Consider the polymerization of styrene in toluene initiated by di$-$t$-$butylperoxide for a solution

containing $0\mathrm{.}04$ moles of initiator and $2$ moles of monomer per liter. The initial rates of initiation,

$Ri,$ and propagation, $Rp,$ are found to be $1\mathrm{.}6{10}^{-10}$ and $6\mathrm{.}4{10}^{-7}M{s}^{-1},$ respectively.

a$)$ Calculate fkd and kp$/$kt$^1/2$

b$)$ Assuming no chain transfer, calculate the initial kinetic chain length.

c$)$ Assuming only disproportionation and under the conditions stated, the transfer constant of

styrene, $CM,$ is $0\mathrm{.}85{10}^{-4}.$ How much does this transfer affect the molecular weight of the

polymer?

d$)$ The molecular weight of this polymer is too high. The desired molecular weight of this

polymer is $40,000g^{-1}.$ How much $CCl4($in g$/$L$)$ should be added to the reaction medium

to attain the desired molecular weight? $CS$ of $CCl4$ is $90{10}^{-4}.$