Molar mass constant
The molar mass constant, usually denoted as Mu, is a physical constant defined as +1/12 of the molar mass of carbon-12: Mu = M(12C)/12 ≈ 1 g/mol.[1] The molar mass of a substance (element or compound) is its relative atomic mass (atomic weight) or relative molecular mass (molecular weight or formula weight) multiplied by the molar mass constant.
The mole and the atomic mass unit (dalton) were originally defined in the International System of Units (SI) in such a way that the constant was exactly 1 g/mol,[2] which made the numerical value of the molar mass of a substance, in grams per mole, equal to the average mass of its constituent particles (atoms, molecules, or formula units) relative to the atomic mass constant, mu = m(12C)/12 = 1 Da. Thus, for example, the average molecular mass of water is approximately 18.0153 daltons, making the mass of one mole of water approximately 18.0153 grams.
On 20 May 2019, the SI definition of mole changed in such a way that the molar mass constant remains very close to 1 g/mol (for all practical purposes) but no longer exactly equal to it. According to the SI, the value of Mu now depends on the mass of a carbon-12 atom in grams, which must be determined experimentally. The 2022 CODATA recommended value of the molar mass constant is:
Mu = 1.00000000105(31)×10−3 kg⋅mol−1.[3]
This is equal to [1 + (1.05 ± 0.31) × 10−9] g/mol, with a relative deviation of about a part per billion from the former defined value, which is larger than its uncertainty but still small enough to be negligible for practical purposes.
The molar mass constant is important in writing dimensionally correct equations.[4] While one may informally say "the molar mass M(X) of an element X is equal to its atomic weight when expressed in grams per mole", the atomic weight (relative atomic mass) Ar(X) is a dimensionless quantity, whereas the molar mass has the SI coherent unit of kg/mol but is usually given in g/mol or kg/kmol (both equal to 0.001 kg/mol). Formally, M(X) is Ar(X) times the molar mass constant Mu: M(X) = Ar(X) · Mu.
Prior to 2019 revision
[edit]The molar mass constant was unusual (but not unique) among physical constants by having an exactly defined value rather than being measured experimentally. From the old definition of the mole,[5] the molar mass of carbon-12, M(12C), was exactly 12 g/mol. From the definition of relative atomic mass,[6] the relative atomic mass (atomic weight) of carbon-12, Ar(12C), is exactly 12. The molar mass constant was thus given by:
The molar mass constant Mu was (and still is) related to the mass of a carbon-12 atom, m(12C), in grams:
As the molar mass constant had a fixed value, the value of the atomic mass of carbon-12 in grams (and thus the value of the dalton in grams) was dependent on the accuracy and precision of the Avogadro constant.
Post-2019 revision
[edit]Because the 2019 revision of the SI redefined the mole and gave the Avogadro constant NA an exact numerical value, the value of the molar mass constant is no longer fixed, and will be subject to increasing precision with future experimentations. The molar mass constant Mu is now dependent on the experimentally determined atomic mass of carbon-12, m(12C), in grams:
One consequence of this change is that the previously defined relationship between the mass of the 12C atom, the dalton, the kilogram, and the Avogadro number is no longer exact. One of the following had to change:
- The mass of a 12C atom is exactly 12 daltons.
- The number of daltons in a gram is exactly equal to the Avogadro number: i.e., NA = (g/Da) mol−1.
The wording of the 9th SI Brochure[Note 1] implies that the first statement remains valid, which means the second is no longer exactly true. The molar mass constant is still very close to 1 g/mol, but no longer exactly equal to it. Appendix 2 to the 9th SI Brochure states that "the molar mass of carbon 12, M(12C), is equal to 0.012 kg⋅mol−1 within a relative standard uncertainty equal to that of the recommended value of NAh at the time this Resolution was adopted, namely 4.5×10−10, and that in the future its value will be determined experimentally",[7][8] which makes no reference to the dalton and is consistent with either statement.
See also
[edit]Notes
[edit]- ^ A footnote in Table 8 on non-SI units states: "The dalton (Da) and the unified atomic mass unit (u) are alternative names (and symbols) for the same unit, equal to 1/12 of the mass of a free carbon 12 atom, at rest and in its ground state."
References
[edit]- ^ Barry N Taylor (2009). "Molar mass and related quantities in the New SI". Metrologia. 46.
- ^ Mohr, Peter J.; Taylor, Barry N. (2005). "CODATA recommended values of the fundamental physical constants: 2002". Rev. Mod. Phys. 77 (1): 1–107. arXiv:1507.07956. Bibcode:2005RvMP...77....1M. doi:10.1103/RevModPhys.77.1.
- ^ "2022 CODATA Value: molar mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.
- ^ de Bièvre, Paul; Peiser, H. Steffen (1992). "'Atomic Weight' — The Name, Its History, Definition, and Units" (PDF). Pure and Applied Chemistry. 64 (10): 1535–1543. doi:10.1351/pac199264101535.
- ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 114–15, ISBN 92-822-2213-6, archived (PDF) from the original on 2021-06-04, retrieved 2021-12-16
- ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "relative atomic mass (atomic weight)". doi:10.1351/goldbook.R05258
- ^ "Resolutions adopted" (PDF). Bureau international des poids et mesures. November 2018. Archived from the original (PDF) on 2020-02-04. Retrieved 2020-02-04.
- ^ Nawrocki, Waldemar (2019-05-30). Introduction to Quantum Metrology: The Revised SI System and Quantum Standards. Springer. p. 54. ISBN 978-3-030-19677-6.