Question

The polypropylene (repeat unit CH₃CHCH₂) in a plastic toy has a molar mass of 2.8x10⁵ g/mol and a repeat unit length of 0.252 pm. Calculate the radius of gyration.

Answer 1

Polymer can be defined as the large molecule which is made up of repeating units of smaller molecules which are linked by covalent bonds.

Polymer mass : The molecular weight of the polymer is called as polymer mass.

μ(polymer)=μ(repeat)∗n                     where n is degree of polymerization.

Rg=  √(nl2/6R)

where,                                                 R = Radius of gyration.

n = degree of polymerization.

l = length of each repeating unit.

for calculating n;

MPolymer= Mrepeat∗n

=(2.8∗10^5g/mol)=[42.08g/mol]∗n

n=(2.8∗105g/mol)/(42.08g/mol)=6.7∗103.n

The molar mass of repeating unit = 42.08 g/mol

Rg= √(  nl2/6R )

=  √ (6.7∗103∗(0.252∗10^(−10))2 /6)

 Rg= 8.4pm radius of gyration.

To know more about Radius of gyration here

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