JEE Main · ChemistryHard
Which of the following statements correctly describes the relationship between the number-average molecular weight and the weight-average molecular weight for a polydisperse polymer sample?
- A.For any polydisperse polymer, the ratio of Mw to Mn is always equal to 1.
- B.The value of Mw is always less than or equal to Mn.
- C.The value of Mw is always greater than or equal to Mn.
- D.The ratio of Mw to Mn is independent of the molecular weight distribution.
Show correct answer & step-by-step solution
Correct answer: C — The value of Mw is always greater than or equal to Mn.
Solution
- The number-average molecular weight is defined as .
- The weight-average molecular weight is defined as .
- By the Cauchy-Schwarz inequality, the variance of the distribution is non-negative, implying .
- Equality holds only for a perfectly monodisperse sample.
- Hence the answer is (C).
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