Considering the following polymer size fractions of a given polymer sample: Fraction Molecular Weight Number of Chains
1 6,500 400
2 10,000 1000
3 1,000,000 8
(a) Calculate the number-average molecular weight of the polymer.
(b) Calculate the weight-average molecular weight of the polymer.
(c) Which average molecular weight did the 8 chains of molecular weight of 1,000,000 most significantly affect? why?
(d) Calculate the polydispersity index(PI = (Mw/Mn) of the polymer

Explanation:

From the information given:

Molecular weight Mi      Number of chains (Ni)      NiMi

400                                           6500                        2600000

1000                                         10000                       10000000

8                                               1000000                   8000000

                                                = 20600000

Thus, the average number of molecular weight =

= 14630.68

b)

weight-average molecular weight  =

400              6500          42.25 × 10⁶        16.9  × 10⁹

1000             10000        100 × 10⁶            100 × 10⁹

8                   1000000    1 × 10¹²               800 × 10⁹

weight-average molecular weight  

= 44509.71

c)

The number average molecular weight is most significantly affected. This is because the number average molecular weight value is worth more in comparison to the weight-average molecular weight.

d)

The polydispersity index (PI) =

PI = 3.04

93.2 ml + 3920 ml = 4013 ml total  

(93.2 ml) * (2.03 m) / (4013 ml) = 0.0471 m

the volume in in l of the diluted solution would be 0.0471 m.