Pre-Equilibrium Approximation

A rate law can only contain concentrations you can actually measure in a flask: starting reactants and sometimes products, never an intermediate that exists briefly mid-mechanism. That creates a puzzle when the slow step, the one that controls the overall rate, involves an intermediate. You need a way to trade that intermediate's concentration for something measurable. That's exactly what the pre-equilibrium approximation does.

It works when the first step of a mechanism is fast and reversible, reaching equilibrium before the slow second step has any real chance to drain it away. Because that first step sits at equilibrium, its forward and reverse rates are equal, so you can write K = [intermediate]/[reactants] and solve for the intermediate. Substitute that expression into the slow step's rate law, and the intermediate disappears, replaced by reactants raised to whatever powers the equilibrium expression demands. The result is an overall rate law built entirely from measurable starting materials, with an observed rate constant that is really a product like k2 times K.

This sits right next to the steady-state approximation, the other tool for erasing intermediates from a rate law. Pre-equilibrium assumes the first step is fast enough to stay balanced; steady-state instead assumes the intermediate's concentration stays roughly constant because it's used up as fast as it forms. Both roads lead to the same destination: a rate law written only in terms of things you can put a number to in the lab.