Isothermal Yield of Allyl Chloride versus Conversion of Propylene

Consider the gas-phase chlorination of propylene with to produce allyl chloride. The reaction network is as follows:
,
,
.
Propylene and allyl chloride are labelled species and , respectively.
The reaction rates are given by
,
,
.
These reaction rate expressions are postulated based on the following observation: step 1 is faster than step 3 at 500°C and step 3 occurs at temperature as low as 100°C, while steps 1 and 2 have negligible velocities.
Yield of allyl chloride versus conversion of propylene for the isothermal behavior of a plug-flow reactor is given by the following relationship:
, where and .
This expression can be easily derived using the Mathematica built-in command DSolve, assuming product-free feed (i.e., and ). Indeed, and are subject to the following differential equation and initial condition:
and .
This Demonstration provides insights into how temperature will affect the yield.

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J. J. Carberry, Chemical and Catalytic Reaction Engineering, Mineola, NY: Dover, 2001.
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