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I think making of the reaction concentration smaller conceptually simulates the reactant not having as much of an affect on reaction rate allowing us to see kind of affect the other reactant has.
By making all but one of the reactants very large, we can isolate the change in the concentration of one specific compound so that the rate law can be experimentally determined as opposed to testing all different trials and keeping different concentration of species the same. Since the concentration is so large, any change in it is negligible and thus can be ommitted in the rate law. The rate reactions produced by this are called psuedo rate laws.
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