During the formation of polymers, different macromolecules have different degree of polymerisation i.e. they have varied chain lengths. Thus, the molecular masses of the individual macromolecules in a particular sample of the polymer are different. Hence, an average value of the molecular mass is taken. There are two kinds of average molecular masses of polymers.
1. Number-average molecular mass
2. Mass-average molecular mass
The two types of molecular masses are defined and calculated as follows:
1. Number-average molecular mass
When the total mass of all the molecules of a sample is divided by the total number of molecules, the result obtained is called the number-average molecular mass. For example, suppose in a particular sample
N_{1} molecules have molecular mass M_{1} each.
N_{2} molecules have molecular mass M_{2} each.
N_{3} molecules have molecular mass M_{3} each and so on. Then, we have
Total mass of all the N_{1} molecules = N_{1}M_{1}.
Total mass of all the N_{2} molecules = N_{2}M_{2}.
Total mass of all the N_{3} molecules = N_{3}M_{3} and so on.
∴ Total mass of all the molecules = N_{1}M_{1} + N_{2}M_{2} + N3M_{3} + .....
= ΣN_{i}M_{i}
Total number of all the molecules = N_{1} + N_{2} + N_{3} + ....
= ΣN_{i}
Hence the number-average molecular mass will be given by
is generally determined by osmotic pressure measurement.
2. Mass-Average molecular mass
When the total mass of groups of molecules having different molecular masses are multiplied with their respective molecular masses, the products are added and the sum is divided by the total mass of all the molecules, the result obtained is called the mass-average molecular mass. Supposing, as before that N_{1}, N_{2}, N_{3}, etc, molecules have molecular mass M_{1}, M_{2}, M_{3} etc. correspondingly.
Total mass of N_{1} molecules = N_{1}M_{1}.
Total mass of N_{2} molecules = N_{2}M_{2}.
Total mass of N_{3} molecules = N_{3}M_{3} and so on.
The products with their respective molecular masses will be (N_{1}M_{1} × M_{1}), (N_{2}M_{2} × M_{2}), (N_{3}M_{3} × M_{3}), etc. i.e. N_{1}M_{1}^{2}, N_{2}M_{2}^{2}, N_{3}M_{3}^{2}, etc.
Sum of the products = N_{1}M_{1}^{2} + N_{2}M_{2}^{2} + N_{3}M_{3}^{2} + ......
= ΣN_{i}M_{i}^{2}
Hence the mass-average molecular mass is given by
is generally determined by technique like ultra centrifugation of sedimentation.