Question

A polymer sample is analyzed by an analytical method, and the following molecular weight information is obtained:

Number Fraction	Molecular Weight Range (Daltons)
5%	5,000 - 10,000
10%	10,000 - 15,000
20%	15,000 - 20,000
40%	20,000 - 25,000
20%	25,000 - 30,000
5%	30,000 - 35,000

(a) calculate Mn

(b) calculate Mw

(c) if the repeat unit of the polymer weighs 200 Daltons, what are the degrees of polymerization you can calculate?

(d) what is the polydispersity of the polymer

Answer 1

(a) M_n = (n₁M₁ + n₂M₂ + n₃M₃ + n₄M₄ + n₅M₅ + n₆M₆) / (n₁ + n₂ + n₃ + n₄ + n₅ + n₆) ..... equation 1

(b) M_w = (n₁M₁² + n₂M₂² + n₃M₃² + n₄M₄² + n₅M₅² + n₆M₆²) / (n₁M₁ + n₂M₂ + n₃M₃ + n₄M₄ + n₅M₅ + n₆M₆) ...... equation 2

Here, n₁ = 5, n₂ = 10, n₃ = 20, n₄ = 40, n₅ = 20 and n₆ = 5

And M₁ = (5,000 + 10,000)/2 = 7500 dalton

M₂ = (10000 + 15000)/2 = 12500 dalton

M₃ = (15000 + 20000)/2 = 17500 dalton

M₄ = (20000 + 25000)/2 = 22500 dalton

M₅ = (25000 + 30000)/2 = 27500 dalton

M₆ = (30000 + 35000)/2 = 32500 dalton

By substituting all the above values in the equations 1 and 2, you can find Mn and Mw.

(c) Number average degree of polymerization = M_n/M₀, where M₀ = The molar mass of repeating unit

And Weith average degree of polymerization = M_w/M₀

(d) The polydispersity of the polymer = M_w/M_n