(a) Calculate the concentration of benzoyl peroxide required to prepare polystyrene with a number average molar mass of 750 kg/mol by bulk polymerization at 60°C.
Assume:
(i) the initiator is 60% efficient, (ii) the rate coefficients for initiator dissociation, propagation, and termination are; 2x10⁻⁶ s⁻¹, 341 dm³ mol⁻¹ s⁻¹, and 4x107 dm³ mol⁻¹ s⁻¹ respectively, (iii) the density of styrene at the polymerization temperature is 0.88 g/cm³, and (iv) that termination by disproportionation, and chain transfer to initiator and monomer, are negligible. (b) Calculate the initial values of (i) the radical concentration and (ii) the rate of bulk polymerization expected for bulk polymerization of styrene at the concentration of benzoyl peroxide determined in (a).