Acid-base equilibria thermodynamics

The pKa of a molecule, a charge-state-related parameter, is a descriptor of an acid-base equilibrium reaction [34,35]. Lipophilicity, often represented by the octanol-water partition coefficient Kp is a descriptor of a two-phase distribution equilibrium reaction [36]. So is solubility [37-39]. These three parameters are thermodynamic constants. On the other hand, permeability Pe is a rate coefficient, a kinetics parameter, most often posed in a first-order distribution reaction [40-42]. 

To probe the thermodynamics of amine encapsulation, the binding affinities for different protonated amines for 1 were investigated. By studying the stabilization of the protonated form of encapsulated amines, the feasibility of stabilizing protonated intermediates in chemical reactions could be assessed. The thermodynamic cycle for encapsulation of a hypothetical substrate (S) is shown in Scheme 7.5. The acid-base equilibrium of the substrate is defined by Ki and the binding constant of the protonated substrate in 1 is defined by K2. Previous work has shown that neutral substrates can enter 1 [94] however, the magnitude of this affinity (K4) remains unexplored. Although neutral encapsulated amines were not observable in the study of protonated substrates, the thermodynamic cycle can be completed with K3, which is essentially the acid-base equilibrium inside 1. 

Since solid acid catalysts are used extensively in chemical industry, particularly in the petroleum field, a reliable method for measuring the acidity of solids would be extremely useful. The main difficulty to start with is that the activity coefficients for solid species are unknown and thus no thermodynamic acidity function can be properly defined. On the other hand, because the solid by definition is heterogeneous, acidic and basic sites can coexist with variable strength. The surface area available for colorimetric determinations may have widely different acidic properties from the bulk material this is especially true for well-structured solids like zeolites. It is also not possible to establish a true acid-base equilibrium. 

The concentration of the ketone enolate is higher than that of the aldehyde enolate. This is true under thermodynamic control as the stability of an enolate increases with its degree of substitution. It is also true under kinetic control since enolization is an acid-base equilibrium, the increased enolate concentration reflects the higher acidity of the ketone protons. 

The first step is to write the two redox equilibria (given below by reactions 1 and 3) including H+, H2O, e, and the acid-base equilibrium (reaction 2), with their corresponding thermodynamic parameters, as shown below. The standard potentials and the Ksp are taken from standard tables (e.g., the CRC Handbook of Chemistry and Physics). 

The enthalpy change of some reactions can be measured directly, but for those that do not go to completion (as is common in acid-base reactions), thermodynamic data from reactions that do go to completion can be combined using Hess s law to obtain the needed data. For example, the enthalpy and entropy of ionization of a weak acid, HA, can be found by measming (1) the enthalpy of reaction of HA with NaOH, (2) the enthalpy of reaction of a strong acid (such as HCl) with NaOH, and (3) the equilibrium constant for dissociation of the acid (usually determined from the titration curve). 

Again the reference point for discussion is Hammett s acidity function treatment (Hammett and Deyrup, 1932 Hammett, 1970). We write the Bronsted acid-base equilibrium in terms of proton loss from BH+ as in eqn (2), for which the thermodynamic equilibrium... 

Inorganic particles can be selectively wetted by the liquid phase if the particles and the liquid undergo favorable energetic interactions, such as polar-polar interactions, hydrogen bonding, or acid-base interactions. Thermodynamic equilibrium and the highest attainable entropy are easily reached in the cases of suspensions in liquids of low molecular weight due to very low liquid viscosity and fast molecular diffusion. 

Similar examples can be given for acid-base reactions. For example, SDS micelles stabilize acridinium cation, leading to a shift of the acid-base equilibrium [8]. From the thermodynamic point of view, such a stabilization is the lowering of the energy levels of the charged forms with respect of their conjugated uncharged forms. 

