steady state (stationary state)

also contains definition of: steady state approximation (treatment)
https://doi.org/10.1351/goldbook.S05962
  1. In a kinetic analysis of a complex reaction involving unstable intermediates in low concentration, 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 X is an unstable intermediate in the reaction sequence:
    Conservation of mass requires that: [A]+[X]+[D]=[A]0 which, since [A]0 is constant, implies: −d[X]dt=d[A]dt+d[D]dt. Since [X] is negligibly small, the rate of formation of D is essentially equal to the rate of disappearance of A, and the rate of change of [X] can be set equal to zero. Applying the steady state approximation (d[X]/dt=0) allows the elimination of [X] from the kinetic equations, whereupon the rate of reaction is expressed: d[D]dt=−d[A]dt=k1k2[A][C]k−1+k2[C]
    Note: The steady-state approximation does not imply that [X] is even approximately constant, only that its absolute rate of change is very much smaller than that of [A] and [D]. Since according to the reaction scheme d[X]/dt=k2[X][C], the assumption that [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.
  2. In a stirred flow reactor a steady state implies a regime so that all concentrations are independent of time.
Sources:
PAC, 1993, 65, 2291. (Nomenclature of kinetic methods of analysis (IUPAC Recommendations 1993)) on page 2298 [Terms] [Paper]
PAC, 1994, 66, 1077. (Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)) on page 1166 [Terms] [Paper]
See also:
PAC, 1990, 62, 2167. (Glossary of atmospheric chemistry terms (Recommendations 1990)) on page 2216 [Terms] [Paper]
PAC, 1996, 68, 149. (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 187 [Terms] [Paper]
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. https://doi.org/10.1351/goldbook.S05962 RIS BibTex EndNote
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