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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)))`

Text Solution

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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`
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Knowledge Check

  • In a polymer sample, 30% of molecules have a molecualr mass of 20,000, 40% have 30,000 and the rest 60,000. What is the weight average molecular mass of the polymer?

    A
    403000
    B
    306000
    C
    43333
    D
    50400

  • In a polymer sample 30% of molecules have a molecular mass 20,000 , 40 % have 30,000 and the rest 60,000 . What is the weight average molecular mass of the polymer

    A
    40300
    B
    30600
    C
    43333
    D
    50400

  • A polymeric sample in which 30% molecules have a molecules mass 20,000 ,40%, have 30,000 and the rest 30% have 60,000 .The (Mbar(n)) and(Mbar(w)) of this sample was:

    A
    `36,000,43,333`
    B
    `43,333,36000`
    C
    `72,000,86,666`
    D
    `86,666,72000`

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