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Intermediates aren't included in the rate law because within the whole mechanism they are produced and used up, so there is no net effect on the rate from the intermediate, so there is no reason to include something that doesn't affect the rate in the rate law.
If a compound or element is both produced and used up, it is an intermediate regardless of how reactive it may be. Most intermediates are very reactive, which is why they are typically short-lived molecules that quickly convert to a more stable form. In other words, they are used up fast.
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