On secondary spatial ranges of transformation products in the environment

Beside a domain of direct impact, environmental chemicals have a second, naturally more extended domain of influence due to their transformation products. In order to estimate the spatial extent of the respective indirect effects, the concept of secondary spatial range of a pair of chemicals is introduced. Roughly speaking, the secondary spatial range is the typical distance of a molecule can reach from the position of release of its precursor before degrading itself in an isotropic environment with the same average geochemical properties as the earth. Starting from a simple model covering global long-range transport and (pseudo-) first-order degradation and/or conversion of a precursor A and its transformation product B, we first show that the secondary range ρAB is always smaller than 1.4843 times the larger of the two characteristic ranges ρA and ρB, of A and B, respectively: ρAB ⩽ 1.4843 max{ρA, ρB}. Secondly, we give a closed formula for secondary ranges as a function of ρA and ρB. Quite surprisingly, it turns out that the secondary range does not depend on the rate constant kAB of the reaction transforming A into B (In typical cases, usable values of kAB are difficult to obtain). For practical applications, we give a simple, yet highly precise approximation formula, allowing for rapid estimation of secondary ranges. By three typical examples, it is then demonstrated how secondary ranges can be estimated simply by inserting 5 measurable constants for chemicals A and B, respectively, into a given formula. Finally, it is argued that secondary ranges should be adequately included in the environmental assessment of precursor compounds.