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$$\ce{4Fe + 3O2 -> 2Fe2O3(s) + 1625~$\mathrm{kJ}$}$$

This should be endothermic because the energy is in the product. However, if the equation is viewed from the perspective of the reactant, it is endothermic.

Is this endo- or exothermic?

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The reaction is exothermic left to right and endothermic right to left. Yes, as you noted, it's wise to note which way you are looking at the reaction, but generally, we look at reactions from left to right (because the arrow generally points left to right). For example, the following reaction is endothermic as written, i.e. very hot water (steam) is very corrosive and adding heat to water encourages further ionization of water.

$$\ce{2H2O ⟶ H3O+ + HO-}$$

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The reaction is exothermic:

A system that releases heat to the surroundings is an exothermic reaction.

Furthermore, forming a chemical bond releases energy and therefore is an exothermic process, such as when Iron and Oxygen bond to form Iron(II) Oxide. Sometimes it's not clear whether more bonds were formed or broken during a chemical reaction so we have to add up the energies to see, unless they are already given to us like in this example.

Lastly, always consider the equation in the direction the arrow is pointing. The standard is to point from left to right, but sometimes it can point both ways simultaneously. In this case, the question should state which direction of the chemical reaction it wants you to consider.

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In the equation given, the energy is not actually in the product, but is written as a product, meaning that 1625 kJ of heat is evolved along with 2 moles of iron(II) oxide.

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An exothermic reaction! As you can see that the products of the reaction involves two chemical species and energy... that is after the reaction you got energy as well as two compounds hence the reaction is an exothermic reaction...

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