Currently the rate equation I found was the one by Burdett et al (1984) Rate [SO3] = k[SO2]*[O2]/RT ; k = (2.6+/-1.3 e 12)*exp(-23000 +/- 1200/T). I hope someone can help me with something that contains H2O or OH in the rate equation.
You can find it on page 356 of the textbook "Atmospheric Chemistry and Global Change", Edited by Guy Brasseur, John Orlando and Geoffrey Tyndall, Oxford University Press, 1999. The atmospheric oxidation of SO2 is described in other atmospheric chemistry textbooks as well.
This reaction is catalyzed by metal ions like Fe(II/III) and Mg. See detailed reaction mechanisms in Inorg Chem 1993, 32(21), 4527-4538 and 1998, 37(19), 4939-4944.