A manufacturer of polystyrene beads claims that they have an average molar mass of 250

Chapter 19, Problem 19.34

(choose chapter or problem)

A manufacturer of polystyrene beads claims that they have an average molar mass of 250 kg mol1. Solutions of these beads are studied by a physical chemistry student by dilute solution viscometry with an Ostwald viscometer in both the good solvent toluene and the theta solvent cyclohexane. The drainage times, tD, as a function of concentration for the two solvents are given in the table below. (a) Fit the data to the virial equation for viscosity, =*(1 + []c + k[]2c2 + ) where k is called the Huggins constant and is typically in the range 0.350.40. From the fit, determine the intrinsic viscosity and the Huggins constant. (b) Use the empirical MarkKuhnHouwinkSakurada equation (eqn 19.25) to determine the molar mass of polystyrene in the two solvents. For theta solvents, a = 0.5 and K = 8.2 105 dm3 g1 for cyclohexane; for the good solvent toluene a = 0.72 and K = 1.15 105 dm3 g1. (c) According to a general theory proposed by Kirkwood and Riseman, the root mean square end-to-end distance of a polymer chain in solution is related to [] by [] = _r 2_3/2/M, where is a universal constant with the value 2.84 1026 when [] is expressed in cubic decimetres per gram and the distance is in metres. Calculate this quantity for each solvent. (d) From the molar masses calculate the average number of styrene (C6H5CH=CH2) monomer units, _n_, (e) Calculate the length of a fully stretched, planar zigzag configuration, taking the C-C distance as 154 pm and the CCC bond angle to be 109. (f) Use eqn 19.33 to calculate the radius of gyration, Rg. Also calculate _r 2_1/2 = n1/2. Compare this result with that predicted by the KirkwoodRiseman theory: which gives the better fit? (g) Compare your values for Mto the results of 19.33. Is there any reason why they should or should not agree? Is the manufacturers claim valid? c/(g dm3 toluene) 0 1.0 3.0 5.0 tD/s 8.37 9.11 10.72 12.52 c/(g dm3 cyclohexane) 0 1.0 1.5 2.0 tD/s 8.32 8.67 8.85 9.03