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Intermediates are a necessary part of the reaction, as the reactants don't necessarily just form into the products in one step so intermediates are formed and used up within reactions. However, they do not show up in the products.
Intermediates are any species that are initially formed at some step in the reaction and then are consumed entirely in the reaction process. So, they won't be in the final products but they will be apparent if you write out all of the steps of the reaction.
In a multi-step reaction, there are intermediates. They are something that forms in an earlier step, but are ultimately used as a reactant in a subsequent step. Thus, they are cancelled out in the net/final equation. They are essential to the mechanism of the reaction, but do not end up in the final equation.
Intermediates are what they sound like. They are molecules that are produced in one reaction and consumed by a second reaction. They occur, because most reactions don't always happen in a single step. Intermediates just represent products in a first reaction and reactants in a second. You can tell, because they are used up.
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