Styrene is polymerized by free$-$radical mechanism in solution. The initial monomer and

initiator concentrations are $1M($molar$)$ and $0\mathrm{.}001M,$ respectively. At the polymerization tem$-$

perature of $60C,$ the initiator efficiency is $0\mathrm{.}30.$ The rate constants at the polymerization tem$-$

perature are as follows:

$k_d=1\mathrm{.}2{10}^{-5}{s}^{-1}$

$k_p=176M^{-1}{s}^{-1}$

$k_t=7\mathrm{.}2{10}^7{M}^{-1}{s}^{-1}$

Given this information, determine the following:

a$)$ Rate of initiation at $1$min and at $5hr.$

b$)$ Steady state free radical concentration at $1$min

c$)$ Rate of polymerization at $5hr$

d$)$ Average free$-$radical lifetime, $$ at $1$min where $$ is defined as the radical

concentration divided by the rate of termination.

e$)$ Number average degree of polymerization at $1$min