Consider the case of a dilute solution of polystyrene in toluene (a good solvent for this polymer). The kinematic viscosity of toluene at 60C is 0.0056 stokes and its density at the same temperature is 0.84 kg/l. The chemical diffusion coefficient for a monodisperse polystyrene of molecular mass M = 520,000 g/mol was determined to be 810-8 cm2/s at T = 60C. a) Find the radius of gyration (half its effective diameter) for this macromolecule in nm. b) Find the diffusion coefficient of polystyrene in a very dilute solution of toluene for degrees of polymerization of 1,500, 3,000, 4,500, 6,000, 7,500 and 9,000 (i.e., the number of monomers contained in a macromolecule). Make a plot of the diffusion coefficient as a function of degree of polymerization (use appropriate scales such that your plot is a straight line).