Answer:
Explanation:
From the information given:
Molecular weight Mi Number of chains (Ni) NiMi
400 6500 2600000
1000 10000 10000000
8 1000000 8000000
[tex]\sum_{Ni} = 1408[/tex] [tex]\sum _{NiMi}[/tex] = 20600000
Thus, the average number of molecular weight = [tex]\dfrac{\sum_{NiMi}}{\sum_{Ni} }[/tex]
[tex]= \dfrac{20600000}{1408}[/tex]
= 14630.68
b)
weight-average molecular weight = [tex]\dfrac{\sum _{NiMi^2} }{\sum _{NiMi}}[/tex]
[tex]Ni[/tex] [tex]Mi[/tex] [tex]Mi^2[/tex] [tex]Ni[/tex] [tex]Mi^2[/tex]
400 6500 42.25 × 10⁶ 16.9 × 10⁹
1000 10000 100 × 10⁶ 100 × 10⁹
8 1000000 1 × 10¹² 800 × 10⁹
[tex]\sum _{NiMi^2} = 916.9 \times 10^9[/tex]
weight-average molecular weight [tex]=\dfrac{916.9 \times 10^9 }{20.6 \times 10^6}[/tex]
= 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) = [tex]\dfrac{\overline {M_W}}{\overline {M_n}}[/tex]
[tex]PI = \dfrac{44509.71}{14630.68}[/tex]
PI = 3.04
