Sodium $(1\mathrm{.}15g)$ and naphthalene $(7\mathrm{.}0g)$ were stirred together in $50mL$ dry

tetrahydrofuran to form a dark green solution of sodium naphthalenide. When $1\mathrm{.}0$

$mL$ of this green solution was introduced into a solution of styrene $(208g)$ in dry

tetrahydrofuran by a rapid injection technique, the latter turned reddish orange.

The total final volume of the mixture was $1L.$ Assume that the injection of the

initiator resulted in instantaneous homogeneous mixing. After $5$ seconds of

reaction at $25C,$ the styrene concentration was determined to be $1\mathrm{.}73{10}^{-2}$

$mo\frac{l}{L}.$ After $10$ seconds the color of the reaction mixture was quenched by adding

a few milliliters of methanol. The polymer was then precipitated and washed with

methanol. Calculate $($a$)$ Overall propagation rate constant; $($b$)$ initial rate of

polymerization; $($c$)$ rate of polymerization after $10s$; $($d$)$ molecular weight of the

final polymer.

Hint: $R_p=-d\frac{M}{d}t=k_p[I]0[M],$ integrating this equation you will get:

$ln([M]\frac{0}{M})=k_p[I]0,$ assuming $[M{]}_0[I]0.$