Status of the redefinition of the mole Dr. Bernd Güttler Physikalisch-Technische Bundesanstalt (PTB) Germany CCQM WG on the mole Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 1 of X Definition of the mole "Let us generally refer to the weight in Wilhelm Ostwald grams of a substance that is numerically identical to the molecular weight of that substance, as one mole...” relation to the international system of units (later called SI) is established unit of mass, no relation to particle number at this stage Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 2 of X Definition of the mole The mole, mol, 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; "Let us generally refer to the weight in its magnitude is set by fixing the grams of a substance that is numerically numerical value of the Avogadro identical to the molecular weight of that constant to be equal to exactly 6.022 substance, as one mole...” 141X·1023 when it is expressed in the unit mol-1. Ostwald 1893 ? proposed definition Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 3 of X Definition of the mole "Let us generally refer to the weight in grams of a substance that is numerically M(X) = Ar(X) x Mu identical to the molecular weight of that substance, as one mole...” nx = Mx/M(X) M(X) molar mass of X Ar(X) Σ rel. atomic masses (dimension less) of X Mu molar mass constant (10-3 kg/mol) Ostwald 1893 Mx mass of X Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 4 of X Molecules per mole: Avogadro's Constant η viscosity r particle radius x average displacement Albert Einstein Jean Perrin "Any two gram-molecules always contain the same number of molecules. This invariable number N is a universal constant which may appropriatly be designated Avogadro's constant." Perrin. J.: Brownian Motion and Molecular Reality aus: Annales de Chimie et de Physique 18, 1-114 (1909) Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 5 of X dual interpretation and base quantity "Stoffmenge": "First of all it (the mole) is understood as a chemical mass unit in accordance with Ostwald's view of a continuum and has an individual value for each type of molecule. The other understanding of the "mole" is that of a number of atoms or molecules that is comprised in a mole.“ Ulrich Stille When you intend to find a more precise wording, for example by introducing a base quantity "Stoffmenge" (amount of substance) it can be considered as the numerical value of the amount of substance." Stille U.: Messen und Rechnen in der Physik, Vieweg & Sohn S. 117f. (1955) Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 6 of X Definition of the mole quantification "Let us generally refer to the weight in 1. The mole is the amount of substance grams of a substance that is numerically of a system which contains as many identical to the molecular weight of that elementary entities as there are atoms in substance, as one mole...” 0.012 kilogram of carbon 12; its symbol is “mol”. 2. When the mole is used, the elementary entities must be specified identification and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. NA Ostwald 1893 current definition (1971) Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 7 of X Definition of the mole 1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is “mol”. 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. current definition (1971) Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 8 of X Definition of the mole 1. The mole is the amount of substance of a system which contains as many M(X) = Ar(X) x Mu elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol M(X) = m(X) x NA is “mol”. 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, m(X) Ar(X) mu electrons, other particles, or specified 12 groups of such particles. mu m( C)/12 NA Avogadro constant current definition (1971) now: u(Mu) = 0 -8 u(NA) = 2 x 10 Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 9 of X Definition of the mole 1. The mole is the amount of substance • In the new SI all 7 base units will be of a system which contains as many definitiondefined by contains constants artefacts: of nature (SI elementary entities as there are atoms in reference constants), 0.012 kilogram of carbon 12; its symbol • number of entities depends on is “mol”. • thekg respective prototype SI reference constants will have exact numerical values, • In this definition, it is understood that 2. When the mole is used, the unbound atoms of carbon 12, at rest elementary entities must be specified • the new SI is expected to be more stableand in since their thereground arestate no artefacts, are referred and may be atoms, molecules, ions, to. electrons, other particles, or specified involved. groups of such particles. current definition (1971) demands for redefinition Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 10 of X Definition of the mole 1. The mole is the amount of substance The mole, mol, is the unit of amount of of a system which contains as many substance of a specified elementary elementary entities as there are atoms in entity, which may be an atom, molecule, 0.012 kilogram of carbon 12; its symbol ion, electron, any other particle or a is “mol”. specified group of such particles; 2. When the mole is used, the its magnitude is set by fixing the elementary entities must be specified numerical value of the Avogadro and may be atoms, molecules, ions, constant to be equal to exactly 6.022 electrons, other particles, or specified 141X·1023 when it is expressed in the groups of such particles. unit mol-1. current definition (1971) proposed definition no artefacts! Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 11 of X Definition of the mole The mole, mol, is the unit of amount of substance of a specified elementary M(X) = Ar(X) x Mu entity, which may be an atom, molecule, ion, electron, any other particle or a M(X) = m(X) x NA specified group of such particles; n = M /M(X) its magnitude is set by fixing the x x numerical value of the Avogadro constant to be equal to exactly 6.022 nx = Nx/NA 141X·1023 when it is expressed in the unit mol-1. N(X) number of particles X -10 proposed definition thennow:: u((MMuu))≤=70 x 10 -8 u((NNAA)) == 30 x 10 Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 12 of X mise en pratique of the mole A mise en pratique for the definition of a unit is a set of instructions that allows the definition to be realized in practice at the highest level. The mise en pratique should describe the primary realizations based on top-level primary methods. CCU would like to see some homogeneity in their content. (report of the 97th meeting of the CIPM (2008)). Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 13 of X mise en pratique of the mole single-electron (SET) pump semiconductor wire The mole can be realized by single-electron detector counting NA electrons in a conductor line with a SET device. N / N nel el A Identification: elementary entities are electrons A semiconductor single-electron-tunneling (SET) pump. Quantification: by sequential counting I Nel ef other units involved: S. P. Giblin et al. Nature Communications 3.930 none DOI 10.1038 ncomms 1935 from: U. Siegner, PTB Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 14 of X mise en pratique of the mole Traceability transfer standard nx cx Vsol primary standard Quantification M n X R(X) x M(X) primary level Identification Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 15 of X the kilogram artefact problem Mass values of the prototypes in 1889, 1950 and 1990 100 red: International Prototype 80 green: BIPM, Official Copies orange: no.25, BIPM , for special use 60 black: national prototypes 40 50 µg 20 /µg 0 m -20 -40 -60 -80 -100 1880 1900 1920 1940 1960 1980 2000 year 8 M(Si)Vsphere NA 3 International Avogadro Cooperation (IAC) M Sia Symposium at 250th ACS National Meeting, Boston, MA, August 19, 2015 page 16 of X Avogadro's constant via Bragg's relationship NSi= VSphere/ VAtom nSi = NSi/NA = MSi/M(Si) NA = (M(Si)/MSi) (VSphere/ VAtom) 8 M(Si)Vsphere NA 3 M Si a 2 cAr (e)M u N Ah 2R http://www.msm.cam.ac.uk/phase- see J. Stenger & E.O. Göbel, Metrologia 49 (2012), L25–L27 trans/2003/MP1.crystals/MP1.crystals.html th page 17 of X Symposium at 250 ACS National Meeting, Boston, MA, August 19, 2015 International Avogadro Coordination Optical sphere interferometer NMIJ, PTB, NMIA sphere Multicollector ICPMS 8 M(Si)V PTB, NMIJ, NIST NA 3 MSi a Surface layer : XRR, XRF, XPS, opt.