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 a molecule can reach from
the position of release of its precursor before degrading itself---in
an isotropic environment with the same
average geo-chemical 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 rAB is
always smaller than 1.4843 times the larger of the two characteristic
ranges
rA and rB of A and B, respectively:
Second we give a closed formula for secondary ranges as a function of rA and rB.
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 then 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 five 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.