POLYMER ENGINEERING - QUESTION 24.3 : The molecular weights M in kg / mol of 3 different monomers a, b and c in a polymer are Ma = 14, Mb = 16 and Mc = 18, with their respective quantities in N units having the ratio of Na : Nb : Nc = 2 : 3 : 5. (a) Find the numerical average molecular weight of the polymer by using the formula (Ma Na + Mb Nb + Mc Nc) / (Na + Nb + Nc). (b) Find the weighted average molecular weight of the polymer by using the formula (Ma Na Ma + Mb Nb Mb + Mc Nc Mc) / (Ma Na + Mb Nb + Mc Nc). (c) Calculate the polydispersity Q by using the answer in (b) divided by answer in (a). (d) Find the volumetric average molecular weight of the polymer by using the formula (Ma Na Ma Ma + Mb Nb Mb Mb + Mc Nc Mc Mc) / (Ma Na Ma + Mb Nb Mb + Mc Nc Mc). (e) Estimate the polydispersity Q by using the answer in (d) divided by answer in (b).
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POLYMER ENGINEERING - ANSWER 24.3 : (a) Numerical average molecular weight = (Ma Na + Mb Nb + Mc Nc) / (Na + Nb + Nc) = (14 x 2 + 16 x 3 + 18 x 5) / (2 + 3 + 5) = 166 / 10 = 16.6 kg / mol. (b) Weighted average molecular weight = (Ma Na Ma + Mb Nb Mb + Mc Nc Mc) / (Ma Na + Mb Nb + Mc Nc) = (14 x 2 x 14 + 16 x 3 x 16 + 18 x 5 x 18) / (14 x 2 + 16 x 3 + 18 x 5) = 2780 / 166 = 16.747 kg / mol. (c) Polydispersity = [ answer in (b) ] / [ answer in (a) ] = (16.747 kg / mol) / (16.6 kg / mol) = 1.0089. (d) Volumetric average molecular weight = (Ma Na Ma Ma + Mb Nb Mb Mb + Mc Nc Mc Mc) / (Ma Na Ma + Mb Nb Mb + Mc Nc Mc) = (14 x 2 x 14 x 14 + 16 x 3 x 16 x 16 + 18 x 5 x 18 x 18) / (14 x 2 x 14 + 16 x 3 x 16 + 18 x 5 x 18) = 46936 / 2780 = 16.883 kg / mol. (e) Polydispersity estimation = [ answer in (d) ] / [ answer in (b) ] = (16.883 kg / mol) / (16.747 kg / mol) = 1.0081. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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