Definition of steady state (or stationary state)

1. (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:

   A X

   X + C D

   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:

   

   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]/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.