Coincidences in chemical kinetics: surprising news about simple reactions. G.S. Yablonsky a,∗ D. Constales b,1 G.B. Marin c a Parks College, Department of Chemistry, Saint Louis University, 3450 Lindell Blvd, Saint Louis, MO 63103, USA. b Department of Mathematical Analysis, Ghent University, Galglaan 2, B-9000 Gent, Belgium. c Laboratory for Chemical Technology, Ghent University, Krijgslaan 281 (S5), B-9000 Gent, Belgium. Abstract New properties of intersections and coincidences of transient concentration curves were discovered and are presented analytically using the classical consecutive mech- anism A → B → C as an example. We identify six different special points, and analyze and classify the 6 possible (out of 612 combinations) patterns of concentra- tion peak and intersection times and values that distinguish the parameter subdo- mains and sometimes can eliminate the mechanism. This developed theory is tested on examples (multi-step radioactive decay, isomerization reaction). The mathemat- ical analysis relies on a combination of elementary and symbolic techniques, special functions and numerical approximations. Key words: Kinetic dependence; coincidence; intersection; consecutive mechanism A → B → C ; golden ratio; time of intersection. “Well met, Gentlemen, this is lucky that we meet so just together at this very door.” — Izaak Walton and Charles Cotton, The Compleat Angler (1676). ∗ Corresponding author. Email addresses: gy@che.wustl.edu (G.S. Yablonsky), dcons@world.std.com (D. Constales), Guy.Marin@UGent.be (G.B. Marin). 1 Financial support from BOF/GOA 01GA0405 of Ghent University is gratefully acknowledged. Preprint submitted to Elsevier 30 August 2010