Question

(1) A mixture is prepared from three ideal polystyrene samples(molar mass: 10,000,50,000,100,000 g/mol); calculate the number- average and weight-average MW of the mixture of equal numbers of molecules from each sample.

(2) Calculate the number- average and weight- average MW of the mixture of equal masses of molecules from each sample.

Answer 1

The Number Average Molecular Weight, Mn

The number average molecular weight is the total weight of all the polymer molecules in a sample, divided by the total number of polymer molecules in a sample.

The Weight Average Molecular Weight, Mw

The weight average is based on the fact that a bigger molecule contains more of the total mass of the polymer sample than the smaller molecules do.

1. Number Average Molecular Weight, Mn = (1* 10000+ 1 * 50000+ 1 * 100000 ) / 3 = 53333.33

    Weight Average Molecular Weight, Mw =

For sample 1, 10000 * 10000 / 160000 = 625

For sample 2, 50000 * 50000 / 160000 = 15625

For sample 3, 100000 * 100000 / 160000 = 625000

                                                              ==> 641250

2. Number Average Molecular Weight, Mn = ( 10000+50000+100000 ) / 3 = 53333.33

    Weight Average Molecular Weight, Mw =

For sample 1, 10000 * 10000 / 160000 = 625

For sample 2, 50000 * 50000 / 160000 = 15625

For sample 3, 100000 * 100000 / 160000 = 625000

                                                              ==> 641250