Question

The number average molecular mass and mass average molecular mass of a polymer are $30,000$ and $40,000$ respectively. The PDI of the polymer is
A. < $1$
B. > $1$
C. $1$
D. $0$

Answer 1

Hint: DI refers to the polydispersity index. It is the ratio of mass average molecular mass to the number average molecular mass of a polymer. This ratio gives an idea about the homogeneity of a polymer. It is a measure of the distribution of molecular mass in a given sample of polymer.

Complete step-by-step answer:
In the question, a polymer is given to us whose
Number average molecular mass $\left( \overline{{{M}_{N}}} \right)$= $30,000$
Mass average molecular mass $\left( \overline{{{M}_{W}}} \right)$= $40,000$
We know that PDI (polydispersity index) is the ratio of mass average molecular mass to number average molecular mass
PDI= $\dfrac{\overline{{{M}_{W}}}}{\overline{{{M}_{N}}}}$
PDI= $\dfrac{40,000}{30,000}=\dfrac{4}{3}=1.34$
Therefore, the polydispersity index of the given polymer is $1.34$ and we know that this is greater than one.

Additional information: The polymer whose molecules have nearly the same molecular masses are called monodisperse polymers. For such polymers the polydispersity index (PDI) is equal to one. Examples of such polymers are natural polymers. The polymers whose molecules have a wide range of molecular masses are called polydisperse polymers. The polydispersity index (PDI) of such polymers is greater than one.

Hence, the correct option is B. > $1$

Note: The dispersity indicates the distribution of individual molecular masses in a batch of polymers. Polydispersity index has a value equal to or greater than one, but as the polymer chain approaches uniform chain length, PDI approaches unity.