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What is the number - average molecular weight? What is the weight average molecular weight and what is the polydispersity index of the sample? Derive

What is the number-average molecular weight?
What is the weight average molecular weight and what is the polydispersity index of the sample?
Derive the equations that can also represent these molecular weights using the mole fraction (xi)
and weight fraction (wi) of polymers with similar molecular weight.
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