Pressure dependence of activity

Basilevsky M V, Weinberg N N and Zhulin V M 1985 Pressure dependence of activation and reaction volumes J. Ohem. Soc. Faraday Trans. 1 81 875-84... 

In general G /RT is a fnnction of T, P, and composition, but for liquids at low to moderate pressures it is a very weak function of P. Therefore the pressure dependence of activity coefficients is usually neglected. Thus, for data at constant T ... 

This theory satisfactorily predicts the heat of solution and the concentration and pressure dependence of activity coefficients of nonpolar solutes as a salting-out effect, when the molecules and ions are not very large and chemical association between ions and solute does not occur. When the... 

In the thennodynamic fomiiilation of TST the pressure dependence of the reaction rate coefficient defines a volume of activation [24, 25 and 26]... 

There is one important caveat to consider before one starts to interpret activation volumes in temis of changes of structure and solvation during the reaction the pressure dependence of the rate coefficient may also be caused by transport or dynamic effects, as solvent viscosity, diffiision coefficients and relaxation times may also change with pressure [2]. Examples will be given in subsequent sections. 

Measuring tire pressure dependence of k at different temperatures shows that the apparent activation energy at constant viscosity decreases with increasing viscosity [46, ( figure A3,6,8). From a detailed analysis one... 

The development of active ceramic-polymer composites was undertaken for underwater hydrophones having hydrostatic piezoelectric coefficients larger than those of the commonly used lead zirconate titanate (PZT) ceramics (60—70). It has been demonstrated that certain composite hydrophone materials are two to three orders of magnitude more sensitive than PZT ceramics while satisfying such other requirements as pressure dependency of sensitivity. The idea of composite ferroelectrics has been extended to other appHcations such as ultrasonic transducers for acoustic imaging, thermistors having both negative and positive temperature coefficients of resistance, and active sound absorbers. 

Recently, Suzuki and Taniguchi93 hydrolyzed n-butylacetate, ethylacetate, and methylacetate with HPSt and 41 (PVA B) (partially-o-benzalsulfonated polyvinylalcohol). The volume of activation, A P+, was obtained from the pressure dependence of reaction rates [ F + = -kT(d Ink/dP)]. The A + increased with increasing hydro-phobidty of the substrate. 

For liquid mixtures at low pressures, it is not important to specify with care the pressure of the standard state because at low pressures the thermodynamic properties of liquids, pure or mixed, are not sensitive to the pressure. However, at high pressures, liquid-phase properties are strong functions of pressure, and we cannot be careless about the pressure dependence of either the activity coefficient or the standard-state fugacity. 

They judged the activation energies to be accurate to 10%. An additional important result was their observation of the pressure dependence of the... 

The effect of pressure on chemical equilibria and rates of reactions can be described by the well-known equations resulting from the pressure dependence of the Gibbs enthalpy of reaction and activation, respectively, shown in Scheme 1. The volume of reaction (AV) corresponds to the difference between the partial molar volumes of reactants and products. Within the scope of transition state theory the volume of activation can be, accordingly, considered to be a measure of the partial molar volume of the transition state (TS) with respect to the partial molar volumes of the reactants. Volumes of reaction can be determined in three ways (a) from the pressure dependence of the equilibrium constant (from the plot of In K vs p) (b) from the measurement of partial molar volumes of all reactants and products derived from the densities, d, of the solution of each individual component measured at various concentrations, c, and extrapolation of the apparent molar volume 4>... 

Volumes of activation can be unambiguously determined only from the pressure dependence of the rate constants. Attempts to obtain volumes of activation from the correlation of rate constants with the solubility parameter 22 or the cohesive energy density parameter (ced)23, which are related to the internal pressure of solvents, have not led to clear-cut results. 

The observation that the transition state volumes in many Diels-Alder reactions are product-like, has been regarded as an indication of a concerted mechanism. In order to test this hypothesis and to gain further insight into the often more complex mechanism of Diels-Alder reactions, the effect of pressure on competing [4 + 2] and [2 + 2] or [4 + 4] cycloadditions has been investigated. In competitive reactions the difference between the activation volumes, and hence the transition state volumes, is derived directly from the pressure dependence of the product ratio, [4 + 2]/[2 + 2]p = [4 + 2]/[2 + 2]p=i exp —< AF (p — 1)/RT. All [2 + 2] or [4 + 4] cycloadditions listed in Tables 3 and 4 doubtlessly occur in two steps via diradical intermediates and can therefore be used as internal standards of activation volumes expected for stepwise processes. Thus, a relatively simple measurement of the pressure dependence of the product ratio can give important information about the mechanism of Diels-Alder reactions. 

Measuring the pressure dependence of the exchange rate constant leads to activation volumes, AV and this technique has become a major tool for the mechanistic identification of solvent exchange mechanisms (8,16,17). In the last 25 years high-pressure, high-resolution NMR probes were developed which allow the application of all NMR techniques described to pressures up to several hundreds of mega Pascals (18). 

In this chapter we focus on the role of the pressure variable in such mechanistic studies. Almost all chemical reactions in solution exhibit a characteristic pressure dependence over a moderate pressure range of a few hundred megapascals. The pressure dependence of an equilibrium (K) or a rate constant (k) results in the reaction volume, AV, or the volume of activation, AV, via the relationships (SlnK/SP), =... 

The pressure dependence of the forward and reverse reactions resulted in significantly positive volumes of activation (36), and the volume profile reported in Fig. 1 clearly demonstrates the dissociative nature of the substitution process. Such conclusions can more easily... 

For the mechanistic interpretation of activation volume data for nonsymmetrical electron-transfer reactions, it is essential to have information on the overall volume change that can occur during such a process. This can be calculated from the partial molar volumes of reactant and product species, when these are available, or can be determined from density measurements. Efforts have in recent years focused on the electrochemical determination of reaction volume data from the pressure dependence of the redox potential. Tregloan and coworkers (139, 140) have demonstrated how such techniques can reveal information on the magnitude of intrinsic and solvational volume changes associated with electron-transfer reactions of transition... 

An attempt is made to account quantitatively for the volumes of activation, AV, of ligand substitution processes. Causes of the pressure-dependence of AV include solvational change, for which a versatile analysis is developed. The pressure-independent AV values of solvent exchange reactions are good measures of the non-sol-vational components of AV for related net reactions. For water exchange, one can predict... 

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