## Wikipedia - Approssimazione dello stato stazionario (it) Wikipedia - Estado estacionário (engenharia química) (pt) Wikipedia - Steady state (chemistry) (en) Wikipedia - Steady state-approksimasjon (kjemi) (no) Wikipedia - Teoria stanu stacjonarnego (chemia) (pl) 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 @[email protected] involving @[email protected] intermediates in low concentration, the rate of change of each such intermediate is set equal to zero, so that the @[email protected] can be expressed as a function of the concentrations of @[email protected] present in macroscopic amounts. For example, assume that X is an @[email protected] intermediate in the reaction @[email protected]:
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Conservation of mass requires that: $[\text{A}] + [\text{X}] + [\text{D}] = [\text{A}]_{0}$ which, since $$[\text{A}]_{0}$$ 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 $$[\text{X}]$$ is negligibly small, the rate of formation of D is essentially equal to the @[email protected] of A, and the rate of change of $$[\text{X}]$$ can be set equal to zero. Applying the steady state approximation ($$\frac{\text{d}[\text{X}]}{\text{d}t} = 0$$) allows the @[email protected] of $$[\text{X}]$$ from the kinetic equations, whereupon the @[email protected] 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 @[email protected] 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]