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Oleum (Latin oleum = "oil"), or fuming sulfuric acid refers to a solution various compositions of sulfur trioxide in sulfuric acid or sometimes more specifically to pyrosulfuric acid, disulfuric acid.

Oleums can be described by the formula xSO₃.H₂O where x is the total molar sulfur trioxide content. The value of x can be varied, to include different oleums. They can also be described by the formula H₂SO₄.xSO₃ where x is now defined as the molar free sulfur trioxide content. Oleum is generally assayed according to the free SO₃ content by weight.

A value for x of 2 gives us the empirical formula H₂S₂O₇ for pyrosulfuric acid also called disulfuric acid. Pure pyrosulfuric acid itself is a solid at room temperature, melting at 36 °C and rarely used either in the laboratory or industrial processes.

Oleum is produced in the contact process. Industrially, the biggest producer of oleum came from the distillation of iron sulfates at Nordhausen, from which the historical name Nordhausen sulfuric acid is derived.

The lead chamber process for sulfuric acid production was notable, because it could not produce sulfur trioxide or even concentrated sulfuric acid directly due to corrosion of the lead, and absorption of NO₂ gas. Until this process was made obsolete by the contact process, oleum had to be obtained through multiple processes.

Oleum is an important intermediate in the manufacture of sulfuric acid, due to its high enthalpy of hydration. When SO₃ is added to water, rather than simply dissolving, it tends to form a fine mist of sulfuric acid, which is difficult to manage. However, SO₃ added to concentrated sulfuric acid readily dissolves, forming oleum which can then be diluted with water to produce additional concentrated sulfuric acid.^{[citation needed]}

One advantage of oleum over sulfuric acid is that it can be shipped in bulk liquid railcars. Certain compositions of Oleum are solid at room temperature, and thus is safer to ship than when liquid. Solid oleum can then be converted into liquid at the destination through steam heating or dilution or concentration. This requires some care to prevent overheating and evaporation of sulfur trioxide.

Oleum is a harsh reagent, and is highly corrosive. One important use of oleum as a reagent is the secondary nitration of nitrobenzene. The first nitration can occur with nitric acid or sulfuric acid, but this deactivates the ring towards further electrophilic substitution. A stronger reagent, oleum, is needed to introduce the second nitro group onto the aromatic ring.

Oleum can also be used in the preparation of trinitrotoluene where it can oxidize the dinitrotoluene ring and promote the substitution of a third nitro group.

Like concentrated sulfuric acid, oleum is such a strong dehydrating agent that if poured onto powdered glucose, or virtually any other sugar, it will draw the elements of water out of the glucose in an exothermic reaction, leaving nearly pure carbon as a solid. This carbon expands outward, hardening as a solid black substance with gas bubbles in it.

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