The analytical and approximated solutions should now be compared in order to decide when it is valid to use the steady state approximation. The analytical solution transforms into the approximate one when  because then  and  Therefore, it is valid to apply the steady state approximation only if the second reaction is much faster than the first ( is a common criterion), because that means that the intermediate forms slowly and reacts readily so its concentration stays low.
The graphs show concentrations of A (red), B (green) and C (blue) in two cases, calculated from the analytical solution.
When the first reaction is faster it is not valid to assume that the variation of [B] is very small, because [B] is neither low or close to constant: first A transforms into B rapidly and B accumulates because it disappears slowly. As the concentration of A decreases its rate of transformation decreases, at the same time the rate of reaction of B into C increases as more B is formed, so a maximum is reached when <br />From then on the concentration of B decreases.
When the second reaction is faster, after a short induction period during which the steady state approximation does not apply, the concentration of B remains low (and more or less constant in an absolute sense) because its rates of formation and disappearance are almost equal and the steady state approximation can be used.
The equilibrium approximation can sometimes be used in chemical kinetics to yield similar results to the steady state approximation. It consists in assuming that the intermediate arrives rapidly at chemical equilibrium with the reactants. For example, Michaelis-Menten kinetics can be derived assuming equilibrium instead of steady state. Normally the requirements for applying the steady state approximation are laxer: the concentration of the intermediate is only needed to be low and more or less constant (as seen, this has to do only with the rates at which it appears and disappears) but it is not required to be at equilibrium.