Analysis Framework for Photodecomposition in Water John L. Mancini 320 Brookmere Court, Ridgewood, N.J. 07450
A framework is presented for analysis of first order photodecomposition in aqueous solutions. The framework is tested using published experimental data on picloram photodecomposition and adequately represents experimental results. The framework may be employed to alter, minimize, and evaluate experimental work.
Analysis Framework. Assuming light extinction a t appropriate wavelengths follows Beer-Lambert’s law, the light IH a t any depth H is defined by: = I,~+C+B)H
(1)
where I H = light intensity a t depth “H” (langleys (ly)/day), I , = light intensity a t the surface (ly/day),H = depth (m), C = chemical concentration (mg/L), N = light extinction component per mg/L of chemical (Urn-mg/L) and P = light extinction component due t o the base solution properties (1/ m). Averaging Equation 1 over the depth and assuming complete vertical mixing yields:
where IAH = depth averaged light intensity (ly/day). In accordance with the first law of photochemistry, the change in concentration must equal the rate a t which light energy is absorbed by the photolyzed compound. Further, the light energy absorbed in the photolysis reaction can be assumed to be proportional to the concentration of picloram and the available light. A measure of the available light is the depth averaged light “IAH”defined by Equation 2. Therefore, the rate of change of picloram may be defined by:
where C = picloram concentration (mg/L), and K, = proportionality constant (My). In the above formulation, the values of H and I , are functions of the physical setting or the experimental setup and can be measured independently. The extinction coefficients N and p are a function of the chemical under consideration and the solvent which can also be measured independently. K , is a function of the compound under consideration and may, in certain cases, be related to the solvent, impurities in the system and pH. Equation 3 may be solved for concentration as a function of time (I).Equation 1 can be examined to determine if the light extinction due to changes in picloram concentration levels is significant. It has been reported ( 2 )that a t a wavelength of 290 nm and picloram concentrations of 1.0 and 0.25 mg/L, 50% of the surface light intensity was observed to occur a t 1.5 and 1.9 m, respectively. Substituting this information into Equation 1 and solving for N and yields: a
O.l/m-mg/L a t 290 nm P = 0.36/m a t 290 nm
The contribution to the light extinction coefficient by the concentration of picloram can be significant at higher picloram 1274
Environmental Science & Technology
concentration levels and a t this individual wavelength. Most of the basic experimental data to be used in this study are a t low picloram concentration levels, and the contribution of other wavelengths results in solution related extinction coefficients which are larger than the 0.36/m calculated above. As an illustration, one set of test conditions considered a picloram concentration of 0.1 mg/L and a solution depth of 3.65 m. The calculated decay rate is changed less than 2% by including the picloram concentration influence in the extinction coefficient. Finally, concentrations in the natural environment are expected to be low. In summary, the light absorbed by picloram can be significant in certain situations, and the basic mathematical framework has been developed. Experimental data obtained by Hedlund and Youngson ( 2 ) indicate that picloram photodecomposes at what appears to be a first order rate. This can occur when the material which is photoactive does not significantly contribute to light absorption. There are two circumstances that could produce this situation: the concentration and depth used in the experimental setup is such that a negligible portion of the incident solar radiation is absorbed; and the solvent and impurities dominate light absorption at active wavelengths; thus the concentration of the photoactive chemical does not significantly contribute to light absorption. Both circumstances appear to contribute to the observed first order behavior. Elimination of the changes in light extinction as a function of picloram concentration allows direct integration of Equation 3 yielding: As N
-
0, NC
