A method and system for characterizing a chemical reaction in an exhaust after-treatment system that includes providing a first molecule that includes a chemical element that is isotopically labelled. The isotopically labelled first molecule is injected into an exhaust stream of the exhaust after-treatment system to supply the isotopically labelled first molecule to an exhaust treatment component, and second molecules including the chemical element that is isotopically labelled that are produced through a chemical reaction of the first molecule with other constituents of the exhaust stream are quantified.