The topochemical transformation of single crystals of Sr3Ir2O7 into Sr3Ir2O7F2 is reported via fluorine insertion. Characterization of the newly formed Sr3Ir2O7F2 phase shows a nearly complete oxidation of Ir 4+ cations into Ir 5+ that in turn drives the system from an antiferromagnetic Mott insulator with a half-filled J ef f = 1/2 band into a nonmagnetic J = 0 band insulator. First principles calculations reveal a remarkably flat insertion energy that locally drives the fluorination process to completion. Band structure calculations support the formation of a band insulator whose charge gap relies on the strong spin-orbit coupling inherent to the Ir metal ions of this compound.