The selectivity of competitive reactions

We consider the reaction scheme of eq. (3.52) and define the kinetics of the desired and undesired reaction respectively  

Competitive reactions in batch reactors Let us consider a batch reactor where 

It follows from eqs. (3.8) and (3.56) that the differential selectivity ratio can be expressed in terms of and as follows  

Integration of the second equation leads to the following relation between the selectivity and the degree of conversion for batch reactors  

The index 1 refers to the conditions at the end of the reaction. This equation is also applicable to plug flow reactors, then the index 1 refers to exit conditions. With eq. (3.58) the selectivity can be calculated as a function of the degree of conversion (without considering the time coordinate), for any value of the reaction orders p and jc. We see at once that when p jc, the selectivity decreases with increasing conversion, and when p jc the selectivity increases. This is illustrated in figure 3.9 for = 2, for p - jc = 1, and for p - jc = -1. 

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In some cases, modifications in the selectivity, in relation to classical heating, have been observed. These modifications have been ascribed to changes in the reaction path under microwave irradiation the more polar path will be favored. Computational studies have shown that the harder transition state must be favored under microwave irradiation. This result opens new possibilities for the application of micro-wave irradiation to organic and inorganic synthesis as dramatic modifications in the selectivity of competitive reactions can be expected if the transition states are of different hardness. 

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