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Why exactly does the slowest reaction limit the instantaneous rate of a reaction even if the faster processes come after? Theoretically, if the products of the slow reaction are required for the fast reaction, the fast reaction limits the rate because even though it is fast, it will not finish in exact synchronization with the end of the slow reaction. There will be a lag between when the net reaction is done and when the slow reaction is done.

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It is the measured overall reaction rate that counts and not which reaction finishes the sequence. If you measure the rate of a reaction that consists of two elemental reactions with rate constants $k_1$ and $k_2$ where $k_1 \gg k_2$ you will get an overall rate constant $k_{\mathrm{tot}} \approx k_2$. This is so, because if the faster reaction takes place after the slower reaction, the faster reaction uses up its reactants (which are the products of the slower reaction) faster than the slower reaction produces its products, so that the faster reaction will consume every new product molecule produced by the slower reaction nearly instantly compared to the time it takes the slower reaction to produce it. The time it takes the faster reaction to consume the newly formed molecule is insignificant.

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