Hydrolysis equilibrium models

Baes and Mesmer s [1976BAE/MES] comprehensive survey and critical review of the hydrolysis of cations is the most frequently cited standard book on metal ion hydrolysis and widely accepted to represent the state of the art for long time after its publication. The authors have in most cases made their own analysis of previously published data and tested a number of different equilibrium models. The choice of models is based on the standard deviation of the experimental average number of coordinated hydroxide ions 0H However, one should complement this method by a calculation of the speci-ation in the various test solutions as done in the present review. Species that occur in low concentrations should be looked upon with suspicion as gradual changes in diffusion potentials and changes in the ionic medium may be erroneously interpreted as minor complexes. The discussion of the hydrolytic behaviour of thorium(IV) is based on the following potentiometric titration studies which are also included in the data evaluation of the present review ... 

The thermodynamic data compilations of Sillen and Martell catalyzed rapid advances in equilibrium models of seawater speciation. These works were followed by additional compilations that were critically important to modern sea-water speciation assessments. In view of these developments, and additional extensive experimental analyses appropriate to seawater. Principal Species assessments ten to fifteen years after the pioneering work of Sillen demonstrated a much improved awareness of the importance of hydrolysis in elemental speciation. 

One of the most important parameters controlling iodine volatility is sump water pH not only will the I2 hydrolysis equilibrium and the iodine partition coefficient be affected by this parameter, but the product yields of radiolytic reactions and the extent of formation of organoiodine compounds as well. Because of the lack of practical experience, the sump water pH to be expected under severe accident conditions has to be calculated on the basis of assumed concentrations of potential sump water ingredients. In Table 7.17. (according to Beahm et al., 1992) an overview of substances to be expected in the sump water, which would effect a shift in solution pH either to lower or to higher values, is given. Besides these chemical substances, radiation may also affect sump water pH irradiation of trisodium phosphate solution (5.3 kGy/h) was reported to decrease the pH from an initial value of 9.0 to about 4.0 after 60 hours of irradiation (Beahm et al., 1992). It is obvious that in such a complicated system definition of the sump water pH to be expected in a real severe reactor accident is a difficult task. Nonetheless, a model for calculation has been developed by Weber et al. (1992). 

Carell and Olin (58) were the first to derive thermodynamic functions relating to beryllium hydrolysis. They determined the enthalpy and entropy of formation of the species Be2(OH)3+ and Be3(OH)3+. Subsequently, Mesmer and Baes determined the enthalpies for these two species from the temperature variation of the respective equilibrium constants. They also determined a value for the species Be5(OH) + (66). Ishiguro and Ohtaki measured the enthalpies of formation of Be2(OH)3+ and Be3(OH)3+ calorimetrically in solution in water and water/dioxan mixtures (99). The agreement between the values is satisfactory considering the fact that they were obtained with different chemical models and ionic media. 

Metal binding by a hydrous oxide from a 10 7 M solution (SOH + Me2+ OMe+ + H+) for a set of equilibrium constants (see Eqs. (i) - (iii) from Example 2.3) and concentration conditions (see text). Corrected for electrostatic interactions by the diffuse double layer model (Gouy Chapman) for 1 = 01 The hydrolysis of Me2+ is neglected. 

The dependences of pH and C-potential on the adsorbed amount of M(H20)2+ at the total metal ion concentrations of 3 x10-3 mol dm-3 are shown in Figures 7 and 8, respectively. The amount adsorbed for each M2+ increases with the pH, and the inflection points are shifted toward the lower pH region in the order of Co2+, Zn2+, Pb2+, Cu2+, which corresponds to the order of the hydrolysis constant of metal ions. To explain the M2+-adsorption/desorption, Hachiya et al. (16,17) modified the treatment of the computer simulation developed by Davis et al. (4). In this model, M2+ binds coordina-tively to amphoteric surface hydroxyl groups. The equilibrium constants are expressed as... 

Recently, Falk and Seidel-Morgenstern [143] performed a detailed comparison between fixed-bed reactors and fixed-bed chromatographic reactors. The reaction studied was an equilibrium limited hydrolysis of methyl formate into formic acid and methanol using an ion-exchange resin as both the catalyst and the adsorbent. The analysis was based on a mathematical model, which was experimentally verified. The comparison was based on the following four assumptions ... 

In Figure 2.4, data for the equilibrium constants of esterification/hydrolysis and transesterification/glycolysis from different publications [21-24] are compared. In addition, the equilibrium constant data for the reaction TPA + 2EG BHET + 2W, as calculated by a Gibbs reactor model included in the commercial process simulator Chemcad, are also shown. The equilibrium constants for the respective reactions show the same tendency, although the correspondence is not as good as required for a reliable rigorous modelling of the esterification process. The thermodynamic data, as well as the dependency of the equilibrium constants on temperature, indicate that the esterification reactions of the model compounds are moderately endothermic. The transesterification process is a moderately exothermic reaction. 

