Are catalysts allowed to remain in the product mixture after reaction is complete?

Answer 1

Practically,..........yes.........

A catalyst typically provides another lower reaction pathway, and thus increases the rate of reaction; I stress that a catalyst typically lowers #E_a#, #"the activation energy"#; it does not alter the thermodynamic parameters of the reaction.
Ideally, a catalyst is not chemically altered during a reaction. Typically, a solid metal surface (and these are the typical catalysts) can become #"poisoned"# during the chemical reaction. Catalysts, even precious metal ones, are typically discarded when this occurs. It is easier to add a new catalyst, they are so active that you do not need a large quantity and this is not an expensive proposition, than fishing out the poisoned catalyst and restoring it.
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Answer 2

No, catalysts are not consumed in the reaction and are typically separated from the product mixture after the reaction is complete.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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