The apparent propagation rate constant for polymerization of styrene in $THF$ at $25C$ using sodium

naphthalene as initiator is $550Lmo{l}^{-1}{s}^{-1}.$ If the initial concentration of styrene is $156\frac{g}{L}$ and

that of sodium naphthalene is $0\mathrm{.}03\frac{g}{L},$ calculate the initial rate of polymerization and, for complete

conversion of the styrene, the number average molecular weight of the polymer formed. Comment upon

the expected value of the polydispersity index $(\frac{?}{\text{b}\text{a}\text{r}}\frac{(M{)}_w}{\frac{?}{?}}$bar $(M{)}_n).$