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The reaction of oleic acid with P2O5 in the presence of pyridine is a classic dehydration reaction. P2O5 acts as a powerful dehydrating agent, removing water molecules from oleic acid to form an unsaturated cyclic anhydride. The exact product will depend on the reaction conditions, but it is likely to be a mixture of various anhydride isomers. Pyridine acts as a base to facilitate the reaction and neutralize the acidic byproducts.