Answer:
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
