Solubility thermodynamic parameters

Fig. 37. Dependence of the thermodynamic parameters AH and AS of triple-helix formation on the imino acid content of the peptides (obtained by cleavage of calf skin-type I collagene with cyanogene and subequent isolation by column chromatrography)3) and of the native neutral salt-soluble skin collagene of various animals. The entropy values are denoted by dotted lines...

The use of direct electrochemical methods (cyclic voltammetry Pig. 17) has enabled us to measure the thermodynamic parameters of isolated water-soluble fragments of the Rieske proteins of various bci complexes (Table XII)). (55, 92). The values determined for the standard reaction entropy, AS°, for both the mitochondrial and the bacterial Rieske fragments are similar to values obtained for water-soluble cytochromes they are more negative than values measured for other electron transfer proteins (93). Large negative values of AS° have been correlated with a less exposed metal site (93). However, this is opposite to what is observed in Rieske proteins, since the cluster appears to be less exposed in Rieske-type ferredoxins that show less negative values of AS° (see Section V,B). 

Streng, W. H. Tan, H. G. H., General treatment of pH solubility profiles of weak acids and bases, n. Evaluation of thermodynamic parameters from the temperature dependence of solubility profiles apphed to a zwitterionic compound, Int. J. Pharm. 25, 135-145 (1985). 

J The concept of counter-phases. When a stable compound penetrates from a binary into a ternary system, it may extend right across the system or exhibit only limited solubility for the third element. In the latter case, any characterisation also requires thermodynamic parameters to be available for the equivalent metastable compound in one of the other binaries. These are known as counter-phases. Figure 6.16 shows an isothermal section across the Fe-Mo-B system (Pan 1992) which involves such extensions for the binary borides. In the absence of any other guide-... 

Parameters describing a particular thermodynamic equilibrium system are derived from experimental quantities obtained by a variety of methods, for example, calorimetry, potentio-metry, and solubility studies. In the ideal case, critical examination of well-studied systems reveals high-quality experimental data that lead to a unique set of thermodynamic constants, which are internally consistent, not only formally, but also from a chemical point of view. In the course of our reviews, however, we encountered several cases of conflicting experimental data that resisted any attempt to cast them into a unique set of thermodynamic parameters. The following summarizes the conflicting data and our pragmatic solutions. 

Although gibbsite and kaolinite are important in quantity in some soils and hydrothermal deposits, they have diminishing importance in argillaceous sediments and sedimentary rocks because of their peripheral chemical position. They form the limits of any chemical framework of a clay mineral assemblage and thus rarely become functionally involved in critical clay mineral reactions. This is especially true of systems where most chemical components are inert or extensive variables of the system. More important or characteristic relations will be observed in minerals with more chemical variability which respond readily to minor changes in the thermodynamic parameters of the system in which they are found. However, as the number of chemical components which are intensive variables (perfectly mobile components) increases the aluminous phases become more important because alumina is poorly soluble in aqueous solution, and becomes the inert component and the only extensive variable. 

It is also common to measure by voltammetry the thermodynamic properties of purely chemical reactions that are in some way coupled to the electron transfer step. Examples include the determination of solubility products, acid dissociation constants, and metal-ligand complex formation constants for cases in which precipitation, proton transfer, and complexation reactions affect the measured formal potential. Also in these instances, studies at variable temperature will afford the thermodynamic parameters of these coupled chemical reactions. 

Lin, S. Y. and J. C. Yang. 1987. Solubility and thermodynamic parameters of diazepam in Pluronic surfactant solutionsActa Pharm. TechnoB3 222-224. 

The influence of steric effects on the thermodynamic parameters of extraction has been discussed in numerous publications (see the review in Ref. 12 and references therein). For a small series of selected extractants, a decrease of log Kex as a function of the length of alkyl substituents has been discovered.6970 However, in other cases, this dependence passes through a maximum or is not regular at all.71 The point is that the increase in the volume and branching of the substituents leads to some changes of molecular properties decrease of solubility in the aqueous phase, increase of steric hindrance upon the complexation, decrease of the extractant s aggregation, etc.12 Some of these factors strengthen extraction, but others weaken it. 

There are many factors that control and limit biocatalysis in carbon dioxide, including, but not limited to, pressure, water content, temperature, and mass transfer, and their influence on each enzyme s activity and stability. It is also important to understand whether one is operating in a one-phase or two-phase reaction medium. To this end, solubility studies should be carried out regularly to determine if the reaction is one or two phases. Only if the reaction is one-phase can one determine the kinetic and thermodynamic parameters with certainty. 

Commercial yeast invertase (Bioinvert ) was immobilized by adsorption on anion-exchange resins, collectively named Dowex (1x8 50-400,1x4 50-400, and 1x2 100-400). Optimal binding was obtained at pH 5.5 and 32°C. Among different polystyrene beads, the complex Dowex-1x4-200/invertase showed a yield coupling and an immobilization coefficient equal to 100%. The thermodynamic and kinetic parameters for sucrose hydrolysis for both soluble and insoluble enzyme were evaluated. The complex Dowex/inver-tase was stable without any desorption of enzyme from the support during the reaction, and it had thermodynamic parameters equal to the soluble form. The stability against pH presented by the soluble invertase was between 4.0 and 5.0, whereas for insoluble enzyme it was between 5.0 and 6.0. In both cases, the optimal pH values were found in the range of the stability interval. The Km and Vmax for the immobilized invertase were 38.2 mM and 0.0489 U/mL, and for the soluble enzyme were 40.3 mM and 0.0320 U/mL. 

