Weight Average Molecular Weight

Weight Average Molecular Weight

Weight Average Molecular Weight

Number Average and Weight Average Molecular Mass MCQs

Weight Average Molar Weight (Mw)

Weight average molecular weight is the weight fraction of molecules in a polymer sample. It is another way of determining the molecular mass of a polymer. It gives the average of the molecular masses of the individual macromolecules in the polymer sample.
When the total molecular weight of group of molecules having particular molecular weights are multiplied with their respective molecular weight, the product are added and the sum is dived by the total weight of all molecules, the result obtained is called weight average molecular weight. Let N1, N2 etc. molecules have molecular weights M1,M2 etc. respectively.
Total molecular weight of N1 molecules = N1M1
Total molecular weight of N2 molecules = N2M2 and so on...
The products with their respective molecular weights will be N1M1 X N2M2

Sum of the products = N1M12 + N2M22 +... = ΣNiMi2
Total weight of all molecules = N1M1 + N2M2 +... = ΣNiMi
Hence, weight average molecular weight (Mw) = N1M12 + N2M22 +... / N1M1 + N2M2 +...
weight average molecular weight (Mw) = ΣNiMi2 / ΣNiMi

Number Average Molecular Weight (Mw)

Under what condition Number Average Molecular Weight and Weight Average Molecular Weight are same ?

We know that-
Number average molecular weight (Mn) = [N1M1 + N2M2 + ...] / [N1 + N2 + ...]
and Weight average molecular weight (Mw) = [N1M12 + N2M22 + ...] / [N1M1 + N2M2 + ...]
If Mn = Mw
[N1M1 + N2M2 + ...] / [N1 + N2 + ...] = [N1M12 + N2M22 + ...] / [N1M1 + N2M2 + ...]
The LHS and RHS can be eqaul only when M1 = M2 = ... = Mi
That means all molecules should have same molecular weight. In that case average has no significance.

Equal number of molecules with M1 = 1,00000 and M2 = 10,000 are mixed. Calculate weight average molecular weight.

AnswerLet, N1 = N2 = 10
M1 = 100000
M2 = 10000
Putting these values in the formula we get-
weight average molecular weight (Mw) = 91818