Styrene $(=0\mathrm{.}909\frac{g}{c}{m}^3)$ polymerizes in bulk when $0\mathrm{.}01M$ di$-$tertbutylperoxide is

added to $50mL$ of monomer and the system is heated to $60C.$ Calculate i$)k_d$ for this

initiator, and ii$)$ the molecular weight of the formed polymer at this temperature if

$f=0\mathrm{.}7$ and the initial rates of polymerization and initiation are ${1\mathrm{.}5}^{**}{10}^{-3}mol{L}^{-1}{s}^{-1}$ and

$4**{10}^{-9}mol{L}^{-1}{s}^{-1},$ respectively. Termination occurs preferentially by disproportionation

but some coupling also occurs $($about $20\%).[4$p