The polymer that is used to make 2-L soda bottles [poly(ethylene terephthalate)] has a repeat unit with molecular formula C₁₀ H₈ O₄ and length 1.075 nm. Calculate the radius of gyration of a chain with a molar mass of 2.30x10⁴ g/mol.



Answer :

Molecular formula of repeating unit is C10H8O4

Rg= square root of (nl2/6)

Rg = Radius of gyration.

n = degree of polymerization.

l = length of each repeating unit.

for calculating n;

M xPolymer = M x repeat x n

2.3∗10^4g/mol= [192.16g/mol]∗n

n=(2.3∗10^4g/mol)/(192.16g/mol)=1.20∗10^2.

The molar mass of repeating unit = 192.16 g/mol.

Rg= square root of (nl2/6R )

=  square root of (1.2∗10^2∗(1.075∗10(−9))^2/6)

= Rg= 4.8nm

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