Title: molar-mass average
Long Title: IUPAC Gold Book - molar-mass average
DOI: 10.1351/goldbook.12215
Status: current

Definition
Any average of the molar mass, molecular weight, relative molar mass, or relative molecular mass for a non-uniform polymer, with the symbol \(\rm{k}\) specifying the type of average.

Notes
1) The various symbols that \(\rm{k}\) can be are given in the terms number-average molar mass, mass-average molar mass, z-average molar mass, (z+1)-average molar mass, and viscosity-average molar mass. For example, with \(\rm{k} \equiv n\), number-average quantities are defined.
2) An infinite number of molar-mass averages can in principle be defined, but only a few types of averages are directly accessible experimentally. The most important averages are defined in terms of simple moments of the distribution functions and are obtained by methods applied to systems in thermodynamic equilibrium, such as osmometry, static light scattering, and sedimentation equilibrium. Hydrodynamic methods, as a rule, yield more complex molar-mass averages.
3) Any molar-mass average can be defined in terms of mass fractions or mole fractions. In this document, the most important molar-mass averages are defined in terms of the mass fraction, \(w_{\rm{M}}\), of the species of molar mass \(M\). These definitions are most closely related to experimental determinations of molar-mass averages.
4) Quantities molecular-weight average, relative-molar-mass average, and relative-molecular-mass average (\(M_{\rm{r,k}}\)) are synonyms. These quantities are dimensionless (pure numbers) and are not associated with any units.

Related Terms
- (z+1)-average molar mass: https://goldbook.iupac.org//terms/view/12219
- mass-average molar mass: https://goldbook.iupac.org//terms/view/12217
- molar mass: https://goldbook.iupac.org//terms/view/12214
- number-average molar mass: https://goldbook.iupac.org//terms/view/12216
- viscosity-average molar mass: https://goldbook.iupac.org//terms/view/12220
- z-average molar mass: https://goldbook.iupac.org//terms/view/12218

Source
- PAC, 2015, 87, 71. 'Definitions of terms relating to individual macromolecules, macromolecular assemblies, polymer solutions, and amorphous bulk polymers (IUPAC Recommendations 2014)' on page 82 (https://doi.org/10.1515/pac-2013-0201)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/12215/html
- json: https://goldbook.iupac.org/terms/view/12215/json
- xml: https://goldbook.iupac.org/terms/view/12215/xml

Citation: Citation: 'molar-mass average' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.12215
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Accessed: 2026-04-18T08:29:08+00:00