## 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:
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Conservation of mass requires that: $[\text{A}] + [\text{X}] + [\text{D}] = [\text{A}]_{0}$ which, since [A]0 is constant, implies: $-\frac{\text{d}[\text{X}]}{\text{d}t} = \frac{\text{d}[\text{A}]}{\text{d}t}+\frac{\text{d}[\text{D}]}{\text{d}t} .$ 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: $\frac{\text{d}[\text{D}]}{\text{d}t} = -\frac{\text{d}[\text{A}]}{\text{d}t} = \frac{k_{1}\,k_{2}[\text{A}]\,[\text{C}]}{k_{-1}\,+k_{2}\,[\text{C}]}$
Note:
The steady-state approximation does not imply that $$[\text{X}]$$ is even approximately constant, only that its absolute rate of change is very much smaller than that of $$[\text{A}]$$ and $$[\text{D}]$$. Since according to the reaction scheme $$\frac{\text{d}[\text{X}]}{\text{d}t} = k_{2}\,[\text{X}]\,[\text{C}]$$, the assumption that $$[\text{X}]$$ 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 (https://doi.org/10.1351/pac199365102291)
PAC, 1994, 66, 1077. 'Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)' on page 1166 (https://doi.org/10.1351/pac199466051077)
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]