05962 IUPAC Gold Book - steady state 10.1351/goldbook.S05962 S05962 current synonyms: stationary state, steady state approximation, steady state treatment, Bodenstein approximation 1 In a kinetic analysis of a complex reaction involving unstable intermediates in lconcentration, the rate of change of each such intermediate is set equal to zero, so that the rate equation can be expressed as a function of the concentrations of chemical species present in macroscopic amounts. For example, assume that $\ce{\textbf{X}}$ is an unstable intermediate in the reaction sequence: Conservation of mass requires that: \[[\ce{A}] + [\ce{X}] + [\ce{D}] = [\ce{A}]_{0}\] which, since \([\ce{A}]_{0}\) is constant, implies: \[-\frac{{\rm{d}}[\ce{X}]}{{\rm{d}}t} = \frac{{\rm{d}}[\ce{A}]}{{\rm{d}}t} + \frac{{\rm{d}}[\ce{D}]}{{\rm{d}}t}.\] Since \([\ce{X}]\) is negligibly small, the rate of formation of $\ce{\textbf{D}}$ is essentially equal to the rate of disappearance of $\ce{\textbf{A}}$, and the rate of change of \([\ce{X}]\) can be set equal to zero. Applying the steady state approximation (\({\rm{d}}[\ce{X}]/{\rm{d}}t = 0\)) allows the elimination of \([\ce{X}]\) from the kinetic equations, whereupon the rate of reaction is expressed: \[\frac{{\rm{d}}[\ce{D}]}{{\rm{d}}t} = -\frac{{\rm{d}}[\ce{A}]}{{\rm{d}}t} = \frac{k_{1}k_{2}[\ce{A}][\ce{C}]}{k_{-1} + k_{2}[\ce{C}]}\]Note: The steady-state approximation does not imply that \([\ce{X}]\) is even approximately constant, only that its absolute rate of change is very much smaller than that of \([\ce{A}]\) and \([\ce{D}]\). Since according to the reaction scheme \({\rm{d}}[\ce{X}]/{\rm{d}}t = k_{2}[\ce{X}][\ce{C}]\), the assumption that \([\ce{X}]\) is constant would lead, for the case in which $\ce{\textbf{C}}$ is in large excess, to the absurd conclusion that formation of the product $\ce{\textbf{D}}$ will continue at a constant rate even after the reactant $\ce{\textbf{A}}$ has been consumed.In a stirred flow reactor a steady state implies a regime so that all concentrations are independent of time. The steady-state approximation does not imply that \([\ce{X}]\) is even approximately constant, only that its absolute rate of change is very much smaller than that of \([\ce{A}]\) and \([\ce{D}]\). Since according to the reaction scheme \({\rm{d}}[\ce{X}]/{\rm{d}}t = k_{2}[\ce{X}][\ce{C}]\), the assumption that \([\ce{X}]\) is constant would lead, for the case in which C is in large excess, to the absurd conclusion that formation of the product D will continue at a constant rate even after the reactant A has been consumed. chemical species https://goldbook.iupac.org//terms/view/CT01038 complex reaction https://goldbook.iupac.org//terms/view/C01208 elimination https://goldbook.iupac.org//terms/view/E02038 flow reactor https://goldbook.iupac.org//terms/view/F02443 rate equation https://goldbook.iupac.org//terms/view/R05141 rate of disappearance https://goldbook.iupac.org//terms/view/R05148 rate of reaction https://goldbook.iupac.org//terms/view/R05156 sequence https://goldbook.iupac.org//terms/view/ST06775 unstable https://goldbook.iupac.org//terms/view/U06569 PAC, 1994, 66, 1077. 'Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)' on page 1166 (https://doi.org/10.1351/pac199466051077) PAC, 1993, 65, 2291. 'Nomenclature of kinetic methods of analysis (IUPAC Recommendations 1993)' on page 2298 (https://doi.org/10.1351/pac199365102291) PAC, 1996, 68, 149. 'A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)' on page 187 (https://doi.org/10.1351/pac199668010149) PAC, 1990, 62, 2167. 'Glossary of atmospheric chemistry terms (Recommendations 1990)' on page 2216 (https://doi.org/10.1351/pac199062112167) https://goldbook.iupac.org/terms/view/S05962/html https://goldbook.iupac.org/terms/view/S05962/json https://goldbook.iupac.org/terms/view/S05962/plain Citation: 'steady state' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.S05962 The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms. If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org . The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using. 2026-06-07T01:22:01+00:00