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Question: If \(\overline {{M_W}} \) is the weight average molecular weight and \(\overline {{M_n}} \)is the nu...

If MW‾\overline {{M_W}} is the weight average molecular weight and Mn‾\overline {{M_n}} is the number average molecular weight of a polymer, the polydispersity index (PDI) of the polymer is given by-
A.Mn‾MW‾\dfrac{{\overline {{M_n}} }}{{\overline {{M_W}} }}
B.MW‾Mn‾\dfrac{{\overline {{M_W}} }}{{\overline {{M_n}} }}
C.MW‾×Mn‾\overline {{M_W}} \times \overline {{M_n}}
D.1MW‾×Mn‾\dfrac{1}{{\overline {{M_W}} \times \overline {{M_n}} }}

Explanation

Solution

Polymers are high molecular mass substances where every molecule is derived from a large number of simple molecules joined together. They are formed from repeated combinations of simplest units known as monomers and the process of formation of polymers is called polymerization.

Complete step by step answer:
Polymers have high molecular weight and high viscosity so their molar mass distribution can be shown by two values-
i. MW‾\overline {{M_W}} ii. Mn‾\overline {{M_n}}
MW‾\overline {{M_W}} is the average molecular weight and Mn‾\overline {{M_n}} is the number average molecular weight of a polymer.
The ratio of these average values of molecular weight by weight and number is called the polydispersity index. It is given as-
⇒\Rightarrow PDI=MW‾Mn‾\dfrac{{\overline {{M_W}} }}{{\overline {{M_n}} }}
It is a measure of molecular weight distribution in a polymer.
Its value is either one or greater than one. It can never be less than one. The polymers with Polydispersity index greater than one are synthesized in laboratories in which they are synthetic polymers.
When MW‾\overline {{M_W}} =Mn‾\overline {{M_n}} then the polydispersity index will become one. PDI has value equal to one for a natural mono-dispersed polymer because the molecules in such a polymer have the same relative molecular mass and have a straight chain.
When the value of polydispersity index is greater than one for poly-disperse polymer as the polymer contains unequal length of chains of monomers.

Hence the correct answer is option B.

Note:
PDI is mainly used to compare the polymers using their relative molecular weights. It is used as following-
We can make useful polymers having use in biomedical fields like- mono-dispersed PEG (polyethylene glycol) is used in drug delivery and tissue engineering.