A new definition for the mole based on the Avogadro constant; a journey from physics to chemistry

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1 A new definition for the mole based on the Avogadro constant; a journey from physics to chemistry Martin Milton NPL The Royal Society, London 24 th January 2012

2 Outline The development of today s understanding of: the quantity amount of substance, the unit mol, and the Avogadro constant. How have we come to a definition whereby we know the mass of a mole, but not the number of entities in it? Is there justification for a change? What would the consequences be? How is the mole realised in practice? some examples of the best uncertainties currently achievable

3 The concept amount of substance Boyle s Law (1662) For a fixed amount of gas kept at a fixed temperature, P and V are inversely proportional Stoichiometry (Lavoisier) the relationship between the amounts of substance that react together, and the products that are formed Law of Multiple Proportions (Dalton 1803) when elements combine, they do so in a ratio of small whole numbers Law of Definite Proportions(Proust 1806) a chemical compound always contains exactly the same proportionof elements by mass Avogadro s Law (1811) Equal volumes of ideal or perfect gases, at the same temperature and pressure, contain the same number of particles, or molecules.

4 The gram-molecule Kilogrammolekueland g-molekuelused by Ostwald and Nernst in their text books in Abbreviation to Mol recorded by Nernst. gramme-molecule-first used in English in the Encyclopaedia Britannica (1893). mole First used in English in the translation of Ostwald s Principles of Inorganic Chemistry (1902).

5 The gram-molecule in use On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat Einstein, 1905 Van t Hoff s Law for the osmotic pressure ΠV= z R T Where z gram-molecules is dissolved in a a volume V Let z=n/n where n suspended particles are present and N signifies the actual number of molecules contained in a gram-molecule The Stokes-Sutherland-Einstein formula RT an A = 6πη D πη

6 The gram-molecule in use On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat Einstein, 1905 Van t Hoff s Law for the osmotic pressure ΠV= z R T Where z gram-molecules is dissolved in a a volume V Let z=n/n where n suspended particles are present and N signifies the actual number of molecules contained in a gram-molecule The Stokes-Sutherland-Einstein formula RT an A = 6πη D πη A new determination of molecular dimensions Einstein, 1906 Calculate the change in viscosity when spheres of radius aare dissolved in a solvent of viscosity η * η η = ( φ ) The total volume of dissolved material per unit volume of solvent φ = πa ρ N M

7 The gram-molecule defined Perrin (1909) It has become customary to name as the gram-molecule of a substance, the massof the substance which in the gaseous state occupies the same volume as 2 grams of hydrogen measured at the same temperature and pressure. Avogadro's proposition is then equivalent to the following: Any two gram-molecules contain the same number of molecules. This invariable number N is a universal constant, which may appropriately be designated Avogadro's Constant." J. B. Perrin, Mouvement brownienetréalité moléculaire, Annalesdechimieet dephysiqeviii 18, (1909). trans: F. Soddy Brownian Movement and Molecular Reality, Taylor and Francis (London) 1910.

8 The Mol in use Stille(PTB) explained in 1955 that Molwas being used in two conceptually different ways. The chemical mass unit for example 1 mol = g of sodium, or 1 mol = g of sodium chloride The number of moles ( frommolzahl)given by the equation: l = ν/ L ν= number of entities L= {N A } Stilleadvocated the use of the Molzahlas a dimensionless quantity rather than the use of the quantitystoffmenge(literally amount of substance ) 1 Mol is the Stoffmengethat contains as many entities as A r (O) g of atomic oxygen. Stille Messen und Rechnen in der Physik 1955

9 Amount of substance Guggenheim.. for special problems it may be advantageous to increase the number of fundamental quantities above the usual number. It can sometimes be useful in dimensional analysis to regard the number of atomsas having dimensions different from a pure number Guggenheim, E. A Units and Dimensions Phil. Mag. 33 pp This quantity was first named Stoffmenge in German and the English translation is amount of substance Guggenheim, E. A The Mole and Related Quantities J ChemEd

10 The 1971 definition of the mole The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in kilogramme of carbon 12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, or other particles, or specified groups of such particles. resolved the confusion arising from the use of both g-mol and kg-mol 12 C and 16 O basis introduced dimensional analysis to chemistry. 14 th CGPM, 1971 McGlashan, Metrologia, 1995, 31,

11 The atomic mass scale The N measured atomic masses are related by the N-1 ratios A r (X)/A r (Y). So we fix the value of the N th ratio A r ( 12 C). m u A r ( 12 C) m( 12 C) A r (X) m(x)

12 Atomic mass unit Atomic masses and fundamental constants atomic level m e A r (e)/a r ( 12 C) m( 12 C) Fixed value Mass A r ( 12 C) m u Mass of the electron Mass of carbon-12

13 the mole (present definition) macroscopic M( 12 C) A r ( 12 C) M u 10-3 kg mol -1 atomic level m e A r (e)/a r ( 12 C) m( 12 C) A r ( 12 C) m u Fixed value Mass

14 the mole (present definition) macroscopic M( 12 C) A r ( 12 C) M u N A N A atomic level m e A r (e)/a r ( 12 C) m( 12 C) A r ( 12 C) m u Fixed value Mass

15 Why change the definition of the mole? There is very little initiative for any change from the communities of users of the mole. there is momentum behind the proposal for a new SI which could include a fixed value for N A A possible rationale for change The mole has been derived from the gramme-molecule the amount of substance of 12g of 12 C. We know the exact mass of a mole (of 12 C), do not know the exact number of entities N A has some uncertainty Is this sufficient to motivate a change?

