The following table lists molecular weight data for a polypropylene material. Compute (a) the number-average molecular weight, (b) the weight-average molecular weight, and (c) the degree of polymerization. please show equations and calculations used. thank you
Molecular Weight Range (g/mol) xi wi
8,000–16,000 0.05 0.02 16,000–24,000 0.16 0.10
24,000–32,000 0.24 0.20 32,000–40,000 0.28 0.30 40,000–48,000 0.20 0.27 48,000–56,000 0.07 0.11

Answers

Answer 1

(a) The number-average molecular weight is 31,800 g/mol.(b) The weight-average molecular weight is 38,700 g/mol. (c) The degree of polymerization is 399.

(a) The number-average molecular weight (Mn) can be calculated using the following equation:

Mn = Σ(xiMi) / Σ(xi)

where xi and Mi are the weight fraction and molecular weight of the polymer, respectively. Substituting the values from the table, we get:

Mn = (0.0512000)+(0.1620000)+(0.2428000)+(0.2836000)+(0.2044000)+(0.0752000) / (0.05+0.16+0.24+0.28+0.20+0.07) = 32117 g/mol

(b) The weight-average molecular weight (Mw) can be calculated using the following equation:

Mw = Σ(wiMi^2) / Σ(wiMi)

Substituting the values from the table, we get:

Mw = (0.0212000^2)+(0.1020000^2)+(0.2028000^2)+(0.3036000^2)+(0.2744000^2)+(0.1152000^2) / (0.0212000)+(0.1020000)+(0.2028000)+(0.3036000)+(0.2744000)+(0.1152000) = 44170 g/mol

(c) The degree of polymerization (DP) can be calculated using the following equation:

DP = Mw / Mmon

where Mmon is the molecular weight of the monomer. For polypropylene, the molecular weight of the monomer is 42 g/mol. Substituting the values, we get: DP = 44170 g/mol / 42 g/mol = 1051.9

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