Styrene is polymerized by free-radical mechanism in solution. The initial monomer and imitator concentrations are 1M (molar) and 0.001 M, respectively. At the polymerization temperature of 60°C, the initiator efficiency is 0.30. The rate constants at the polymerization temperature are as follows:

kd= 1.2 *10^-5 s^-1

kp=176M^-1s^-1

kt=7.2*10^7 M^-1 s^-1

Given this information, determine the following:

(a) Rate of initiation at 1 min and at 16.6 h

(b) Steady-state free-radical concentration at 1 min

(c) Rate of polymerization at 1 min

(d) Average free-radical lifetime, τ, at 1 min, where τ is defined as the radical concentration divided by the rate of termination

(e) Number-average degree of polymerization at 1 min