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I think if they mention an excess reactant, there will always be a limiting reactant and yes, if they state that oxygen is in excess and there is only one other reactant besides oxygen, then this reactant will be the limiting reactant.
No, there will always be at least one limiting reactant in a chemical reaction. If there's no limiting reactant, then it means there's an infinite quantity of reactants, and the reaction would run forever. In a reaction with two reactants, either they are both used up simultaneously, or one is a limiting reactant, and the other is in excess.
Yes. It can be assumed that the oxygen is in excess means that the other reactant is what is limiting since all of it is being used up in the reaction rather than the reactant oxygen being not totally used up. For some of the questions we did, they just give you the weight of a single reactant, that is usually the limiting reactant, and the mass of the product so that you could find the percentage yield of that product, etc. If we don't know the masses of both reactants we can't compare their theoretical and actual mass amounts to find which is the limiting reactant so there should be some indication in this case of what is excess and what is limiting.
Just to add on to the discussion above, I think there always is a limiting reactant. so if O2 is the excess reactant, you'll have to calculate which is the limiting reactant since it's not always the case where you only have two reactants. But I agree that there is always a limiting reactant in questions like these and you can almost always find it through the given conditions. hope this helps!
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