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In exothermic reactions, heat is released, whereas heat is absorbed in endothermic reactions. But exothermic reactions are often described as being associated with an increase in temperature, and the opposite is the case for endothermic reactions.

How does heat release result in a higher temperature of the system, and heat absorption result in lower temperature? Shouldn't it be the other way around?

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    $\begingroup$ Endothermic reaction is cooling the mixture, exothermic is heating - clear now? BTW this thing was asked here like a dozen times already and isn't any better because of it. $\endgroup$
    – Mithoron
    Mar 14 at 16:22
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    $\begingroup$ Exothermic means that, to hold the temperature constant during the reaction, heat has to be removed. If the heat is not removed, the temperature must rise. $\endgroup$ Mar 14 at 17:16
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Your confusion is understandable. I looked at the answers linked in the comment on your OP, and I'd like to explain it differently from how they do. Hopefully this explanation will get to the heart of your confusion.

You are thinking (incorrectly) that an exothermic reaction works something like this:

The system has a certain amount of thermal energy. In an exothermic reaction, some of the system's thermal energy is relased to the environment, and thus the system must lose thermal energy and thus decrease in temperature. I.e., you're imagining something like what happens when a warm block of metal is placed in a cool cup of water. The metal releases some of its thermal energy to the water, and thus cools.

But that's not what happens in an exothermic reaction. In an exothermic reaction, the system internally generates extra thermal energy. This is generated through a chemical reaction in which chemical energy (essentially, the energy in chemical bonds) is converted to thermal energy. Now, if the system is internally generating extra thermal energy, any of a number of things can be done with this energy. The two most common pictures are as follows:

  1. The system is in a large (relative to the system) constant-temperature heat bath, and is surrounded by diathermal (heat-conducting) walls. In this case, because the temperature of the system is kept constant, the thermal energy flows out (i.e., is released) into the bath.

  2. The system is adiabatic, i.e., is surrounded by a perfect thermal insulator. In this case, the extra thermal energy stays within the system, causing its temperature to increase.

The reverse of what I wrote above applies to an endothermic reaction.

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