Styrene was added to a solution of sodium naphthalene in tetrahydrofuran at $25C$ so that the initial

concentrations of styrene and sodium naphthalene in the reaction mixture were $0\mathrm{.}2mo\frac{l}{L}$ and $0\mathrm{.}001$

$mo\frac{l}{L},$ respectively. Five seconds after the addition of styrene its concentration was determined to be

$1\mathrm{.}73{10}^{?3}mo\frac{l}{L}.$ Calculate $($a$)$ overall propagation rate constant; $($b$)$ initial rate of polymerization; $($c$)$

rate of polymerization after $10s$; and $($d$)$ number average molecular weight of the polymer after $10s.$