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We know that the slow step is the rate determining step, so if the first step is the slow step then the rate law is of that step is the overall rate law. However if the second or third step is the slow step would the overall rate law be just the rate law of that step or do we also take into account the rate law of the previous steps ?
The overall rate law of the reaction is dependent on the slowest reaction mechanism. So the overall rate law would be equal to the rate law of the slowest step regardless of the reaction rates of the other steps. Since the slowest step is the "bottleneck" for the whole reaction you only need to take into account the rate law of that step.
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