page_title: Reaction progress kinetic analysis
section_title: The steady-state approximation
hierarchical_section_title: Reaction progress kinetic analysis / Catalytic kinetics and catalyst resting state / The steady-state approximation
caption_attribution_description: English: Two examples of catalytic kinetics displaying steady-state behavior. For each case, i) describes the catalytic cycle with relevant rate constants and concentrations, ii) displays the concentration of product and reactant over the course of the reaction, iii) describes the rate of the reaction as substrate is consumed from right to left, and iv) describes the catalyst resting state as substrate is consumed from right to left. The arbitrary rate constants used to describe these scenarios are as follows for a) k1= 1 (1/(M*s)), k-1= 500 (1/s), and k2= 1000 (1/s) and b) k1= 75 (1/s), k-1= 2400 (1/(M*s)), k2= 75 (1/s), k-2=150 *1/(M*s)), and k3= 3000 (1/s). The data used to generate these plots were obtained by kinetic simulations with CopasiIU free software.
context_page_description: In chemistry, reaction progress kinetic analysis 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 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 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.
context_section_description: 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.)
caption: a) The simplest case of steady state kinetics involves one substrate reversibly forming an intermediate complex (to which the steady-state approximation is applied) with the catalyst, followed by irreversible product formation. b) In a more complex example, two substrates bind the catalyst to sequentially form two intermediates (and the steady-state approximation is applied to both) followed by irreversible product formation. Note that because I2 is kinetically invisible, this is the same as for the case where I1 goes directly to free product and catalyst. For both (a) and (b), i) describes the catalytic cycle with relevant rate constants and concentrations, ii) displays the concentration of product and reactant over the course of the reaction, iii) describes the rate of the reaction as substrate is consumed from right to left, and iv) shows that the catalyst resting state is entirely the free catalyst while the concentrations of the intermediates remain small and approximately unchanging as substrate is consumed from right to left.
exif: {}