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For different chemical reactions, does the activation energy of that reaction directly relate to the reaction rate? In other words, would a reaction always be slower if it had a higher activation energy than another reaction?

Of course, one of the reactants will be kept constant and the other reactant will differ for each reaction.

If pressure, catalyst, temperature, concentration, particle size, and other factors affecting reaction rate is kept constant, would the activation energy for each reaction be inversely proportional to the reaction rate?

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