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I believe that the enthalpy of formation is a type of reaction enthalpy. Every formation reaction is a reaction, but not every reaction is a formation reaction. Therefore, enthalpy of formation is just one example of reaction enthalpy.
Reaction enthalpy is the change in heat that occurs when a reaction takes place. To calculate this, you would add the different 's of each reaction that took place in order to form the product, i.e. Hess's Law. The enthalpy of formation is the change in enthalpy when an element in its standard state reacts to form a product that is a compound.
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