Calculate the average molecular mass of a polymer sample in which 30% molecules have a molecular mass 20,000, 40% have 30,000, and rest have 60,000.
Strategy: Work out number average molecular mass `(overline(M_(n)))` as well as weight average molecular mass `(bar(M_(w)))`

Explanation

Considering a total of 100 molecules, the `(overline(M_(n)))` and `(overline(M_(n)))` of the sample will be:
`overline(M_(n)) = (sum N_(i) M_(i))/(underset(i)sum N_(i))`
`((30 xx 20,000) + (40 xx 30,000) + (30 xx 60,000))/((30 + 40 + 30))`
`= 36,000`
`overline(M_(n)) = (sum N_(i) M_(i)^(2))/(underset(i)sum N_(i) M_(i))`
`((30)(30,000)^(2) + (40)(30,000)^(2) + (30)(60,000)^(2))/(((30 xx 20,000 + 40 xx 30,000 + 30 xx 60,000)))`
`= 43,333`