Heterogeneous systems kinetic results

An interesting method, which also makes use of the concentration data of reaction components measured in the course of a complex reaction and which yields the values of relative rate constants, was worked out by Wei and Prater (28). It is an elegant procedure for solving the kinetics of systems with an arbitrary number of reversible first-order reactions the cases with some irreversible steps can be solved as well (28-30). Despite its sophisticated mathematical procedure, it does not require excessive experimental measurements. The use of this method in heterogeneous catalysis is restricted to the cases which can be transformed to a system of first-order reactions, e.g. when from the rate equations it is possible to factor out a function which is common to all the equations, so that first-order kinetics results. 

Further evidence has been obtained to support the contention that the active catalysts are metal complexes dissolved in solution. With experiments reported in Table II, the kinetics of oxidation under standard conditions in the presence of various metal salts are compared with the rates of reaction when solid residues have been filtered from solution. The agreement between the rates in Cases 1 and 3 of Table II (where the amount of metal available is dictated by the solubility of metal complexes) shows that solid precipitates play little or no part in catalysis in all the systems studied. The amount of metal in solution has been measured in Cases 2 and 3 metal hydroxide complexes (Case 2) are not as soluble as metal-thiol complexes, and neither is as soluble as metal phthalocyanines (19). The results of experiments involving metal pyrophosphates are particularly interesting, in that it has previously been suggested that cobalt pyrophosphates act as heterogeneous catalysts. The result s in Table II show that this is not true in the present system. 

Because reactions in solids tend to be heterogeneous, they are generally described by rate laws that are quite different from those encountered in solution chemistry. Concentration has no meaning in a heterogeneous system. Consequently, rate laws for solid-phase reactions are described in terms of a, the fraction of reaction (a = quantity reacted -r- original quantity in sample). The most commonly encountered rate laws are given in Table 1. These rate laws and their application to solid-phase reactions are described elsewhere. 1 4 10-12 Unfortunately, it is often merely assumed that solid-phase reactions are first order. This uncritical analysis of kinetic data produces results that must be accepted only with great caution. 

Until velocity coefficients and radical concentrations are known with greater certainty one cannot be sure how closely the true state of affairs is approximated by an algebraic treatment. Further effort to describe these heterogeneous systems by formal kinetics does not appear warranted at present. Progress is more likely to result from detailed investigations into the physical state of these systems. It seems quite possible that polymerization is occurring simultaneously on the particles and, because of slow precipitation, in the liquid phase as well. This would correspond to the situation described in a later section for aqueous polymerization. 

The homopolymerization of DADMAC is possible in several organic solvents such as acetone, l-methyl-2-pyrrolidone, tetramethylurea, or dimethylform-amide. Various initiation methods including radical, ionic, or x-ray induced polymerization have been employed [19]. Since the monomer solubility is limited in these solvents, and the resulting homopolymer is soluble only in water, methanol and acidic acid, the polymerization in aqueous solutions are preferred. Polymerization in both homogeneous and heterogeneous systems have been studied and the kinetics and mechanisms were investigated in aqueous solution and in inverse-emulsion [6-16,52,53]. 

The rate of calcite dissolution is known to depend on the hydrodynamic conditions of the environment and on the rate of heterogeneous reaction at the mineral surface. Numerous laboratory studies demonstrate transport and surface-controlled aspects of calcite reactions in aqueous solutions, but until recently, no study has been comprehensive enough to enable comparison of kinetic results among differing hydro-chemical systems. 

It is the purpose of this paper to describe some of the major mechanisms that control arsenic in aquatic systems. Particularly, this paper addresses the problem of arsenic speciation and compartmentalization in sediments. To this end, results obtained from speciation, compartmentalization, kinetic, and adsorption studies using both field and laboratory samples will be interfaced in a descriptive model for arsenic in heterogeneous systems. The model has particular significance... 

When a few percent of formic acid was added to gaseous formaldehyde at about 500 mm pressure a rapid polymerization was observed, the velocity was some hundredfold greater than with pure formaldehyde. It appeared that formic acid was a powerful initiator of formaldehyde polymerization under these conditions. The polymerization was confined to the surface of the vessel and the kinetics were those of a heterogeneous system. Because of the much faster formaldehyde polymerization promoted by formic acid the purity of the formaldehyde became less important. The erratic results of earlier investigators were best explained by varying degrees of purity of earlier preparations of formaldehyde monomer. 

In none of the above examples where tetrahedral intermediates have been shown to be kinetically important is it possible to demonstrate an accumulation of the tetrahedral intermediate by spectrophotometric means. The tetrahedral intermediate has been observed directly only under nonhydrolytic conditions (Bender, 1953). When metal alkoxides are added to haloacetic acid esters or diethyl oxalate in di-n-butyl ether, the resulting heterogeneous system shows a diminution in intensity of the carbonyl stretching band in the infrared. The equilibrium towards the addition intermediate is greatest for the more negatively substituted esters, as would be expected. The parent haloacetic acids do not exhibit... 

With respect to ion-exchange kinetics, the great complexity of soils has resulted in a penchant for the easy approximations of homogeneous models, even where the premise of a quasi-continuum of liquid and solid is hard to accept. The theory of heterogeneous systems offers the Nernst-Planck equations, but these also can provide no more than an approximation for migration of ions in soil constituents. 

Finally, by definition, catalysis is purely a kinetic phenomenon. Many studies, directed at the elucidation of catalytic phenomena in both homogeneous and heterogeneous systems, emphasize the characterization of such systems and identification of the species present, by structural and spectroscopic methods. It is only to the extent that the results of such studies are related to the rates of the catalytic reactions through appropriate kinetic measurements that they are relevant to the catalytic process. This point is illustrated by... 

The complexity observed in polymer fluorescence decay kinetics is further exacerbated when fluorescent polyelectrolytes are dissolved in aqueous media [29,30,33,35,37,43,120,122,128-132] segregation of the macromolecular structure into hydrophobic and hydrophilic-rich domains results in differing degrees of water penetration which further complicates the time-resolved fluorescence [26]. Within this context, more recent attempts to describe time-resolved polymer photophysical data include use of the blob model [133,134], which accounts for the range of environments encountered in heterogeneous systems by invoking a distribution of rate constants for excimer formation. 

There are a number of factors which may influence the activity or selectivity of a polymer-immobilized catalyst. Substrate diffusion is but one. This article has reviewed the mathematical formalism for interpreting reaction rate data. The same approach that has been employed extensively in heterogeneous systems is applicable to polymer-immobilized systems. The formalism requires an understanding of the extent of substrate partitioning, the appropriate intrinsic kinetic expression and a value for the substrate s diffusion coefficient. A simple method for estimating diffusion coefficients was discussed as were general criteria for establishing the presence of substrate transport limitations. Application of these principles should permit one to identify experimental conditions which will result in the intrinsic reaction rate data needed to probe the catalytic properties of immobilized catalysts. 

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