HW09 Soln

# HW09 Soln - 12.1 What is the average molecular weight of a...

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Unformatted text preview: 12.1 What is the average molecular weight of a polypropylene, (C 3 H 6 ) n , with a degree of polym- erization of 500? SOLUTION As explained on p. 387 of the text, the molecular weight of a polymer is calculated by taking the product of the molecular weight of a single mer (molecule) times the the number of mers in the polymeric structure, also known as the &amp;quot;degree of polymerization&amp;quot; designated as ( n ). A sample calculation of the type requested here is also presented in Example 12.2 on the same page (387). Following the procedure outlined in Example 12.2, the operating mathematical expression is Mol. wt. (C 3 H 6 ) n = n Mol. wt. (C 3 H 6 ) Substituting values of the atomic weights of C and H from Appendix 1 (page A-1 of the text), Mol. wt. (C 3 H 6 ) 500 = [500] (3 [12.01 amu] + 6 [1.008 amu]) and solving, the answer is obtained Mol. wt. (C 3 H 6 ) 500 = 21,040 amu . Problem 12.1 J. F. Shackelford, Introduction to Materials Science for Engineers , 7 th Edition, Prentice Hall, New Jersey (2009) Problem 12.1 Solution Professor R. Gronsky page 1 of 1 12.10 If the polymer evaluated in Problem 12.9 is polypropylene, what would be the ( a ) coiled length and ( b ) extended length of the average molecule? Reference : 12.9 The distribution of the degree of polymerization of a polymer can be rep- resented in tabular form as follows n Range n i (Mid value) Population fraction 1100 50 101200 150 201300 250 0.01 301400 350 0.10 401500 450 0.21 501600 550 0.22 601700 650 0.18 701800 750 0.12 801900 850 0.07 9011,000 950 0.05 1,0011,100 1,050 0.02 1,1011,200 1,150 0.01 1,2011,300 1,250 0.01 = 1.00 Calculate the average degree of polymerization for this system. SOLUTION ( a ) Following the leads given in Example 12.3 (p. 390 of the text), the &amp;quot;coiled length&amp;quot; of the kinked molecular chain for a linear polymer is given by Equation 12.4 of the text (p. 387), also known as the root-mean-square length, where the number of bonds m contained in linear polymers (such as polypropylene) is given by Equation 12.6 (p., 388), and n is the degree of polymerization. Combining these equations, L = l m m = 2 n L = l 2 n Problem 12.10 J. F. Shackelford, Introduction to Materials Science for Engineers , 7 th Edition, Prentice Hall, New Jersey (2009) Problem 12.10 Solution Professor R. Gronsky page 1 of 2 and substituting for the length of the single CC bond (0.154 nm) and the degree of polymeriza- tion (answer to 12.9 found in the Appendix (page AN-5), n = 612), Solving, the coiled length is ( b ) Again following the leads given in Example 12.3 (p. 390 of the text), the extended length of a linear polymer like polypropylene is given by Equation 12.5 of the text (p. 388), where the number of bonds m contained in linear polymers (such as polypropylene) is given by Equation 12.6 (p., 388), and n is the degree of polymerization. Combining these equations, and substituting for the length of the single CC bond (0.154 nm) and the degree of polymeriza-and substituting for the length of the single CC bond (0....
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HW09 Soln - 12.1 What is the average molecular weight of a...

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