The holistic thermodynamic approach based on material (charge, concentration and electron) balances is a firm and valuable tool for a choice of the best a priori conditions of chemical analyses performed in electrolytic systems. Such an approach has been already presented in a series of papers issued in recent years, see [1-4] and references cited therein. In this communication, the approach will be exemplified with electrolytic systems, with special emphasis put on the complex systems where all particular types (acid-base, redox, complexation and precipitation) of chemical equilibria occur in parallel and/or sequentially. All attainable physicochemical knowledge can be involved in calculations and none simplifying assumptions are needed. All analytical prescriptions can be followed. The approach enables all possible (from thermodynamic viewpoint) reactions to be included and all effects resulting from activation barrier(s) and incomplete set of equilibrium data presumed can be tested. The problems involved are presented on some examples of analytical systems considered lately, concerning potentiometric titrations in complex titrand + titrant systems. All calculations were done with use of iterative computer programs MATLAB and DELPHI. 

Table 4-1 lists some rate constants for acid-base reactions. A very simple yet powerful generalization can be made For normal acids, proton transfer in the thermodynamically favored direction is diffusion controlled. Normal acids are predominantly oxygen and nitrogen acids carbon acids do not fit this pattern. The thermodynamicEilly favored direction is that in which the conventionally written equilibrium constant is greater than unity this is readily established from the pK of the conjugate acid. Approximate values of rate constants in both directions can thus be estimated by assuming a typical diffusion-limited value in the favored direction (most reasonably by inspection of experimental results for closely related... 

First, the simple thermodynamic description of pe (or Eh) and pH are both most directly applicable to the liquid aqueous phase. Redox reactions can and do occur in the gas phase, but the rates of such processes are described by chemical kinetics and not by equilibrium concepts of thermodynamics. For example, the acid-base reaction... 

The comparison of I —> N and N —> I may also be explained by the buffered pH in the diffusion layer and leads to an interesting comparison between a process under kinetic control versus one under thermodynamic control. Because the bulk solution in process N —> I favors formation of the ionized species, a much larger quantity of drug could be dissolved in the N —> I solvent if the dissolution process were allowed to reach equilibrium. However, the dissolution rate will be controlled by the solubility in the diffusion layer accordingly, faster dissolution of the salt in the buffered diffusion layer (process I—>N) would be expected. In comparing N—>1 and N —> N, or I —> N and I —> I, the pH of the diffusion layer is identical in each set, and the differences in dissolution rate must be explained either by the size of the diffusion layer or by the concentration gradient of drug between the diffusion and the bulk solution. It is probably safe to assume that a diffusion layer at a different pH than that of the bulk solution is thinner than a diffusion layer at the same pH because of the acid-base interaction at the interface. In addition, when the bulk solution is at a different pH than that of the diffusion layer, the bulk solution will act as a sink and Cg can be eliminated from Eqs. (1), (3), and (4). Both a decrease in the h and Cg terms in Eqs. (1), (3), and (4) favor faster dissolution in processes N —> I and I —> N as opposed to N —> N and I —> I, respectively. 

Confinement of water into regions with dimensions of only a few nanometers, such as typically those found in PEMs, accompanied by a strong electrostatic field due to the anions, will result in a significantly lower dielectric constant for the water than that observed in bulk water. Measurement of this structural ordering of the water has not been accomplished experimentally to date, and this was the motivation to the recent calculation of the dielectric saturation of the water in PEMs with an equilibrium thermodynamical formulation. " In addition to information concerning the state of the water this modeling has provided information concerning the distribution of the dissociation protons in sulfonic acid-based PEMs. 

ADCA 7-Amino-3-desacetoxycephalosporanic acid APA 6 Aminopenicillanic acid HPG D-p-Hydroxyphenylglycine HPGA D-p-Hydroxyphenylglycine amide Keq Concentration based equilibrium constant Kth Thermodynamic equilibrium constant... 

Note that A is called the conjugate base of HA and BH+ the conjugate acid of B. Proton transfer reactions as described by Eq. 8-1 are usually very fast and reversible. It makes sense then that we treat such reactions as equilibrium processes, and that we are interested in the equilibrium distribution of the species involved in the reaction. In this chapter we confine our discussion to proton transfer reactions in aqueous solution, although in some cases, such reactions may also be important in nonaqueous media. Our major concern will be the speciation of an organic acid or base (neutral versus ionic species) in water under given conditions. Before we get to that, however, we have to recall some basic thermodynamic aspects that we need to describe acid-base reactions in aqueous solution. 

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