Question

Calculate the weight-average molecular weight of a polymer sample with the following information:- The polydispersity index (PDI) of the sample is 1.5.- The number-average molecular weight (Mn) of the sample is 20,000 g/mol. - The weight fraction (w) of the polymer with a molecular weight of 30,000 g/mol is 0.2, and the weight fraction of the polymer with a molecular weight of 10,000 g/mol is 0.8.

Answer 1

To calculate the weight-average molecular weight  Mw  of the polymer sample, we can use the following formula:Mw =  wi * Mi where wi is the weight fraction of the polymer with molecular weight Mi.Given the weight fractions and molecular weights of the two polymers in the sample:w1 = 0.2  for M1 = 30,000 g/mol w2 = 0.8  for M2 = 10,000 g/mol Mw =  0.2 * 30,000  +  0.8 * 10,000 Mw = 6,000 + 8,000Mw = 14,000 g/molNow, we can use the polydispersity index  PDI  to verify our result. The PDI is the ratio of the weight-average molecular weight  Mw  to the number-average molecular weight  Mn :PDI = Mw / MnGiven that the PDI is 1.5 and Mn is 20,000 g/mol:1.5 = Mw / 20,000Mw = 1.5 * 20,000Mw = 30,000 g/molHowever, this result contradicts our previous calculation of Mw  14,000 g/mol . There seems to be an inconsistency in the given information. Please double-check the provided data and ensure it is accurate.