Steady-State Approximation



Imagine for me a hypothetical system of chemical components: some chemical A undergoes a sort of change to form an intermediate chemical I, which in turn itself undergoes some sort of change to form a product B.


In chemistry, reactions like these are often studied in conjuncture with reaction kinetics and reaction rates, i.e. how fast will this process unfold? If we're interested in the rate at which I produce B, I'll need to generate a rate function that can describe how the concentration of B changes with respect to time. Well in this case, if this reaction is first order in each step, (the rate at which you form the product is a constant multiple of the concentration of the reactant), you can firstly relate the rate of B forming with respect to the concentration of your intermediate:

Or in fancy calculus terms:

But here is where we run into the real problem with our system: how can we quantify the concentration of the intermediate? We didn't specifically add any intermediate, and the concentration of said intermediate is initially in flux as our reaction begins to progress.

Enter Steady-State.

If you investigate these types of consecutive reactions you'll find that, given enough time, your system typically reaches a point where the rate of I produced is going to be equivalent to the rate of I being consumed. This is useful because we can define the rate in as a function of [A], and the rate out as a function of [B]. i.e. defining the production of products as a function of initial concentrations of reactants.


Reducing problems to be functions of that which you can control can make life a lot easier.

I believe that this process of thought is not strictly confined to the realm of reaction kinetics. In a world that seems to constantly be in a state of fluctuation, finding the steady-states within the noise, I find, can help alleviate the stress that naturally comes from a system so far out from equilibrium. And being a source of steady-state to those in your life, being someone who's reliant and dependable, can help others in their own quests to find that piece of calm and steady: even among life's most chaotic of systems.

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