steady state (stationary state)

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:
$− d [X] d t = d [A] d t + d [D] d t$ .
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 ( $d [X] d t = 0$ ) allows the elimination of $[X]$ from the kinetic equations, whereupon the rate of reaction is expressed:
$d [D] d t = − d [A] d t = k 1 k 2 [A] [C] k −1 + k 2 [C]$

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 $d [D] d t = k 2 [X] [C]$ , 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.
In a stirred flow reactor a steady state implies a regime so that all concentrations are independent of time.