Phosphorus kinetic models

Several kinetic models have appeared to describe phosphorus reactions in soils. Enfield (1978) classified models for estimating phosphorus concentrations in percolate waters derived from soil that had been treated with wastewater into three categories (1) empirical models that are not based on known theory (2) two-phase kinetic models that assume a solution phase and some adsorbed phase and (3) multiphase models, which include solution, adsorbed, or precipitated phases. Mansell and Selim (1981) classified models as shown in Table 9.2. The reader is urged to consult this reference for a complete discussion of the phosphorus kinetic models. For the purpose of this discussion, attention will be given to models that assume reversible phosphorus removal from solution, which can occur simultaneously by equilibrium and nonequilibrium reactions, and mechanistic multiphase models for reactions and transport of phosphorus applied to soils. 

Onken and Matheson (1982) studied kinetics of phosphorus dissolution in EDTA (ethylenediamine tetraacetic acid) solution for several soils. They examined eight kinetic models (Table 2.2) and found that phosphorus dissolution in EDTA solution was best described using the two-constant rate, Elovich, and differential rate equations as indicated by high r2 and low SE values. None of the models best described the dissolution for all soils. 

TABLE 2.2 Summary of r2 and SE of Eight Kinetic Models for Phosphorus Dissolution in EDTA Solution from Six Test Locations Varying in Plant Response to Applied Phosphorus"... 

Transport models that assume reversible kinetic reactions for applied phosphorus Transport models that assume irreversible kinetic reactions for applied phosphorus Transport models that assume both reversible and irreversible reactions for applied phosphorus Nontransport sorption models that assume both reversible and irreversible kinetic reactions for applied phosphorus... 

Nontransport Model That Assumes Two Types of Phosphorus Sorption Sites. Fiskell et al. (1979) studied phosphorus sorption on soils and found that the two-side model of Selim et al. (1976b) described their data much better than a one-site nonlinear kinetic model. 

Overman, A. R., and Chu, R. L. (1977a). A kinetic model of steady state phosphorus fixation in a batch reactor. I. Effect of soil/solution ratio. Water Res. 11, 771-775. 

Berner, R.A. (1974) Kinetic models for early diagenesis of nitrogen, sulfur, phosphorus, and silicon in anoxic marine sediments. In The Sea (Goldberg, E.D., ed.), pp. 427 -50, John Wiley, New York. 

Klump J. V. and Martens C. S. (1987) Biogeochemical cycling in an organic-rich coastal marine basin 5. Sedimentary nitrogen and phosphorus budgets based upon kinetic models, mass balances, and the stoichiometry of nutrient regeneration. Geochim. Cosmochim. Acta 51, 1161-1173. 

Dahl suggested a kinetic model for the nucleophilic substitution reaction at tri-covalent phosphorus with a P-N bond with alcohols (Scheme 2.135) [41]. The reaction proceeds in the presence of an ammonium salt as a catalyst. In the first step, the phosphoramidite is protonated in a fast equilibrium (1). In the second step, replacement of the amino group takes place (2). This step is slow and is the rate-determining step. Regeneration of the catalyst in the last step closes the catalytic cycle (3). 

Scheme 2.135 Kinetic model for the nucleophilic substitution reaction at trivalent phosphorus with a P-N bond with alcohols.

The kinetics of catalysis of cyclotrimerization was studied on the model system phenyl isocyanate/ace-tonitrile (solvent). Acetonitrile (AN, 99.64%, from Vinstron Corp.) was purified by refluxing with phosphorus pentoxide (5 g/1), then with calcium hydride (2 g/1) followed by distillation under nitrogen. Phenyl isocyanate was obtained from the Upjohn Company with a purity of 99.5%, and was purified by distillation. Tolylene diisocyanates (2,4 and 80/20 2,4/2,6 isomers) were obtained from the Mobay Chemical Co., and were purified by distillation. Cyclic sulfonium zwitterions (SZ) were obtained from the Dow Chemical Co. 

Other kinetically allowed mechanistic models, i.e. hydroxide ion attack on the monoanion, can be rejected on the grounds that the required rate coefficients far exceed that found for alkaline hydrolysis of phosphate triesters. At pH > 9 two new reactions appear, one yielding a 1,6-a.nhydro sugar by nucleophilic attack through a five-membered transition state of the 1-alkoxide ion upon C-6 with expulsion of phosphate trianion. The second is apparently general-base catalysis by 1-alkoxide of water attack on C-6 or phosphorus through greater than six-membered cyclic transition states. 

Mechanistic Multiphase Model for Reactions and Transport of Phosphorus Applied to Soils. Mansell et al. (1977a) presented a mechanistic model for describing transformations and transport of applied phosphorus during water flow through soils. Phosphorus transformations were governed by reaction kinetics, whereas the convective-dispersive theory for mass transport was used to describe P transport in soil. Six of the kinetic reactions—adsorption, desorption, mobilization, immobilization, precipitation, and dissolution—were considered to control phosphorus transformations between solution, adsorbed, immobilized (chemisorbed), and precipitated phases. This mechanistic multistep model is shown in Fig. 9.2. 

Another kinetically equivalent possibility must be considered the free imidazole in these catalysts may be acting as a nucleophile at phosphorus, not as a base. This is not yet excluded experimentally, but it seems unlikely. No intermediate phosphoimidazole is detectable, but of course it might be hydrolyzing rapidly. However, molecular models for such a reaction of VII with VIII are very strained, and essentially impossible with the naphthalene substrate to be described below. Only with the extra water molecule of the general-base mechanism do the models fit well. 

B. Angele, and K. Kirchner (1980) The poisoning of noble metal catalysts by phosphorus compounds. II. The kinetics of poisoning and a mathematical model, Chem. Eng. Sci 35 2903-2909... 

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