Oleum is also known as fuming sulfuric acid or Nordhausen acid. It has the chemical formula H2S2O7, and can be formed by dissolving excess SO3 into sulfuric acid. See sulfuric acid for more information.
Oleum is an important chemical used in the manufacture of sulfuric acid. If SO3 is added directly to water, it tends to polymerize rather than form sulfuric acid. If SO3 is added to sulfuric acid instead, it forms oleum which can then be mixed with water to form more sulfuric acid.
