Question

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nber-average and weight-average molecular weight. Is it possible to have a polypropylene polymer with the following molecular weight data and a num degree of polymerization of 1134? Why or why not? Molecular Weight Range (g/mol) 8000-20000 W 0.02 0.05 20000-32000 0.08 0.15 32000-44000 0.17 0.21 44000-56000 0.29 0.28 56000-68000 0.23 0.18 68000-80000 0.16 0.10 80000-92000 0.05 0.03 The chemical formula for the polypropylene monomer is C3H6. The atomic weights of carbon and hydrogen are 12.01 g/mole and 1.008 g/mole, respectively. In the table above, two columns were left blank for your convenience in doing your computation.

Answer 1

Given informations and calculation is given below:

Molecular Weight Range (g/mol)	wi	xi	Total Mass of Each Type of Molecule (xiwi)	$\frac{x_{i}w_{i}}{\sum x_{i}w_{i}}$
8000-20000	0.02	0.05	0.001	0.0053
20000-32000	0.08	0.15	0.012	0.063
32000-44000	0.17	0.21	0.0357	0.189
44000-56000	0.29	0.28	0.0812	0.43
56000-68000	0.23	0.18	0.0414	0.22
68000-80000	0.16	0.10	0.016	0.085
80000-92000	0.05	0.03	0.0015	0.0079

No: average molecular weight is given below:

$\frac{\sum x_{i}w_{i}}{\sum x_{i}}$

$\sum x_{i}w_{i}=0.1888$

$\sum x_{i}$ = 1

No: average molecular weight is 0.1888/1 = 0.1888

Wiwi
0.0001
0.005
0.032
0.125
0.0506
0.0136
0.00036

Weight Average Molecular Weight = $\sum W_{i}w_{i}=0.22666$

Atomic mass of Carbon = 12.01g/mole

Atomic mass of hydrogen = 1.008g/mole

Degree of polymerisation = Molecular weight of polymer / Molecular weight of monomer units

Molecular weight of monomer units = 12.01 x 3 + 1.008 x 6
= 36.03 + 6.048 = 42.078

Minimum molecular weight of given polypropylene polymer = 8000

Maximum molecular weight of given polypropylene polymer = 92000

Degree of polymerisation with minimum molecular weight = 8000 / 42.078
= 190.123

Degree of polymerisation with maximum molecular weight = 92000 / 42.078
= 2186.42

It is possible to have a polypropylene polymer with degree of polymerisation of 1134.

Beacuse degree of polymerisation with minimum molecular weight is 190.123 and degree of polymerisation with maximum molecular weight is 2186.42.

So,1134 is in between two values.