allow one to artificially enter the reaction at any point. These experiments are critical for RPKA of catalytic reactions, as they enable one to probe a number of mechanistic possibilities including catalyst activation (induction periods), catalyst deactivation, and product inhibition described in further detail below. Determining catalyst turnover frequency Prior to further mechanistic investigation, it is important to determine the kinetic dependence of the reaction of interest on the catalyst. The turnover frequency (TOF) of the catalyst can be expressed as the reaction rate normalized to the concentration of catalyst: TOF = This TOF is determined by running any two or more same-excess experiments in which the absolute catalyst concentration is varied. Because the catalyst concentration is constant over the course of the reaction, the resulting plots are normalized by an unchanging value. If the resulting plots overlay perfectly, then the reaction is, in fact, first-order in catalyst. If the reaction fails to overlay, higher-order processes are at work and require a more detailed analysis than described here. It is also worth noting that the normalization-overlay manipulation described here is only one approach for interpretation of the raw data. Equally valid results may be obtained by fitting the observed kinetic behavior to simulated rate laws. Exploring catalyst activation and deactivation As described above, same-excess experiments are conducted with two or more experiments holding the excess, (e) constant while changing the absolute concentrations of the substrates (in this case, the catalyst is also treated as a substrate.) Note that this construction causes the number of equivalents and therefore the mole percentage of each reagent/catalyst to differ between reactions. These experiments enable one to artificially "enter" the reaction at any point, as the initial concentrations of one experiment (the intercepting reaction) are chosen to map directly onto the anticipated concentrations at some intermediate time, t, in another (the parent reaction). One would expect the reaction progress, described by the rate vs. substrate concentration plots detailed above, to map directly onto each other from that interception point onward. This will hold true, however, only if the rate of the reaction is not altered by changes to the active substrate/catalyst concentration (such as by catalyst activation, catalyst deactivation, or product inhibition) before that interception. A perfect overlay of multiple experiments with the same-excess but different initial substrate loadings suggests that no changes in the active substrate/catalyst concentration occur over the course of the reaction.