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When using the pre-equilibrium approach, you are trying to make sure that the proposed rate law is the same as the experimentally determined rate law. You use the pre-equilibrium approach to reason what the rate law for the equation is when the slow step has a reaction intermediate in it. By using the ratio of the rate constants at equilibrium to replace the concentration of the intermediate in terms of what you know, you can determine if the rate law for the slow step.
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