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# Number average molecular weight

The number average molecular weight is a way of determining the molecular weight of a polymer. Polymer molecules, even ones of the same type, come in different sizes (chain lengths, for linear polymers), so the average molecular weight will depend on the method of averaging. The number average molecular weight is the common, mean, average of the molecular weights of the individual polymers. It is determined by measuring the molecular weight of n polymer molecules, summing the weights, and dividing by n [1].

$\bar{M}_n=\frac{\sum_i N_iM_i}{\sum_i N_i}$

The number average molecular weight of a polymer can be determined by gel permeation chromatography, viscometry (Mark-Houwink equation), and all colligative methods like vapor pressure osmometry or end-group titration.

An alternative measure of the molecular weight of a polymer is the weight average molecular weight. The ratio of the weight average to the number average is called the polydispersity index.

High Number-Average Molecular Weight Polymers may be obtained only with a high fractional monomer conversion in the case of step-growth polymerization, as per the Carothers' equation.

## References

1. ^ http://www.polymerchemistryhypertext.com/molecular_weight_definitions.htm