In chemistry, reaction progress kinetic analysis (RPKA) is a subset of a broad range of kinetic techniques utilized to determine the rate laws of chemical reactions and to aid in elucidation of reaction mechanisms. While the concepts guiding reaction progress kinetic analysis are not new, the process was formalized by Professor Donna Blackmond (currently at Scripps Research Institute) in the late 1990s and has since seen increasingly widespread use. Unlike more common pseudo-first-order analysis, in which an overwhelming excess of one or more reagents is used relative to a species of interest, RPKA probes reactions at synthetically relevant conditions (i.e. with concentrations and reagent ratios resembling those used in the reaction when not exploring the rate law.) Generally, this analysis involves a system in which the concentrations of multiple reactants are changing measurably over the course of the reaction. As the mechanism can vary depending on the relative and absolute concentrations of the species involved, this approach obtains results that are much more representative of reaction behavior under commonly utilized conditions than do traditional tactics. Furthermore, information obtained by observation of the reaction over time may provide insight regarding unexpected behavior such as induction periods, catalyst deactivation, or changes in mechanism.
Monitoring reaction progress Reaction progress kinetic analysis relies on the ability to accurately monitor the reaction conversion over time. This goal may be accomplished by a range of techniques, the most common of which are described below. While these techniques are sometimes categorized as differential (monitoring reaction rate over time) or integral (monitoring the amount of substrate and/or product over time), simple mathematical manipulation (differentiation or integration) allows interconversion of the data obtained by either of the two. Regardless of the technique implemented, it is generally advantageous to confirm the validity in the system of interest by monitoring with an additional independent method.
Reaction progress NMR NMR spectroscopy is often the method of choice for monitoring reaction progress, where substrate consumption and/or product formation may be observed over time from the change of peak integration relative to a non-reactive standard. From the concentration data, the rate of reaction over time may be obtained by taking the derivative of a polynomial fit to the experimental curve. Reaction progress NMR may be classified as an integral technique as the primary data collected are proportional to concentration vs. time. While this technique is extremely convenient for clearly defined systems with distinctive, isolated product and/or reactant peaks, it has the drawback of requiring a homogeneous system amenable to reaction in an NMR tube. While NMR observation may allow for the identification of a reaction intermediates, the presence of any given species over the course of the reaction does not necessarily implicate it in a productive process. Reaction progress NMR may, however, often be run at variable temperature, allowing the rate of reaction to be adjusted to a level convenient for observation. Examples of utilization of reaction progress NMR abound, with notable examples including investigation of Buchwald–Hartwig amination (One might note that considerable debate surrounded the best approach to mechanistic development of the Buchwald-Hartwig amination as indicated by a number of contradictory and competing reports published over a short period of time. See the designated article and references therein.)
In situ FT-IR In situ infrared spectroscopy may be used to monitor the course of a reaction, provided a reagent or product shows distinctive absorbance in the IR spectral region. The rate of reactant consumption and/or product formation may be abstracted from the change of absorbance over time (by application of Beers' Law). Even when reactant and product spectra display some degree of overlap, modern instrumentation software is generally able to accurately deconvolute the relative contributions provided there is a dramatic change in the absolute absorbance of the peak of interest over time. In situ IR may be classified as an integral technique as the primary data collected are proportional to concentration vs. time. From these data, the starting material or product concentration over time may be obtained by simply taking the integral of a polynomial fit to the experimental curve. With increases in the availability of spectrometers with in situ monitoring capabilities, FT-IR has seen increasing use in recent years. Examples of note include mechanistic analysis of the amido-thiourea catalyzed asymmetric Strecker synthesis of unnatural amino acids and of the Lewis base catalyzed halolactonization and cycloetherification.
In situ UV-vis Analogously to the in situ IR experiments described above, in situ UV-visible absorbance spectroscopy may be used to monitor the course of a reaction, provided a reagent or product shows distinctive absorbance in the UV spectral region. The rate of reactant consumption and/or product formation may be abstracted from the change of absorbance over time (by application of Beer's Law), again leading to classification as an integral technique. Due to the spectral region utilized, UV-vis techniques are more commonly utilized on inorganic or organometallic systems than on purely organic reactions, and examples include exploration of the samarium Barbier reaction.
