As background for polymer analyses, here is a list of molecular masses Total Mass of Each Type of Number of Molecules, A Mass of Each Molecule, M Molecule, MA and the # of molecules with that mass determined from a combination 800.000 800,000 of size exclusion chromatography and mass spectrometry. 750.000 2.250,000 700,000 3.500,000 The number average molecular weight is the total weight of the sample 650.000 5,200.000 divided by the number of molecules in the sample. What's the total weight of 10 600.000 6,000.090 the sample? First find the total weight of each type (or weight) of polymer. 13 550.000 7.150,000 This means that you multiply the weight of the molecule by the number of 20 $00,000 10,060.000 molecules of that weight. For example, there are 13 molecules with a weight 13 450,000 5.850,000 of 550,000 so the total weight of molecules with a weight of 550,000 is 13 x 10 400.000 4,000.000 550,00 or 7,150,000. (This seems like a really big number, but remember 350.000 2,600.000 size DOES matter with polymers: these are really big molecules.) If you do 300,000 1.500,000 this for all the types (or weights) of molecules and add the weights together 250.000 750,000 you have the total welght of the sample. In mathematical form, the total 200,000 200,000 mass is 2 MiMi, where Mi is the number of molecules of weight Mi and the Total Mass = 2 MM = 50,000,000Number of Mass of Each Total Mass of Weight Fraction Molecules Each Molecule Type of Molecule Type of Molecule (Wi) (N.) (M.) To get the number average molecular weight you divide the total weight of (N.M.) (NiMV _ NAME) (MAM.) the sample by the total number of the molecules. How do you get the total 800,000 800,000 0.016 12,800 number of molecules? Try 2 / (oh no! - you're starting to think like a 3 750.000 2,250,000 0.045 33,750 5 mathematician!). In this case 2 Wi = 100. The number average molecular 700.000 3,500.000 0.070 49,000 650,000 5,200.000 0.104 67,600 Weight for this sample is then 2 MM/ 2 M = 50,000,000/100 = 500,000. 10 600.000 Again, it's a really big number because polymers are really big molecules! 6,000.000 0.120 72,000 13 $50,000 7,150,000 0.143 78,650 The calculation of the weight average molecular weight requires that you 20 500.000 10,000,000 0.200 100.000 know the Weight Fraction, wi, of each type of molecule (or the fraction of 13 450.000 5,850.000 0.117 52.650 the total weight represented by each type of molecule). You don't know the 10 400,000 1,000,000 weight fractions from the original data, but you can calculate them. So, wh 0.080 32,000 is the weight fraction? Like any fraction, it's the amount of the thing of 350,000 2,800.000 0.056 19,600 interest divided by the total amount. For weight fraction of one type of 300,000 1,500,000 0.030 9,000 molecule, It is the weight of that type of molecule divided by the total welg 250,000 750,000 0.015 3,750 of the sample. Or, expressed in mathematical form, it is NiM/ 2 NM. Notice 200.000 200,000 0.004 800 that you have already calculated both /M and 2 MM when you calculated Weight Average Molecular Weight = 2 will = 531,600 Notice that the number average and the weight average molecular are not the same. The distribution of molecular weights in a polymer sample is often described by the ratio of the weight average molecular weight to the number average molecular weight. In this case the ratio is 531,600/500,000 = 1.063. This ratio is the Polydispersity Index (or PDI).2. SLO 4. Calculate the Mn, Mw, and polydispersity index (PDI) for the polymer sample that contains the following molecules: Number of Total Mass of Weight Fraction of Mass of Each Each Each Type of each Type of Molecule Molecule Molecules Molecule (w;) (M.) (N.) (N.* M.) (NiMi/ENiMi) (w. M.) 500000 1 400000 300000 200000 IHNUN 100000 10 11 Totals = 22 M. = M. = M/M =