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The catalyst will appear from the beginning in the proposed reaction mechanism, but it will not appear in the overall equation because it will not be used up in the reaction and will therefore appear as both a reactant and a product in the elementary reactions, causing it to cancel out overall.
The catalyst will be needed for the reaction to occur and therefore will be present before the reaction takes place. It will then get made again (or not used up) so the catalyst will then be present before the reaction takes place and after the reaction takes place.
It is important to differentiate between a catalyst and an intermediate. A catalyst is present from the beginning of the reaction and is not consumed. However, an intermediate is produced by the reaction and is used up in the reaction.
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