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.