The failure of the plots to overlay is generally indicative of catalyst activation, deactivation, or product inhibition under the reaction conditions. These cases may be distinguished by the position of the reaction progress curves relative to each other. Intercepting reactions lying below (slower rates at the same substrate concentration) the parent reactions on the rate vs. substrate concentration plot, are indicative of catalyst activation under reaction conditions. Intercepting reactions lying above (faster rates at the same substrate concentration) the parent reactions on the rate vs. substrate concentration plot, are indicative of catalyst deactivation under reaction conditions; further experimentation is necessary to distinguish product inhibition from other forms of catalyst death. One key difference between the intercepting reaction and the parent reaction described above is the presence of some amount of product in the parent reaction at the interception point. Product inhibition has long been known to influence catalyst efficiency of many systems, and in the case of same-excess experiments, it prevents the intercepting and parent reactions from overlaying. While same-excess experiments as described above cannot attribute catalyst deactivation to any particular cause, product inhibition can be probed by further experiments in which some initial amount of product is added to the intercepting reaction (designed to mimic the amount of product expected to be present in the parent reaction at the same substrate concentration). A perfect overlay of the rate vs. substrate concentration plots under same-excess-same product conditions indicates that product inhibition does occur under the reaction conditions used. While the failure of the rate vs. substrate concentration plots to overlay under same-excess-same product conditions does not preclude product inhibition, it does, at least, indicate that other catalyst deactivation paths must also be active. Same-excess experiments probing catalyst deactivation and product inhibition are among the most widely used applications of reaction progress kinetic analysis. Among the numerous examples in the literature, some include investigation of the amino alcohol-catalyzed zinc alkylation of aldehydes, the amido-thiourea catalyzed asymmetric Strecker synthesis of unnatural amino acids, and the SOMO-activation of organocatalysts. Determining reaction stoichiometry Differential methods for extracting rate constants With the wealth of data available from monitoring reaction progress over time paired with the power of modern computing methods, it has become reasonably straightforward to numerically evaluate the rate law, mapping the integrated rate laws of simulated reactions paths onto a fit of reaction progress over time. Due to the principles of the propagation