# GATE (TF) Textile 2022 Question Paper Solution | GATE/2022/TF/17

###### Question 17 (Textile Technology & Fibre Science)

Polydispersity index of a polymer is 5 and its weight average molecular weight is 8400 g/mol. The number average molecular weight (g/mol) of the polymer (in integer) is ___________.

Here given,
Polydispersity index of a polymer=5
Weight average molecular weight(g/mol) of polymer=8400 g/mol
Number average molecular weight(g/mol) of polymer=?

Now by formula,

Polydispersity index=Weight average molecular weight(Mw)/Number average molecular weight(Mn)

5=8400/Mn

Mn=8400/5

Mn=1680

i.e. ,Number average molecular weight(Mn)=1680 g/mol (Answer)

### What is Polydispersity index ?

The polydispersity index (PDI) is a measure of the distribution of molecular weight in a polymer sample. It is defined as the ratio of the weight-average molecular weight (Mw) to the number-average molecular weight (Mn) in a polymer sample. The PDI is a dimensionless parameter that provides information on the breadth of the molecular weight distribution in a polymer sample.

The PDI ranges from 1 (indicating a monodisperse sample, where all molecules have the same weight) to greater than 1 (indicating a polydisperse sample, where molecules have a broad range of weights). The higher the PDI, the broader the distribution of molecular weights in the sample, indicating a higher degree of heterogeneity in the sample.

The PDI is an important parameter in polymer science and engineering, as it can affect the physical and mechanical properties of a polymer, such as viscosity, melt flow, and tensile strength. The PDI is also important in polymer processing, as it affects the processing and performance of the polymer in various applications.