Hydrolysis. NMR results show that TBT carboxylates undergo fast chemical exchange. Even the interfacial reaction between TBT carboxylates and chloride is shown to be extremely fast. The hydrolysis is thus not likely to be a rate determining step. Since the diffusivity of water in the matrix is expected to be much greater than that of TBTO, a hydrolytic equilibrium between the tributyltin carboxylate polymer and TBTO will always exist. As the mobile species produced diffuses out, the hydrolysis proceeds at a concentration-dependent rate. Godbee and Joy have developed a model to describe a similar situation in predicting the leacha-bility of radionuclides from cementitious grouts (15). Based on their equation, the rate of release of tin from the surface is ... 

In one case, a small peptide with enzyme-like capability has been claimed. On the basis of model building and conformation studies, the peptide Glu-Phe-Ala-Ala-Glu-Glu-Phe-Ala-Ser-Phe was synthesized in the hope that the carboxyl groups in the center of the model would act like the carboxyl groups in lysozyme 17). The kinetic data in this article come from assays of cell wall lysis of M. lysodeikticus, chitin hydrolysis, and dextran hydrolysis. All of these assays are turbidimetric. Although details of the assay procedures were not given, the final equilibrium positions are apparently different for the reaction catalyzed by lysozyme and the reaction catalyzed by the decapeptide. Similar peptide models for proteases were made on the basis of empirical rules for predicting polypeptide conformations. These materials had no amidase activity and esterase activity only slightly better than that of histidine 59, 60). 

In comparison, no structural modification of model B was seen before 120 h of aging (80 °C). However, after 120 h two small doublets appeared in the NMR spectrum and several additional peaks became noticeable in the NMR spectrum. It was determined by NMR and IR spectroscopy that the hydrolysis products were an imide/carboxylic acid and an imide/anhydride. Model B was then aged for 1200 h at 80 °C to quantitatively determine the amount of hydrolysis products as a function of time. The relative intensity of the peaks due to carboxylic acid is constant after some time. The authors suggest that an equilibrium occurs between model B and the products formed during hydrolysis, and therefore, the conversion to hydrolysis products is limited to about 12%. This critical fraction is probably enough to cause some degradation of polymeric materials, but research on six-membered polyimides has remained active. 

Though this system is perhaps an extreme example of slow sorption kinetics, it illustrates that the assumption of rapid equilibrium between the sediment and aqueous phases is questionable. The importance of such an observation to the investigation of hydrolysis kinetics in sediment/water systems must be emphasized. Certainly, any model of hydrolysis kinetics in sediment/water systems must include explicit expressions for the kinetics of the sorption/desorption process. 

These experiments indicated (a) that profilin-actin-ATP can participate in actin filament, (b) that the derived rate and equilibrium constants define a model which satisfies a closed thermodynamic cycle, and (c) that contrary to earlier suggestions, there is no absolutely need to invoke any special property of profilin in promoting irreversible ATP hydrolysis during actin polymerization. 

The surface complexation models quantify adsorption with experimentally determined equilibrium constants. Another, less widely used approach considers the relationship between the equilibrium constant for the adsorption reaction and the associated free energy change (James and Healy, 1972). Attempts have been made to determine the chemical contribution to the overall adsorption free energy by fitting adsorption isotherms to the experimental data values of -50, -33 and —45 kj mol were found for the change in chemical free energy associated with adsorption of Cr, Ni and Zn, respectively, on ferrihydrite (Crawford et al., 1993). Values ranging from -21 to 241 kJ mol were found for Ni on hematite the actual value depended upon the hydrolysis species that were assumed to exist (Fuerstenau and Osseo-Assare, 1987). 

In 1986 Pohl and Osterholtz [12] showed with model compounds that hydrolysis and re-formation of siloxane bonds of silane coupling agents are in true equilibrium (Fig. 4). The rates of both hydrolysis and condensation are catalyzed by acids and bases. 

Equilibrium constants for the hydrolysis of silanols and alcohols on a silica surface are shown in Table 2. Constants for two silanes are derived from Pohl s study with model compounds, while the others are estimated from the trend of... 

Equilibrium constant determination for alkoxysilane hydrolysis. Triethyl-silanol was selected as a model compound for determination of the equilibrium constant for equation (1), since under neutral conditions the condensation to disiloxane was observed to take place only over an extended period of time (i.e. years), eliminating equilibria (2) and (3) as interfering factors. 

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