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Analysis of the Progression of Sequential Reactions

by Jack McGeachy


Submitted : Spring 2010

Sequential reactions consist of linked reactions in which the product of the first reaction becomes the substrate of a second reaction. Sequential reactions occur in industrially important processes, such as the chlorination of methane. In a series of sequential reactions, the concentration of each chemical species changes throughout the course of the reactions. A generalized series of three sequential reactions was analyzed in order to determine the times at which each chemical species reaches its maximum. In order to determine the concentration of each species as a function of time, the differential rate laws for each species were solved. The solution of each gave the concentration curve of the chemical species. The concentration curves of species A1 and A2 possessed discreet maxima, which were determined through slope-analysis. The concentration curve of the final product, A3, did not possess a discreet maximum, but rather approached a finite limit. Naturally, the concentration of the starting product was at its maximum at the starting time. The concentration curves were generalized for any intermediate species, An, and any final product, An+1. Slope-analysis of the general intermediate species concentration curve gave an expression for the time at which any intermediate species reaches its maximum. Naturally, the generalized curve for the final product was not amendable to slope-analysis, since it does not possess a discreet maximum. The resulting expression for tmax can be employed to maximize the yield of a particular intermediate species. Analogously, the concentration curve for the final product can be used to estimate the time required for reaction completion. Moreover, the generalized concentration curves suggests that higher-order intermediates will be obtained in lower yield and as more complicated mixtures than lower-order intermediates; both factors complicate the production of high-order intermediates in sequential batch reactions.



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Advisors :
Razvan Teodorescu, Mathematics and Statistics
Scott Campbell, Chemical & Biomedical Engineering
Suggested By :
Scott Campbell