Table lists the polymer mass fractions (m) and ratios of propagation to chain transfer rates (KM, KH, and K) for each active site type in a 5-site-type catalyst used to make polyethylene resins at 80 C in a fluidized-bed gas phase reactor operated at steady state. These parameters are definided in Eq. (with kt = 0), T= KtM kp m KM Kx Kg (mol-L-) + kty [H] Ktg 1 + Kp [M] k, [M] = Table Polymerization kinetic parameters for a 5-site-type catalyst. Site 3 Site 1 0.1 Site 2 0.25 1 x 10-4 0.03 5 x 10-5 5 x 10-5 0.01 2.5 x 10-5 0.3 2.5 x 10-5 0.005 1.25 x 10-5 KM + KH where [M] and [H2] are the concentrations of ethylene and hydrogen at the active sites (dissolved in the amorphous polymer phase), respectively. M = [H] [M] 1 mi 1 + KB [M] a) Plot the MWD of a polyethylene sample made at the following polymerization conditions: [M] = 0.6 mol/L and [H] = 0.04 mol/L. The molar mass of ethylene is 28 mol/g. Site 4 0.25 1.25 x 10-5 0.0025 6.25 x 10-6 b) If you need to make a resin with M = 60,000 by changing only the concentration of hydrogen in the reactor, what would be the required [H]? What would be the values of the Mw and D at these conditions? 71 Hint: The average molecular weights, M and Mw, of polymers made with a catalyst having n site types are, Site 5 0.1 6.25 x 10-6 0.00125 3.13 x 10-6 and Mw = [m.Mw W i=1 You should be able to prove these relations based on your knowledge of how Mn and Mw of polymer populations are calculated.