Question

7. Please calculate the number-averaged molecular weight and weight-averaged molecular weight for the following polymer. (6 pt) Fraction Mass(g) Mx 104(g/mol)1.24 1.521.361.282.301.504.28 1.21 1181.4567 0.23 0.18 0.56 0.82 3.76 8. A student mixed two batches of PS accidently in the lab, what would be number-averaged molecular weight and weight-averaged molecular weight for this PS mixture. (6 pt) Batch Mass(g) Mw (g/mol) Mn (g/mol 15 75,000 50,000 150,000 120,000

Answer 1

7. Number average molecular weight, M_n

The number average molecular weight is defined as the total weight of polymer divided by the total number of molecules.

This can also be written as:

MN=∑NiMi/∑Ni

Ni (Number of Molecules)	Mi(Mass of Each Molecule)	Total Mass of Each Type of Molecule, NiMi
1	1.21	1.21
2	1.18	2.36
3	1.45	4.35
4	1.67	6.68
5	0.23	1.15
6	0.18	1.08
7	0.56	3.92
8	0.82	6.56

Total Mass of Each Type of Molecule, N_iM_i = 27.31
Mn= 27.31/36= 0.7586

Weight average molecular weight, Mw

The weight average molecular weight depends not only on the number of molecules present, but also on the weight of each molecule.

Mw=∑WiMi

Ni (Number of Molecules)	Mi(Mass of Each Molecule)	Total Mass of Each Type of Molecule, NiMi	Weight Fraction Type of Molecule	WiMi
1	1.21	1.21	0.044	0.053
2	1.18	2.36	0.086	0.101
3	1.45	4.35	0.159	0.230
4	1.67	6.68	0.245	0.409
5	0.23	1.15	0.0421	0.010
6	0.18	1.08	0.039	0.007
7	0.56	3.92	0.143	0.080
8	0.82	6.56	0.240	0.196

Mw= 1.0868