Six narrow molecular weight standards for Polymer A were synthesized. Below are

Question

Six narrow molecular weight standards for Polymer A were synthesized. Below are molecular weight and intrinsic viscosity measurements. What are the Mark-Houwink-Sakarada constants, K and a. The data were recorded on a new sample of Polymer A. The intrinsic viscosity was determined to be 1.04 dl/g. What is the viscosity average molar mass of this sample?

M g/mol

[n] (dl/g)

46000

0.258

82000

0.408

152000

0.663

253000

0.893

348000

1.226

856000

2.210

M g/mol

[n] (dl/g)

46000

0.258

82000

0.408

152000

0.663

253000

0.893

348000

1.226

856000

2.210

Explanation / Answer

Mark-Houwink-Sakarada equation is given by

[n] = K [M]^a

for two different conditions

[n]2/[n]1 = ( [M2]/[M1] )^a

now

consider condition1 and condition2

0.408 / 0.258 = [82000/46000]^a

solving we get

a= 0.7928

the constant a value is 0.7928

now

consider

[n1] = K [M1]^a

0.258 = K [46000]^0.7928

K = 5.187 x 10-5

so the constant K value is 5.187 x 10-5

now given

n = 1.04

so

use

[n] = K[M]^a

1.04 = 5.187 x 10-5 x [M]^0.7928

solving we get

M = 266977 g/mol

so the molar mass is 266977 g/mol

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