The following data was obtained for the thermally initiated bulk polymerization of monomer M$,$ where $[$M$]=8\mathrm{.}3$ M$,$ and a radical initiator, I, was used at $60$ oC:

Given that:

Rp x $10^3($mol$.$L$-1.$s$-1)$ DP

$0\mathrm{.}0058350$

$0\mathrm{.}0105550$

$0\mathrm{.}0203330$

$0\mathrm{.}0501317$

$0\mathrm{.}10592$

$0\mathrm{.}15358$

$1/$DP$=k_t[$M$*]/k_p[$M$]+\frac{k_{tr,x}}{k_p}\frac{[X]}{[M]}$ and $R_p=k_p[M][M*]$ Where X is any species in the polymerization undergoing chain transfer $($you can ignore chain transfer to polymer$).$

a$)$ Calculate CM$,$ kp$/$kt$1/2,$ and fkd in this polymerization system if it is experimentally observed that Rp $=4\mathrm{.}0$ x$10-4.[$I$]1/2.$ Hint: When developing an expression to plot, consider what species can undergo chain transfer in this system.

b$)$ Is chain transfer to initiator important in this system? If it is$,$ describe how to calculate CI $($you do not have to calculate it$,$ just describe how it would be done $$ hint: you would need a plot to do it$!)$