Multiple Reactions and Relative Rates

Both reactions would run simultaneously and this could be described by revising (19.77) to include these and any other parallel reactions. 

If we assume that the above two reactions run at exactly the same rate, then the simultaneous changes in all four species with reaction progress can be calculated in the following manner. 

This appears fairly simple and would be, except that the same problem of requiring non-thermodynamic information presents itself again. We encountered this first in choosing hematite rather than magnetite as the most likely product in reaction (19.69). In fact, we cannot realistically presume both reactions a and b will run at precisely the same rate. If the rates are different, then the net reaction path (or changes in species concentrations) could differ considerably from this simplified case. This means we need to introduce into the calculation some way of defining reaction rates. 

The reaction rate can also be expressed by the derivative with respect to time of equation (19.76). 

Taking the different reaction rates Va and Vb into account, the calculation (19.81) can then be rephrased in terms of changes with time or relative rates. For example, if reaction a progresses faster than b, then must increase faster than The relative rates can be calculated from 

---