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I believe it has something to do with simplifying the rate law by assuming that all reactants are in great excess except for one, which will be used to determine the rate of reaction. If something is in great excess, then some time later, it will have minimal change relative to reactants that are in more minimal amounts. Only the reactant with the noticeable change in concentration will be analyzed.
Pseudo-1st-order reaction is one example, which is the circumstance where a second order reaction appears to be first order. That is when one of the reactants in the rate equation is present in great excess over the other in the reaction mixture. So the rate constant of one of the reactants combines with that of another reactants to create the rate constant for the pseudo-1st-order reaction.
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