average molar mass

or (formerly) average molecular weight

any of a series of numeric characteristics of a macromolecular system that are useful for assessing the extent of its polydispersity. The three most important are the number-average molar mass, M_n, the mass-average molar mass, M_m, and the Z-average molar mass, M_z. These three characteristics are given by the expressions:
M_n=Σn_iM_i/Σn_i (kg mol⁻¹)

M_m=Σn_iM_i²/Σn_iM_i (kg mol⁻¹)

M _z=Σn_iM_i³/Σn_iM_i² (kg mol⁻¹)
: where n_i is the amount of substance of species i and M_i is the molar mass of species i. Measurement of a colligative property, e.g. osmotic pressure, or end-group analysis, gives M_n; light scattering, dielectric dispersion, or fluorescence depolarization measurements give M_m; and data obtained by equilibrium ultracentrifugation will yield either M_m or M_z depending on how they are treated. For polydisperse or heterogeneous systems, M_z > M_m > M_n, whereas for monodisperse systems these three characteristics are equal (i.e. equal to the relative molecular mass, M_r, of the single species).

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