Problem $1$

Styrene is being polymerized at steady state in a $1,000L$ continuous reactor that can be

modeled as two perfectly mixed regions as shown in the figure below.

A solution of Styrene monomer and the initiator AIBN in toluene is fed to the larger region.

The flow rate of the feed is $1,500\frac{L}{h},$ the concentration of Styrene in the feed is $4mo\frac{l}{L},$ and

the concentration of the initiator is $0\mathrm{.}01mo\frac{l}{L}.$ the temperature of both zones is $200C$ and at

this temperature the initiator decomposes by a first$-$order process with a rate constant of $9\mathrm{.}25$

$s^{-1}.$ The rate equation for Styrene disappearance is:

$-r_p(mo\frac{l}{L}*s)=k[S][I{]}^{\frac{1}{2}}$

Where $S$ is the concentration of Styrene, I is the concentration of undecomposed initiator,

and $k=0\mathrm{.}925\frac{L^{\frac{1}{2}}}{m}o{l}^{\frac{1}{2}}*s$ at $200C.$

What are the concentrations of undecomposed initiator in $V_1$ and $V_2?$

What is the fractional conversion of Styrene in the effluent stream?