Question

The number average molar mass and mass average molar mass of a polymer are respectively $30,000$ and $40,000$. The polydispersity index (PDI) of the polymer is:
A.$- 1$
B.$0$
C.$>1$
D.$<1$

Answer 1

As in question the number average molar mass and mass average molar mass of a polymer is given and the polydispersity index of the polymer is the ratio of $\dfrac{{{M_w}}}{{{M_n}}}$ .By using above formula we will be able to find the polydispersity index.

Complete step by step answer:

Polydispersity index (PDI) is defined as the ratio of the mass average molar mass $\left( {{M_w}} \right)$ to number average molar mass$\left( {{M_n}} \right)$. As the $\left( {{M_w}} \right)$ is always higher than that of the $\left( {{M_n}} \right)$. So, the ratio should always be $1$ or greater than $1$.
Polydispersity is the measure of the heterogeneity of any polymer or in a wider context, any organic compound.
If we consider a polymer which has a uniform sized chain then such type of polymer will be strong, smooth and impenetrable whereas the more heterogeneous polymer having high polydispersity will be a polymer with a lot varying chain sizes. Such a type of polymer will be weak and considered to be raw.
As a matter of fact, this is the case also. Natural polymer which is found tends to have higher dispersion and also, are weak, have shorter life. But above all they provide higher breathability and comfort.
Now, if we see the synthetic polymers, they tend to have lower dispersity. They are strong. Long lived and generally smooth. They have their own applications and provide better insulation.
$PDI = \dfrac{{{M_w}}}{{{M_n}}}\\\ = \dfrac{{40,000}}{{30,000}}\\\ = 1.333$
Therefore, Option C is correct. And the polydispersity index (PDI) of the polymer is $\rangle 1$.

Note:
Basically, the dispersity index measures the deviation from the uniformity of dispersion.
For example:
If the weight distribution is uniform then we can say that ration is $1$ .
If it is between $1 - 1.1$ , it is considered to be a narrow distribution.
If it is between $1 - 2$ , it is considered to be of moderate distribution.
If it is between $2$ , it is considered to be a broad distribution.