The following table lists molecular weight data for a polypropylene material. Molecular Weight Range (g/mol) xi wi 8,000 - 16,000 0.07 0.03 16,000 - 24,000 0.15 0.09 24,000 - 32,000 0.26 0.21 32,000 - 40,000 0.27 0.27 40,000 - 48,000 0.18 0.28 48,000 - 56,000 0.07 0.12
Click here to access Table 14.3. Atomic weights for several elements are included in the following table: Carbon 12.01 g/mol Chlorine 35.45 g/mol Fluorine 19.00 g/mol Hydrogen 1.008 g/mol Oxygen 16.00 g/mol Nitrogen 14.01 g/mol Compute the following:
(a) the number-average molecular weight, Enter your answer for part (a) in accordance to the question statement g/mol
(b) the weight-average molecular weight, Enter your answer for part (b) in accordance to the question statement g/mol
(c) the degree of polymerization.

a) the number-average molecular weight is 32,400 g/mol

b) the weight-average molecular weight is 36,320 g/mol

c) the degree of polymerization is 770

Explanation:

Given the data in the question;

Molecular                  Mean        Number      Weight      Number        Weight

weight                                                                             average         average

(g/mol)                    Mi(g/mol)         xi                wi          xiMi                  wiMi

8,000-16,000            12,000        0.07           0.03         840                360

16,000-24,000          20,000       0.15           0.09         3000              1800

24,000-32,000         28,000       0.26           0.21          7280              5880

32,000-40,000         36,000       0.27           0.27         9720               9720

40,000-48,000         44,000       0.18            0.28         7920              12320

48,000-56,000         52,000       0.07           0.12          3640              6240

∑                                                                                Mn=32,400     Mw=36,320

so;

a)  the number-average molecular weight

Mn = ∑Mixi

so from the table above; summation of Row Mixi

Mn = ∑Mixi = 32,400

Therefore, the number-average molecular weight is 32,400 g/mol

b) the weight-average molecular weight

Mw = ∑Miwi

so from the table above; summation of Row Miwi

Mw = ∑Miwi = 36,320

Therefore, the weight-average molecular weight is 36,320 g/mol

c) the degree of polymerization

the degree of polymerization of polypropylene can be determined using number-average molecular and repeat unit molecular weight.

now, for polypropylene { CH₂ = CH - CH₃ }

the repeat unit consist of 3 carbon atoms and 6 hydrogen atoms

given that;

Atomic weight of Carbon mC = 12.01 g/mol and

Atomic weight of  Hydrogen mH = 1.008 g/mol

now we find the repeat unit molecular weight of polypropylene

m = nCmC + nHmH

where n is the number of repeat of atoms

so we substitute

m = ( 3 × 12.01) + ( 6 × 1.008)

m = 36.03 + 6.048

m = 42.078 g/mol

now we calculate the degree of polymerization;

DP = Mn / m

so we substitute

DP = 32,400 / 42.078

DP = 769.9985 ≈ 770

Therefore,  the degree of polymerization is 770