Rate equations for constant-volume batch reactors

Rate Equations for Constant-Volume Batch Reactors 

In applying a rate equation to a situation where the volume of a given reaction mixture (i.e. the density) remains constant throughout the reaction, the treatment is very much simplified if the equation is expressed in terms of a variable X, which is defined as the number of moles of a particular reactant transformed per unit volume of reaction mixture (e.g. Cao Ca) at any instant of time t. The quantity X is very similar to a molar concentration and has the same units. By simple stoichiometry, the moles of the other reactants transformed and products generated can also be expressed in terms of x, and the rate of the reaction can be expressed as the rate of increase in X with time. Thus, by definition, 

The equations which result when these integrations are carried out for reactions of various orders are discussed in considerable detail in most texts dealing with the physico-chemical aspects of chemical kinetics13-4). Table 1.1 shows a summary of some of the simpler cases the integrated forms can be easily verified by the reader if desired. 

One particular point of interest is the expression for the half-life of a reaction f,/2 this is the time required for one half of the reactant in question to disappear. A first order reaction is unique in that the half-life is independent of the initial concentration of the reactant. This characteristic is sometimes used as a test of whether a 

Reaction type Rate equation Integrated form 

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REACTOR DESIGN-GENERAL PRINCIPLES Table 1.1. Rate Equations for Constant Volume Batch Reactors... 

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