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In a polymer sample, 30% molecules have ...

In a polymer sample, 30% molecules have molecular mass 20000, 40% have molecular mass 30000 and the rest 30% have 60000. Calculate their number average and mass average molecular masses.

Text Solution

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Number-average molecular mass of the polymer is
`bar(M_n)=(sumN_i M_i)/(underset(i)(sum) N_i)`
`=((30 xx 20,000)+(40+30,000) + (30 xx 60,000))/(30+40+30)`
`=30,000g "mol"^(-1)`
Weight - average molecular mass of the polymer is
`bar(M_n)=(sumN_i M_i^2)/(sum_i N_i M_i)`
`=(30(20,000)^(2) + 40(30,000)^(2)+30(60,000)^(2))/(30 xx 20,000 + 40 xx 30,000 + 30 xx 60,000)`
`=43 , 333000` g `"mol"^(-1)`
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