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The standard enthalpy of formation specifically refers to the amount of enthalpy for the formation of 1 mole of a substance, so that's why the units for it is kJ/mol. The standard reaction enthalpy has no mention of mols (hence no mols in the units, just kJ as the standard unit) and refers to the whole reaction's enthalpy.
Standard enthalpy of formation is the change of enthalpy when only one mole of that molecule is formed by its constituent elements ie elements found in their natural forms such as H2 and N2. Standard reaction enthalpy is the change in enthalpy that occurs in a system when matter is transformed by a given chemical reaction. This is not dependent on the amount of moles in the reaction, but can be converted to the enthalpy change in just one mole change.
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