfortunately, acceptance by the CIPM of recent CCU recommendations for redefining the mole and kilogram (while keeping the inexactly known carbon-12-based dalton definition) would inject even more confusion into this subject, because the proposed definitions violate a basic compatibility condition relating the mole, kilogram and dalton, stemming from the fundamental concept of the mole itself. However, there are a number of alternative mole-concept-compatible and easily comprehended definitions worthy of consideration, where, in each case, a compatible dalton must be an exact sub-multiple of the (redefined) kilogram. These alternatives should receive much wider discussion before final decisions are made in the major restructuring of the international system of units.     

Coil-to-globule transitions of interfacial copolymers in better than theta-solvents

Experimental studies of the coil-to-globule transitions exhibited in better than -solvents by interfacial copolymers ofN-isopropylacrylamide and acrylamide imply that a lower bound for the value of n in then-clusters of poly(N-isopropylacrylamide) (PNIPAM) is 3. The corresponding upper bound is therefore likely to be 5 or 6. Statistical copolymers of PNIPAM containing upwards of 0.75 mole fraction of acrylamide (whose homopolymer does not itself displayn-clustering) exhibited this transition, which disappeared at higher mole fractions of acrylamide. Interfacial homopolymers ofN-ethylacrylamide and its statistical copolymers withN-isopropylacrylamide exhibitedn-clustering at all compositions.     

Kinetics of heat release during the reaction ofn-decane with nitrogen dioxide in the liquid phase

The rates of heat release in the nitrogen dioxide—n-decane system at a molar ratio of nitrogen oxides ton-decane (β) from 2.4·10⁻³ to 3.1 and gaseous volumes per mole ofn-decane (V(g)) equal to 0.05–4.5 were studied in the 55.2–92.8 °C temperature range. The initial rate of the process is determined by the interaction of NO₂ withn-decane. The equilibrium constants of dissociation of N₂O₄ inn-decane and Henry's constants of NO₂ and N₂O₄ in ann-decane solution were determined by complex analysis of the thermodynamic equilibrium in the NO₂—n-decane system and dependences of the initial rates onV(g) and β. The experimentally observed self-acceleration of the process in the region of high β and lowT values was suggested to be due to the reaction of N₂O₄ with intermediate oxidation products. The rate constants of the reaction of NO₂ withn-decane were compared with analogous values determined in its mixtures with HNO₃ solutions. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1789–1794, October, 1997.     

Development of a certified reference material of nitrous oxide in nitrogen for emission gas measurement

A reference gas mixture of nitrous oxide (N₂O) in nitrogen, filled in a 10-L high-pressure aluminum alloy gas cylinder, has been developed as a certified reference material for emission measurement of exhaust gases from automobiles. As an example of certified values, mole fraction of N₂O is 302.36 μmol/mol. An electronic mass comparator with a home-made automatic cylinder exchanger, gas-filling equipment, and a gas chromatograph with a thermal conductivity detector have been used for the production of this CRM. The gas chromatographic analysis has of sufficient precision. The mole fraction of N₂O has good long-term stability for 10 years and is independent of inner pressure in the gas cylinder. As these results, a relative expanded uncertainty (coverage factor is 2) of the certified value has become 0.28 %. This sufficiently small uncertainty of the N₂O mole fraction will be advantageous in the calibration of analytical instruments for emission gas analysis.     

Quasielastic light-scattering studies of micellar sodium dodecyl sulfate solutions at the low concentration limit

Correlation functions of scattered light intensity of carefully purified sodium dodecyl sulfate (SDS) solutions were measured as a function of tenside concentration and NaCl concentration of the aqueous phase. The correlation functions were analyzed by taking into account the influence of the Coulomb interaction between the micelle (macroion) and small electrolyte ions on the diffusion coefficient. Values of the hydrodynamic radius, the aggregation number, and the effective surface charges were obtained. The aggregation number increases from N = 27 to N = 95 upon increasing the NaCl concentration from 0 to 0.05 mole per liter, while it remains constant when the salt concentration increases further up to 0.2 mole per liter. The effective charge of the micelles decreases with increasing NaCl content in the whole concentration region studied. These results could be interpreted qualitatively in terms of a model which relates the existence of an equilibrium size of the micelles to the balance between hydrophobic and Coulomb interactions. Our results lead to the conclusion that at least up to an NaCl concentration of 0.2 mole per liter the SDS-micelles exhibit an oblate spherical shape rather than a cylindrical form.     

