Problem $2$: Production of cumene

You are going to produce cumene from propylene and benzene using the elementary,

reversible gas phase reaction:

$C_3{H}_6+C_6{H}_{6}harr{C}_9{H}_{12}$

which as forward and reverse rate constants of $k_f$ and $k_r,$ respectively. The research

scientists at MN Chemicals have collected the following kinetic and equilibrium data

for this reaction.

a$.$ What is the activation energy and pre$-$exponential factor for the forward rate

constant? What is the heat of reaction?

$-63k\frac{J}{m}ol$

You are synthesizing cumene using a PFR with a volume of $150$L$.$ The reactants are fed

into the isothermal, isobaric reactor with a molar flow rate of $14\mathrm{.}4mo\frac{l}{m}in$ at a

propylene: benzene molar ratio of $2$:$1$ and a total volumetric flow rate of $100\frac{L}{m}in.$

Hint: Use the partial pressures of the gases instead of the molar concentrations in your

rate expressions.

b$.$ What conversion do you achieve if the reactor is operated at $100C?[0\mathrm{.}1]$

c$.$ What conversion do you achieve if the reactor is operated at $150C?[0\mathrm{.}68]$

d$.$ Determine the equilibrium conversions at $100C$ and $150C$ as a function of

concentrations of various species? $[$at $100C,x=0\mathrm{.}95$; at $150C,x=0\mathrm{.}68]$