Question

Polydispersity index of a polymer is 5 and its weight average molecular weight is 8400 g/mol. The number average molecular weight (g/mol) of the polymer (in integer) is ________________.

Hint:

The number average molecular weight can be calculated from the weight average molecular weight using the polydispersity index (PDI).

Answer 1

Correct Answer: 1680

The relationship between the weight average molecular weight (\(M_w\)) and the number average molecular weight (\(M_n\)) is given by the polydispersity index (\(PDI\)): \[ PDI = \frac{M_w}{M_n} \] Given: - \( PDI = 5 \) - \( M_w = 8400\ \text{g/mol} \) Thus, we can solve for \( M_n \): \[ M_n = \frac{M_w}{PDI} = \frac{8400}{5} = 1680\ \text{g/mol} \] Thus, the number average molecular weight of the polymer is: \[ \boxed{1680\ \text{g/mol}} \]