Write the formula to determine the average molecular weight of polymers.

Hint:The weight average molecular weight ($M_n$) measurement method involves the counting of the total number of molecules, regardless of their shape or size, in the unit mass of the polymer.

Complete step by step answer:

Instead of a particular number, polymer molecular weight is defined as a distribution since polymerization occurs to generate various chain lengths in such a way. Average molecular weight ($M_w$) and Weight average molecular weight ($M_n$) are two ways of characterising the molecular weight of the polymer.

This type of measuring device is needed in cases where certain properties are based only on the number of molecules or repeated units and not on their weight or scale. These are called colligative properties, such as boiling point elevation, freezing point depression, vapour pressure depression, and osmotic pressure changes.

The weight average molecular weight of polymers $M_n$ is calculated by the formula as follows:
$M_n= \dfrac{ \Sigma{N_iM_i}}{\Sigma {N_i}}$


Where,
$M_i$ is the molecular weight of a chain,
$N_i$ is the number of chains of that molecular weight,
i is the number of polymer molecules.
Additional information:
Polymers are products composed of molecules that are long, repeated chains.
Based on the form of molecules being bonded and how they are bonded, the products have special properties.
Like rubber and polyester, some polymers bend and stretch.
Others, like epoxy and glass, are rough and durable.

Note:
The process of polymerization is driven by random events, whether by chain growth or by step-growth. The consequence is a mixture of polymers which differ in chain length. A polymeric material, therefore, can not be characterised by a single molecular weight, like an ordinary substance. Instead, a statistical average calculated from the molecular weight distribution has to be used.