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What can happen to the reaction rate of a system that is heated and then cooled?

Your question isn't quite clear; however, reaction rates increase, generally, with increase in T and decrease with decrease in T. Another way to interpret the problem is that an increase in T may "climb the hill" to a point over the activation energy of the system where the reaction proceeds, then the reaction continues after it is cooled. If this isn't in the ball park, please repost and clarify.

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