16 the mole (present definition) macroscopic M( 12 C) A r ( 12 C) M u N A N A atomic level m e A r (e)/a r ( 12 C) m( 12 C) A r ( 12 C) m u Fixed value Mass

17 the mole (new definition) macroscopic M( 12 C) A r ( 12 C) M u Fixing N A means that another quantity in this system has to be determined experimentally. N A N A atomic level m e A r (e)/a r ( 12 C) m( 12 C) A r ( 12 C) m u Fixed value Mass

18 A new definition for the mole The proposed new definition would reverse the present definition specify the number of entities in one mole equal to N A exactly. some uncertainty in the mass of one mole one mole of carbon-12 = 12g +/-u(α 2 ). The molar masses and the atomic masses will have the same (relative) uncertainties. A single entity will be an exact amount of substance. Both approaches will be the same in practice to within +/-u(α 2 )

19 Possible definition 201X? 201X The mole is the unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles; its magnitude is set by fixing the numerical value of the Avogadro constant to be equal to exactly X when it is expressed in the unit mol The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in kilogramme of carbon 12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, or other particles, or specified groups of such particles.

20 The debate about a new definition for the mole Many users are confused about the existing use of the mole. The mole has always been used in conceptually different, but equivalent ways chemical mass unit number of moles amount of substance n= m/ A r (X) M u l = ν / {N A } n= ν / N A Much of the discussion originates from authors who believe that one of these is correct to the exclusion of the others. Would a change in the definition put an end to this discussion?

21 The Avogadro constant Invention of new physical methods: diffusion, Brownian motion, oil drop Improvement in X-ray wavelength measurements Atomic weight and chemical purity problems with Silicon U(M M ) contributes 61% of the published uncertainty of the 2003 natural Si result Becker, Rep Prog Phys 2001

22 Compound CIPM 81/91 formula Giacomo et al (1982) N O High accuracy measurements (I) the composition of the atmosphere Revised values (2004) To be published ± (Calculated by difference) ± NIST (1970) Ar ± Kim et al (2004) CO ± Metrologia 18 (1982) Metrologia 41 (2004) ± Measured ± NIST (1970) ± expanded uncertainties (k=2) Measurement Nitrogen mole fraction in dry 10 Pure Pure CO2 air directly by GC/TCD Pure Ar Pure O2 O Pure N2 N CH/N % 5 % CO2/N % CH4/N CH/N % CO2/N /N % + CO % O2+ + N2Balance % CH % Ar Relative uncertainty of 60 parts-per-million achieved with respect to standards prepared gravimetrically Courtesy of Dr Jin SeogKim, KRISS, Korea

23 Compound CIPM 81/91 formula Giacomo et al (1982) N O High accuracy measurements (I) the composition of the atmosphere Revised values (2004) To be published ± (Calculated by difference) ± NIST (1970) Ar ± Kim et al (2004) CO ± Metrologia 18 (1982) Metrologia 41 (2004) ± Measured ± NIST (1970) ± expanded uncertainties (k=2) Measurement Nitrogen mole fraction in dry 10 Pure Pure CO2 air directly by GC/TCD Pure Ar Pure O2 O Pure N2 N CH/N % 5 % CO2/N % CH4/N CH/N % CO2/N /N % + CO % O2+ + N2Balance % CH % Ar Relative uncertainty of 60 parts-per-million achieved with respect to standards prepared gravimetrically Courtesy of Dr Jin SeogKim, KRISS, Korea

24 Compound CIPM 81/91 formula Giacomo et al (1982) N O High accuracy measurements (I) the composition of the atmosphere Revised values (2004) To be published ± (Calculated by difference) ± NIST (1970) Ar ± Kim et al (2004) CO ± Metrologia 18 (1982) Metrologia 41 (2004) ± Measured ± NIST (1970) ± expanded uncertainties (k=2) Measurement Nitrogen mole fraction in dry 10 Pure Pure CO2 air directly by GC/TCD Pure Ar Pure O2 O Pure N2 N CH/N % 5 % CO2/N % CH4/N CH/N % CO2/N /N % + CO % O2+ + N2Balance % CH % Ar Relative uncertainty of 60 parts-per-million achieved with respect to standards prepared gravimetrically Courtesy of Dr Jin SeogKim, KRISS, Korea

25 High accuracy measurements (II) highly pure metals Raw Zn % 16 determined impurities Vacuum distilled Zn % 43.0 mg/kg 0.5 mg/kg 38.5 kg/mm 2 Vickers micro hardness 32.6 kg/mm 2 BAM-M601 w [mg/g] Cd 0.55 ± 0.06 Fe 2.20 ± 0.09 Cu 1.89 ± 0.11 Tl 2.25 ± 0.09 Pb 15.7 ± 0.3 Courtesy of Dr Heinrich Kipphardt, BAM, Germany

26 High accuracy measurements (II) highly pure metals Raw Zn % 16 determined impurities Vacuum distilled Zn % 43.0 mg/kg 0.5 mg/kg 38.5 kg/mm 2 Vickers micro hardness 32.6 kg/mm 2 BAM-M601 w [µg/g] Cd 0.55 ± 0.06 Fe 2.20 ± 0.09 Cu 1.89 ± 0.11 Tl 2.25 ± 0.09 Pb 15.7 ± 0.3 Courtesy of Dr Heinrich Kipphardt, BAM, Germany

27 Summary The mole and the Avogadro constant Emergence of ideas of stoichiometry and thermodynamic ensemble (18 th and 19 th centuries) Accurate chemical measurement (21 st century) The mole has been used in conceptually different ways chemical mass unit number of moles amount of substance At present, we know the mass of a mole (of 12 C), but not the number of entities. is there sufficient momentum behind proposals to change? where should u(α 2 ) lie?

28 Acknowledgements Dr Bernd Güttler(PTB) Prof Ian Mills The National Measurement System is the UK s national infrastructure of measurement

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