Neco 2023 Chemistry Question 5

The intrinsic viscosity [\eta] of a dilute solution of polymethyl methacrylate (PMMA) in a given solvent at 25°C is measured to be 0.80 dL·g^{-1}. For this polymer-solvent system the Mark-Houwink parameters are K = 1.0\times10^{-4}\,\text{dL·g^{-1}} and a = 0.70. (a) Calculate the number‑average molecular weight M_n of the polymer. (b) Determine the degree of polymerization (DP) assuming the repeat‑unit molar mass is 100 g·mol^{-1}. (c) If a cross‑linking agent reduces the intrinsic viscosity by 20 % relative to the uncross‑linked polymer, estimate the fraction of repeat units that are involved in cross‑links, assuming the reduction in [\eta] is directly proportional to the fraction of cross‑linked units.