https://doi.org/10.1351/goldbook.12218
The equation for z-average molar mass is \[M_{\rm{z}} = \frac{\sum\limits_{M} w_{M}M^{2}}{\sum\limits_{M} w_{M}M}\]
The equation for z-average molecular weight is \[M_{\rm{r,z}} = \frac{\sum\limits_{M_{\rm{r}}} w_{M_{\rm{r}}}M_{\rm{r}}^{2}}{\sum\limits_{M_{\rm{r}}} w_{M_{\rm{r}}}M_{\rm{r}}}\]
Notes:
- For definition of the symbols, see molar-mass average.
- Quantities z-average molecular weight, z-average relative molar mass, and z-average relative molecular mass, (\(M_{\rm{r,z}}\)) are synonyms. These quantities are dimensionless (pure numbers) and are not associated with any units.