The activity of soluble and immobilized invertase was determined by varying the temperature of the standard test within a range of 30-60°C ( 30, 35, 40, 45, 50, 55, and 60°C). A blank was prepared under the same conditions for each temperature employed. The activation energy (E/ kj/ mol) was determined by the Arrhenius method, and the thermodynamic parameters were calculated by conventional equations (Eqs. 3-5) (12). The stability of both forms of invertase (aqueous invertase solution [diluted 1 5000, v/v] or an aqueous suspension of Dowex/invertase (100 mg powder/mL]) was evaluated by maintaining the enzyme solution or suspension for 12 min in acetate buffer (0.010 M, pH 5.5) at each... 

The activation energy (Ea), calculated through the inclination of log v x T 1 (Eqs. 6 and 7), and the thermodynamic parameters (AH, AS, and AG), calculated through Eqs. 3-5, for both forms of invertase are presented in Table 2. As can be seen, the values of those parameters were quite similar for both soluble and immobilized invertase. This fits very well with the previous assumption that the immobilization technique has little effect on enzyme structure. It could be speculated that the reaction catalyzed by either soluble or insoluble invertase is constituted by identical thermodynamic systems. 

In the range of temperatures selected for evaluation, the soluble invertase presented detectable instability only at 55°C (Table 3 and Fig. 4). Hence, the thermodynamic parameters for the heat inactivation of invertase (AG, AH, A S and Ea ) were not determined, because the correlation log k x T 1 might necessarily be established, as proposed by Owusu and... 

Ben-Naim (1972b, c) has examined hydrophobic association using statistical mechanical theories of the liquid state, e.g. the Percus-Yevick equations. He has also examined quantitative aspects of solvophobic interactions between solutes using solubility data for ethane and methane. The changes in thermodynamic parameters can be calculated when two methane molecules approach to a separation of, 1-533 x 10-8 cm, the C—C distance in ethane, and the solvophobic quantities 8SI/i, s 2 and 8SiS2 can be calculated. In water (solvophobic = hydrophobic) 5si/i is more negative than in other solvents and decreases as the temperature rises both 8s iH%... 

Determination of the thermodynamic parameters for the transfer of non-polar organic compounds from aqueous to non-aqueous phases has been extensively used to estimate the free energy changes involved in hydrophobic interactions (Nemethy, 1967 Jencks, 1969). The experimental difficulties involved in the accurate determination of solubilities together with the approximations necessitated by limiting the measurements to simple organic compounds are the inherent disadvantages of this model. 

Thermodynamics is the basis of all chemical transformations [1], which include dissolution of chemical components in aqueous solutions, reactions between two dissolved species, and precipitation of new products formed by the reactions. The laws of thermodynamics provide conditions in which these reactions occur. One way of determining such conditions is to use thermodynamic potentials (i.e., enthalpy, entropy, and Gibbs free energy of individual components that participate in a chemical reaction) and then apply the laws of thermodynamics. In the case of CBPCs, this approach requires relating measurable parameters, such as solubility of individual components of the reaction, to the thermodynamic parameters. Thermodynamic models not only predict whether a particular reaction is likely to occur, but also provide conditions (measurable parameters such as temperature and pressure) in which ceramics are formed out of these reactions. The basic thermodynamic potentials of most constituents of the CBPC products have been measured at room temperature (and often at elevated temperatures) and recorded in standard data books. Thus, it is possible to compile these data on the starter components, relate them to their dissolution characteristics, and predict their dissolution behavior in an aqueous solution by using a thermodynamic model. The thermodynamic potentials themselves can be expressed in terms of the molecular behavior of individual components forming the ceramics, as determined by a statistical-mechanical approach. Such a detailed study is beyond the scope of this book. 

This equation can be used to write the temperature dependence of the solubility product constant pA sp- Thus, AHq, ASq, and the specific heats from the data books can be used to calculate the thermodynamic parameters as well as the solubility product constant. Consequently, by manipulating the processing temperature of a CBPC, one can solubilize the starter oxides. 

In the solution-diffusion case, P is given by P = sD, where 5 is the solubility coefficient and D is the diffusion coefficient. Accordingly, P is a product of kinetic parameter D and thermodynamic parameter. s. In such membranes, the solubility coefficient is a dominant factor that controls the value of P. Since a larger gas generally has the higher solubility coefficient, while the diffusivity is low, the permeability of a larger gas has the higher value of P, and the value of P follows the order of molecular size, i.e., P 2 < P02 < Pcoi-... 

Electrochemical cells can also be used to determine other thermodynamic parameters such as equilibrium constants. For example, the solubility product for the sparingly soluble salt AgCl may be determined by comparing the properties of the silver silver chloride electrode (9.2.23) with those of the silver silver ion electrode (9.2.39). The potentials of these electrodes are equal when they are in a saturated solution of AgCl, that is, when the activities of these ions are those given by equilibrium (9.2.40). Therefore, under these conditions... 

DAS/SAH] Das, R. C., Sahu, G., Satyanarayana, D., Misra, S. N., Silver-silver selenocyanate electrode determination of standard electrode potential, solubility product of AgSeCN and various thermodynamic parameters at 35, 40, 45 and 50°C, Electrochim. Acta, 19, (1974), 887-890. Cited on page 307. 

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