C$\mathrm{.}1.$ The following propagation rate constants $($units of Lmol$-1)$ are reported for the free

radical copolymerization of styrene $(M_1)$ and butadiene $(M_2)$ :

$k_{11}-0\mathrm{.}032$;$k_2=0\mathrm{.}8$;$k_{22}=0\mathrm{.}0066$;$k_{22}=0\mathrm{.}0066$;$k_{21}=0\mathrm{.}00024$

$($a$)$ Given this information, calculate the reactivity ratios for styrene and butadiene.

$($b$)$ Calculate the instantaneous composition $($mole $\%$ styrene$)$ of a copolymer formed

from an equimolar solution of the two comonomers?

$($c$)$ Would you expect the number$-$average degree of polymerization to be a linear or

nonlinear function of polymerization time? Explain.