Why the invariant atomic-scale unit,entity, is essential for understanding stoichiometry without ‘Avogadro anxiety’

The Avogadro constant is generally considered to be the relevant physical invariant for stoichiometry, intimately associated with the SI base unit for the amount of a specified substance. Unfortunately, it has dimensions of reciprocal amount rather than of amount itself, and this appears to be the source of the widespread confusion permeating this subject. It would make sense, instead, to use its reciprocal—an amount consisting of a single representative entity—as the fundamental invariant for amount. Major simplifications in comprehension then result. In particular, the mole would be redefined in a straightforward way as a designated exact number of elementary entities, making stoichiometric calculations much more easily comprehended. Unfortunately, acceptance by the CIPM of recent CCU recommendations for redefining the mole and kilogram (while keeping the inexactly known carbon-12-based dalton definition) would inject even more confusion into this subject, because the proposed definitions violate a basic compatibility condition relating the mole, kilogram and dalton, stemming from the fundamental concept of the mole itself. However, there are a number of alternative mole-concept-compatible and easily comprehended definitions worthy of consideration, where, in each case, a compatible dalton must be an exact sub-multiple of the (redefined) kilogram. These alternatives should receive much wider discussion before final decisions are made in the major restructuring of the international system of units.     

Microsolvated and Chelated Butylzinc Cations: Formation,Relative Stability,and Unimolecular Gas‐Phase Chemistry

Solutions of butylzinc iodide in tetrahydrofuran, acetonitrile, and N,N‐dimethylformamide were analyzed by electrospray ionization mass spectrometry. In all cases, microsolvated butylzinc cations [ZnBu(solvent)_n]⁺, n=1–3, were detected. The parallel observation of the butylzincate anion [ZnBuI₂]^? suggests that these ions result from disproportionation of neutral butylzinc iodide in solution. In the presence of simple bidentate ligands (1,2‐dimethoxyethane, N,N‐dimethyl‐2‐methoxyethylamine, and N,N,N′,N′‐tetramethylethylenediamine), chelate complexes of the type [ZnBu(ligand)]⁺ form quite readily. The relative stabilities of these complexes were probed by competition experiments and analysis of their unimolecular gas‐phase reactivity. Fragmentation of mass‐selected [ZnBu(ligand)]⁺ leads to the elimination of butene and formation of [ZnH(ligand)]⁺. In marked contrast, the microsolvated cations [ZnBu(solvent)_n]⁺ lose the attached solvent molecules upon gas‐phase fragmentation to produce bare [ZnBu]⁺, which subsequently dissociates into [C₄H₉]⁺ and Zn. This difference in reactivity resembles the situation in organozinc solution chemistry, in which chelating ligands are needed to activate dialkylzinc compounds for the nucleophilic addition to aldehydes.     

The Radical Anions of N,N′-Dicyanoquinone Diimines,a New Class of Electron Acceptors

The radical anions of 12 N,N′-dicyanoquinone diimines, a new class of electron acceptors, hace been characterized by their hyperfine data with the use of ESR and ENDOR spectroscopy. The largest coupling constant (0.30–0.45 mT), due to the two ¹⁴N nuclei in the exocyclic positions, gives rise to a conspicuous broadening of the peripheral ESR lines by an incomplete averaging of the hyperfine anisotropy. The most plausible interpretation of the experimental results for the radical anions of N,N′-dicyano- 1,4-benzoquinone diimine ( 1 ) and N,N′-Dicyano-9,10-anthraquinone diimine ( 9 ) is in terms of both ‘syn’- and ‘anti’-configurations contributing to the ESR and ENDOR spectra and having equal proton- and ¹⁴N-coupling constants. The π-spin distribution in the radical anions of N,N′-dicyanoquinone diimines is compared with those in the analogous ions of tetracyanoquinodimethanes and quinones.     

Lithiation of diene polymers

It was found that the metallation of diene polymers with n-butyllithium in n-heptane takes place in the presence of a tert amine, i.e. N,N,N′,N′-tetramethylethylenediamine. Butyllithium was added to the diene polymer in n-heptane in the presence of an equimolar amount of the amine, and the mixture was allowed to react at 80°C. for 60 min. under nitrogen. As a result, 27% and 9% per monomer unit for polybutadiene and polyisoprene, respectively, were metallated. The effects of the concentrations of the diene polymer, butyllithium, and the amine on the reaction were studied at 80°C., and the reaction mechanism was discussed. The overall rate of metalation was proportional to the diene polymer concentration and to the square root of the butyllithium concentration. The overall activation energies of metalation were 6.6 and 8.4 kcal./mole for polybutadiene and polyisoprene, respectively. Many kinds of polymer derivative were obtained by treating the metalated polymers with various reagents, such as carbon dioxide, Michler's ketone, trimethylchlorosilane, triphenylchlorosilane, benzaldehyde, and pyridine.