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Solutions of practice problems_A6.docx

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14.5 Below, molecular weight data for a polypropylene material are tabulated. Compute (a) the number-average molecular weight, (b) the weight-average molecular weight, and (c) the degree of polymerization. Molecular Weight Range (g/mol) xi wi 8,000–16,000 0.05 0.02 16,000–24,000 0.16 0.10 24,000–32,000 0.24 0.20 32,000–40,000 0.28 0.30 40,000–48,000 0.20 0.27 48,000–56,000 0.07 0.11 Solution (a) From the tabulated data, we are asked to compute M n , the number-average molecu
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  14.5  Below, molecular weight data for a polypropylene material are tabulated. Compute (a) the number-average molecular weight, (b) the weight-average molecular weight, and (c) the degree of polymerization.   Molecular Weight Range (g/mol) x  i   w  i    8,000  –  16,000 0.05 0.02 16,000  –  24,000 0.16 0.10 24,000  –  32,000 0.24 0.20 32,000  –  40,000 0.28 0.30 40,000  –  48,000 0.20 0.27 48,000  –  56,000 0.07 0.11 Solution (a) From the tabulated data, we are asked to compute  M n , the number-average molecular weight. This is carried out below. Molecular wt Range Mean  M i    xi    xi M i  8,000-16,000 12,000 0.05 600 16,000-24,000 20,000 0.16 3200 24,000-32,000 28,000 0.24 6720 32,000-40,000 36,000 0.28 10,080 40,000-48,000 44,000 0.20 8800 48,000-56,000 52,000 0.07 3640  ____________________________  M n  =  x i  M  i  =33,040 g/mol  (b) From the tabulated data, we are asked to compute  M w , the weight-average molecular weight. Molecular wt. Range Mean  M  i   w i   w i  M  i  8,000-16,000 12,000 0.02 240 16,000-24,000 20,000 0.10 2000 24,000-32,000 28,000 0.20 5600 32,000-40,000 36,000 0.30 10,800   40,000-48,000 44,000 0.27 11,880 48,000-56,000 52,000 0.11 5720  ___________________________  M w  = w i  M  i  =36,240 g/mol  (c) Now we are asked to compute the degree of polymerization, which is possible using Equation 14.6. For polypropylene, the repeat unit molecular weight is just m  = 3(  A C ) + 6(  A H ) = (3)(12.01 g/mol) + (6)(1.008 g/mol) = 42.08 g/mol And  DP  =  M n m =33,040 g/mol42.08 g/mol=785    14.7  Is it possible to have a poly(methyl methacrylate) homopolymer with the following molecular weight data and a of polymerization of 527? Why or why not?   Molecular Weight Range (g/mol) w  i x  i 8,000  –  20,000 0.02 0.05 20,000  –  32,000 0.08 0.15 32,000  –  44,000 0.17 0.21 44,000  –  56,000 0.29 0.28 56,000  –  68,000 0.23 0.18 68,000  –  80,000 0.16 0.10 80,000  –  92,000 0.05 0.03 Solution This problem asks if it is possible to have a poly(methyl methacrylate) homopolymer with the given molecular weight data and a degree of polymerization of 527. The appropriate data are given below along with a computation of the number-average molecular weight. Molecular wt. Range Mean  M  i    x i    x i  M  i  8,000-20,000 14,000 0.05 700 20,000-32,000 26,000 0.15 3900 32,000-44,000 38,000 0.21 7980 44,000-56,000 50,000 0.28 14,000 56,000-68,000 62,000 0.18 11,160 68,000-80,000 74,000 0.10 7400 80,000-92,000 86,000 0.03 2580  _________________________  M n  =  x i  M  i   = 47,720 g/mol  For PMMA, from Table 14.3, each repeat unit has five carbons, eight hydrogens, and two oxygens. Thus, m  = 5(  A C ) + 8(  A H ) + 2(  A O )   = (5)(12.01 g/mol) + (8)(1.008 g/mol) + (2)(16.00 g/mol) = 100.11 g/mol  Now, we will compute the degree of polymerization using Equation 14.6 as  DP   =  M  n m  = 47,720 g/mol100.11 g/mol = 477  Thus, such a homopolymer is   not possible  since the calculated degree of polymerization is 477 (and not 527).
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