In many multistep mechanisms, a reactive intermediate is produced and consumed rapidly. After a short initial transient, its concentration may remain small and change much more slowly than the individual formation and consumption rates.

The steady-state approximation sets the intermediate's net rate of change approximately to zero:

$$\boxed{\frac{d[I]}{dt}\approx0}.$$

This does not mean no molecules of I are reacting. It means formation and consumption occur at nearly equal rates, so the intermediate concentration changes only slightly on the timescale used to describe the overall reaction.

Consider the mechanism

$$\mathrm{A+B\xrightarrow{k_1}I},$$

$$\mathrm{I\xrightarrow{k_{-1}}A+B},$$

$$\mathrm{I\xrightarrow{k_2}P}.$$

The intermediate is formed at rate

$$k_1[A][B]$$

and consumed through both outgoing steps at total rate

$$k_{-1}[I]+k_2[I].$$

Therefore

$$\frac{d[I]}{dt} =k_1[A][B]-(k_{-1}+k_2)[I].$$

Under the steady-state approximation,

$$0\approx k_1[A][B]-(k_{-1}+k_2)[I],$$

so

$$\boxed{[I]\approx\frac{k_1[A][B]}{k_{-1}+k_2}}.$$

Product forms through the final step:

$$r_P=k_2[I].$$

Substituting the steady-state intermediate concentration gives

$$\boxed{r_P\approx \frac{k_1k_2}{k_{-1}+k_2}[A][B]}.$$

The unmeasured intermediate has again been eliminated from the observable rate law.

Steady state is not equilibrium

At equilibrium, opposing thermodynamic processes have no net reaction progress and the macroscopic composition is stationary. A kinetic steady state can instead sustain a continuing flux: intermediates are continually formed and consumed while products continue to accumulate.

The approximation is useful only when the intermediate actually relaxes rapidly to a low, slowly varying concentration relative to the slower evolution of the main reactants and products. It can fail during the initial transient, when an intermediate accumulates substantially, or when its formation and consumption occur on comparable slow timescales.

Steady-state elimination is a central tool for deriving useful rate laws from mechanisms too complex for a single rate-determining-step picture.