Molar mass constant

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The molar mass constant, symbol Mu, is a physical constant which relates atomic weight and molar mass. Its value is defined to be 1×10–3 kg/mol.[1]

The molar mass constant is important in writing dimensionally correct equations.[2] It is common to see phrases such as

The molar mass of an element is the atomic weight in grams per mole.

However atomic weight is a dimensionless quantity, and cannot take the units of grams per mole. Formally, the operation is the multiplication by a constant which has the value 1 g/mol, that is the molar mass constant.

The molar mass constant is unusual (but not unique) among physical constants by having an exactly defined value rather than being measured experimentally. It is fixed by the definitions of the mole and of relative atomic mass. From the definition of the mole,[3] the molar mass of carbon 12 is exactly 12 g/mol. From the definition of relative atomic mass,[4] the relative atomic mass of carbon 12, that is the atomic weight of a sample of pure carbon 12, is exactly 12. The molar mass constant is given by

M_{\rm u} = {{M({}^{12}{\rm C})}\over{A_{\rm r}({}^{12}{\rm C})}} = {1\ {\rm g/mol}}

The speed of light, the electric constant and the magnetic constant are other examples of physical constants whose values are fixed by the definitions of the International System of Units (SI),[1] in these cases by the definitions of the metre[5] and the ampere.[6]

The relatively simple value of the molar mass constant in SI units is also a consequence of the way in which the International System of Units is defined. It is possible to quote the value of the molar mass constant in other units: for example, it is equal to (1/453.592 37) lb/mol ~ 2.204 623 262 × 10−3 lb/mol.[7] But it is also 1 lb/lbmol or 1 kg/kgmol, much simpler than even the number given above for the SI units (1×10–3 kg/mol).

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[edit] References

  1. ^ a b Mohr, Peter J.; Taylor, Barry N. (2005). "CODATA recommended values of the fundamental physical constants: 2002". Rev. Mod. Phys. 77: 1–107. doi:0034-6861/2005/77(1)/1(107). 
  2. ^ de Bièvre, P.; Peiser, H. S. (1992). "'Atomic Weight' – The Name, Its History, Definition and Units". Pure Appl. Chem. 64: 1536–43. 
  3. ^ Bureau International des Poids et Mesures (2006). The International System of Units (SI) (8th Edn). ISBN 92-822-2213-6. pp. 114–15.
  4. ^ International Union of Pure and Applied Chemistry. "relative atomic mass (atomic weight)". Compendium of Chemical Terminology Internet edition.
  5. ^ Bureau International des Poids et Mesures (2006). The International System of Units (SI) (8th Edn). ISBN 92-822-2213-6. p. 112.
  6. ^ Bureau International des Poids et Mesures (2006). The International System of Units (SI) (8th Edn). ISBN 92-822-2213-6. p. 113.
  7. ^ International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry (2nd Edn). Oxford: Blackwell Science. ISBN 0-632-03583-8. p. 111. Electronic version.