Density Dependence of Two Competing Reactions

The large effects due to rapid changes in density with pressure can be eliminated if two reactions are considered that have the same reagents, but produce two different products. In this case there will be two rate coefficients, k and k , and also other thermodynamic quantities which will be indicated by the single and double primes. The ratio of the rate coefficients will be of importance as this will indicate the ratio of products that will be obtained. By subtracting two equations of the form of eq (1.3-22), the following expression for this ratio is obtained  

Because the reagents are the same in both cases eq (1.3-23) will simplify to 

The following relationship is true for partial molar volumes at infinite dilution  

Therefore, assuming that all reagents, transition states and products are at infinite dilution, the following expression is obtained from eq (1.3-24), after the molar volume terms cancel  

The term involving the compressibility, (dVldp)T,x can now be divided out of equation (1.3-26) to give 

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