Question

Mention the formulas of weight average molecular mass and number average molecular mass.

Answer 1

Number average molecular weight, MN

The number average molecular weight is defined as the total weight of polymer divided by the total number of molecules.

Total weight =∑i=1∞NiMi

where Ni is the number of molecules with weight Mi

Total number =∑i=1∞Ni

The number average molecular weight is therefore given by:

MN¯¯¯¯¯¯¯¯=∑i=1∞NiMi∑i=1∞Ni

This can also be written as:

MN¯¯¯¯¯¯¯¯=∑i=1∞xiMi

where xi is the number fraction (or mole fraction) of polymer with molecular weight Mi.

Weight average molecular weight, Mw

The weight average molecular weight depends not only on the number of molecules present, but also on the weight of each molecule.  To calculate this, Ni is replaced with NiMi.

MW¯¯¯¯¯¯¯¯¯