please show work. thank you PROBLEMS 1.1 A sample of polystyrene is found to hav

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please show work. thank you

PROBLEMS 1.1 A sample of polystyrene is found to have a number-average molar mass of 89,440 g mol^-1. Neglecting contributions from end groups, calculate the number-average degree of polymer ization of this sample. Assuming that the sample has a molar mass dispersity of 1.5, calculate its weight-average molar mass. 1.2 Calculate the mean repeat unit molar mass for a sample of poly[ethylene-stat-(vinyl acetate)]that comprises 12.9 wt% vinyl acetate repeat units. Given that its number-average molar mass is 39.870 g mol. calculate the number-average degree of polymerization of the copolymer. 1.3 Three mixtures were prepared from three very narrow molar mass distribution polystyrene samples with molar masses of 10,000, 30,000 and 100,000 g mol^-1 as indicated below: (a) Equal numbers of molecules of each sample (b) Equal masses of each sample (c) By mixing in the mass ratio 0.145:0.855 the two samples with molar masses of 10,000 and 100,000 g mol^-1 For each of the mixtures, calculate the number-average and weight-average molar masses and comment upon the meaning of the values.

Explanation / Answer

Here the monomer is styrene (C8H8).

Hence the molecular mass of the monomer, M0 = 104.15 g/mol

Given the number average molar mass, Mn = 89440 g/mol

Now the number-average degree of polymerization can be calculated from the following formulae

number-average degree of polymerization,

DPn = Mn / M0 = 89440 g/mol / 104.15 g/mol = 859 (answer)

Molar mass dispersity is defined as the ratio of mass average molar mass(Mw) to the number average molar mass(Mn)

Hence Molar mass dispersity = 1.5 = Mw/Mn = Mw / 89440 g/mol

= > Mw = 1.5 x 89440 g/mol = 134160 g/mol (answer)

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