Equations, mathematical consecutive reactions

Table 8.3 Mathematical equations to describe the concentrations3 of the three species A, B and C involved in the consecutive reaction, A — B — C...

The complications arising from the existence of these consecutive reactions seems to hinder the testing of the theory of bimolecular changes which we have applied to the other examples, since at least two values of k must be involved. These cannot be separately determined by mathematical means, since the differential equations for bimolecular consecutive reactions are not soluble in simple form, and calculation even by differential methods is not possible in ignorance of what part of the pressure change is due to each reaction. 

With these kinetic data and a knowledge of the reactor configuration, the development of a computer simulation model of the esterification reaction is iavaluable for optimising esterification reaction operation (25—28). However, all esterification reactions do not necessarily permit straightforward mathematical treatment. In a study of the esterification of 2,3-butanediol and acetic acid usiag sulfuric acid catalyst, it was found that the reaction occurs through two pairs of consecutive reversible reactions of approximately equal speeds. These reactions do not conform to any simple first-, second-, or third-order equation, even ia the early stages (29). 

However, when one gets down to detailed quantitative equations to represent real, actual reactions with several steps in consecutive sequence, the mathematics become very complex. Thus, the change in the limiting current with time introduces complications that one tries to avoid in other transient methods by working at low times (constant current or constant potential approaches) or at times sufficiently high that the current becomes entirely diffusion controlled. However, taking into account the... 

A universal method of handling the problem is mathematical modelling, i.e., a quantitative description by means of a set of equations of the whole complex of interrelated chemical, physical, fluiddynamic, and thermal processes taking place concurrently or consecutively in a reactor. Constants of these equations are determined in laboratory experiments. If the range of determining factors (reactive mass compositions, temperature, reaction rates, and so on) in an actual process lie within or only slightly outside the limits studied in laboratory experiments, the solution of the determining set of equations provides a reliable idea of the process operation. 

Consider a gas-liquid system where the reaction taking place in absorption is reaction 27 (reference is made here to the pr viuos lecture on the mathematical layout. Equations are numbered consecutively with that lecture). The equilibrium constant K, see Eq.28, is in actual practice always very large (values of the order of 10 for equimolar reactions are typical) which is not surprising since K is a measure of the ratio of the chemical capacity of the reactive liquid to the physical capacity of the non-reactive solvent should such a ratio not be large, there would be no reason to use a chemically reactive liquid rather than simply the non-reactive solvent. 

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