Reaction calorimetry Calorimetry may be used to monitor the course of a reaction, since the instantaneous heat flux of the reaction, which is directly related to the enthalpy change for the reaction, is monitored. Reaction calorimetry may be classified as a differential technique since the primary data collected are proportional to rate vs. time. From these data, the starting material or product concentration over time may be obtained by simply taking the integral of a polynomial fit to the experimental curve. While reaction calorimetry is less frequently employed than a number of other techniques, it has found use as an effective tool for catalyst screening. Reaction calorimetry has also been applied as an efficient method for mechanistic study of individual reactions including the prolinate-catalyzed α-amination of aldehydes and the palladium catalyzed Buchwald-Hartwig amination reaction.
Further techniques While Gas Chromatography, HPLC, and Mass Spectrometry are all excellent techniques for distinguishing mixtures of compounds (and sometimes even enantiomers), the time resolution of these measurements is less precise than that of the techniques described above. Regardless, these techniques have still seen use, such as in the investigation of the Heck reaction where the heterogeneous nature of the reaction precluded utilization of the techniques described above. and SOMO-activation by organocatalysts Despite their shortcomings, these techniques may serve as excellent calibration methods.
Data manipulation and presentation
Reaction progress data may often most simply be presented as plot of substrate concentration ([A]t) vs. time (t) or fraction conversion (F) vs. time (t). The latter requires minor algebraic manipulation to convert concentration/absorbance values to fractional conversion (F), by:
F =
where [A]0 is the amount, absorbance, or concentration of substrate initially present and [A]t is the amount, absorbance, or concentration of that reagent at time, t. Normalizing data to fractional conversion may be particularly helpful as it allows multiple reactions run with different absolute amounts or concentrations to be compared on the same plot.
Data may also commonly be presented as a plot of reaction rate (v) vs. time (t). Again, simple algebraic manipulation is required; for example, calorimetric experiments give:
v =
where q is the instantaneous heat transfer, ΔH is the known enthalpy change of the reaction, and V is the reaction volume.
Data from reaction progress kinetics experiments are also often presented via a rate (v) vs. substrate concentration ([S]) plot. This requires obtaining and combining both the [S] vs. t and the v vs. t plots described above (note that one may be obtained from the other by simple differentiation or integration.) The combination leads to a standard set of curves in which reaction progress is read from right to left along the x-axis and reaction rate is read from bottom to top along the y-axis. While these plots often provide a visually compelling demonstration of basic kinetic trends, differential methods are generally superior for extracting numerical rate constants. (see below)
Catalytic kinetics and catalyst resting state
In catalytic kinetics, two basic approximations are useful (in different circumstances) to describe the behavior of many systems. The situations in which the pre-equilibrium and steady-state approximations are valid can often be distinguished by reaction progress kinetic analysis, and the two situations are closely related to the resting state of the catalyst.
The steady-state approximation
Under steady-state conditions, the catalyst and substrate undergo reversible association followed by a relatively rapid consumption of the catalyst–substrate complex (by both forward reactions to product and reverse reactions to unbound catalyst.) The steady-state approximation holds that the concentration of the catalyst-substrate complex is not changing over time; the total concentration of this complex remains low as it is whisked away almost immediately after formation. A steady-state rate law contains all of the rate constants and species required to go from starting material to product, while the denominator consists of a sum of terms describing the relative rates of the forward and reverse reactions consuming the steady-state intermediate. For the simplest case where one substrate goes to one product through a single intermediate:
In a slightly more complex situation where two substrates bind in sequence followed by product release:
Increasingly complex systems can be described simply with the algorithm described in this reference.
In the case of the steady-state conditions described above, the catalyst resting state is the unbound form (because the substrate-bound intermediate is, by definition, only present at a minimal concentration.)
The pre-equilibrium approximation
Under pre-equilibrium conditions, the catalyst and substrate undergo rapid and reversible association prior to a relatively slow step leading to product formation and release. Under these conditions, the system can be described by a "one-plus" rate law where the numerator consists of all rate constants and species required to go from starting material to product, and the denominator consists of a sum of terms describing each of the states in which the catalyst exists (and 1 corresponds to the free catalyst). For the simplest case where one substrate goes to one product through a single intermediate:
In the slightly more complex situation where two substrates bind in sequence followed by product release:
In the case of the simple pre-equilibrium conditions described above, the catalyst resting state is either entirely or partially (depending on the magnitude of the equilibrium constant) the substrate bound complex.
Saturation kinetics