Steady State Approximation:

In chemistry, a steady state is a situation in which all state variables are constant in spite of ongoing processes that strive to change them. For an entire system to be at steady state, i.e. for all state variables of a system to be constant, there must be a flow through the system. One of the most simple examples of such a system is the case of a bathtub with the tap open but without the bottom plug: after a certain time the water flows in and out at the same rate, so the water level (the state variable being Volume) stabilizes and the system is at steady state.

The steady state concept is different from chemical equilibrium. Although both may create a situation where a concentration does not change, in a system at chemical equilibrium, the net reaction rate is zero (products transform into reactants at the same rate as reactants transform into products), while no such limitation exist in the steady state concept. Indeed, there does not have to be a reaction at all for a steady state to develop.

The steady state approximation, occasionally called the stationary-state approximation, involves setting the rate of change of a reaction intermediate in a reaction mechanism equal to zero.

It is important to note that steady state approximation does not assume the reaction intermediate concentration to be constant (and therefore its time derivative being zero), it assumes that the variation in the concentration of the intermediate is almost zero: the concentration of the intermediate is very low, so even a big relative variation in its concentration is small, if considered quantitatively.

Its use facilitates the resolution of the differential equations that arise from rate equations, which lack an analytical solution for most mechanisms beyond the most simple ones. The steady state approximation is applied, for example in Michaelis-Menten kinetics.

As an example, the steady state approximation will be applied to two consecutive, irreversible, homogeneous first order reactions in a closed system. (For heterogeneous reactions, see reactions on surfaces.) This model corresponds, for example, to a series of nuclear decompositions like

²³⁹U → ²³⁹Np → ²³⁹pu

If the rate constants for the following reaction are k₁ and k₂;

A → B → C

combining the rate equations with a mass balance for the system yields:

Reaction Rates:

Steady State:

If the steady state approximation is applied then, the derivative of the concentration of the intermediate is set to zero.

therefore

So