Polymerization engineering

$5-3$ The apparent propagation rate constant for polymerization of styrene in THF at $25C$ using sodium naphthalene as initiator is $550\frac{L}{m}ol.$ s$.$ 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 $(\frac{M_w}{M_n}).$

$[$Ans$.R_p=0\mathrm{.}165mo\frac{l}{L}.s$;$M_n=1\mathrm{.}56{10}^6\frac{g}{m}ol]$