Reaction Rates and Conversion in Nonisothermal Systems

Thus far in discussing kinetics we have confined our interests to analysis of expressions of the form 

From one point of view, the solution depends on obtaining a relationship between temperature and composition, so the terms of equation (1-164) can be expressed in terms of a single dependent variable and, hopefully, integrated analytically. Alternatively, one could look for a temperature-time relationship. This may not be easy to do, however, since the time-temperature or composition-temperature history of a reaction in which heat is evolved or consumed is a function of the rate itself. Obviously, one must look to another relationship in addition to that of mass conservation in order to obtain this history. 

1 Coupling of the Energy-Conservation Equation to the Mass-Conservation Equation 

In the following we discuss some simple types of homogeneous adiabatic reactions to illustrate the application of the coupled conservation equations (1-15) and (1-165). Since the treatment of nonadiabatic reactions depends on the detail concerning heat transfer with the surroundings, a topic more conveniently associated with particular reactor types, we will for the moment be content with what can be learned from the limiting kinds of temperature behavior—isothermal and adiabatic. 

2 Rates and Conversions in Some Simpie Adiabatic Reactions 

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