Solution pressure dependence

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

When it was recognized (31) that the SD model does not explain the negative solute rejections found for some organics, the extended solution—diffusion model was formulated. The SD model does not take into account possible pressure dependence of the solute chemical potential which, although negligible for inorganic salt solutions, can be important for organic solutes (28,29). 

In terms of the solubilities of solutes in a supercritical phase, the following generalizations can be made. Solute solubiUties in supercritical fluids approach and sometimes exceed those of Hquid solvents as the SCF density increases. SolubiUties typically increase as the pressure is increased. Increasing the temperature can cause increases, decreases, or no change in solute solubiUties, depending on the temperature effect on solvent density and/or the solute vapor pressure. Also, at constant SCF density, a temperature increase increases the solute solubiUty (16). 

The fluid pressure in the rock at the bottom of a well is commonly defined as pore pressure (also called formation pressure, or reservoir pressure). Depending on the maturity of the sedimentary basin, the pore pressure will reflect geologic column overburden that may include a portion of the rock particle weight (i.e., immature basins), or a simple hydrostatic column of fluid (i.e., mature basins). The pore pressure and therefore its gradient can be obtained from well log data as wells are drilled. These pore pressure data are fundamental for the solution of engineering problems in drilling, well completions, production, and reservoir engineering. 

By the variance, or number of degrees of freedom of the system, we mean the number of independent variables which must be arbitrarily fixed before the state of equilibrium is completely determined. According to the number of these, we have avariant, univariant, bivariant, trivariant,. . . systems. Thus, a completely heterogeneous system is univariant, because its equilibrium is completely specified by fixing a single variable— the temperature. But a salt solution requires two variables— temperature and composition—to be fixed before the equilibrium is determined, since the vapour-pressure depends on both. 

As previously noted, the equilibrium constant is independent of pressure as is AG. Equation (7.33) applies to ideal solutions of incompressible materials and has no pressure dependence. Equation (7.31) applies to ideal gas mixtures and has the explicit pressure dependence of the F/Fq term when there is a change in the number of moles upon reaction, v / 0. The temperature dependence of the thermodynamic equilibrium constant is given by... 

In a solution where a nonzero volume change between the electronic isomers, HS and LS, is encountered, the position of the spin equilibrium will depend on pressure. The volume change, usually denoted here AF°, may be obtained from the study of the pressure dependence of equilibrium properties such as the magnetic susceptibility or the electronic spectrum. In favorable cases, A F° values may be derived from the amplitude of sound absorption observed in ultrasonic relaxation measurements of a spin equilibrium as will be shown in the... 

The simplicity and accuracy of such models for the hydration of small molecule solutes has been surprising, as well as extensively scrutinized (Pratt, 2002). In the context of biophysical applications, these models can be viewed as providing a basis for considering specific physical mechanisms that contribute to hydrophobicity in more complex systems. For example, a natural explanation of entropy convergence in the temperature dependence of hydrophobic hydration and the heat denaturation of proteins emerges from this model (Garde et al., 1996), as well as a mechanistic description of the pressure dependence of hydrophobic... 

Refaee M,Tezuka T, Akasaka K, et al. Pressure-dependent changes in the solution structure of hen egg-white lysozyme./. Mol. Biol. 2003 327 857-865. 

When spread from dilute hexane solution, acid-dependent enantiomeric discrimination was observed in the 11/A compression isotherms of the monolayer at 25°C (Fig. 12). It is interesting to note that at higher subphase acidities, both racemic and enantiomeric film systems become more highly expanded, and the surface pressures where enantiomeric discrimination commences occur at high (85-90 A2/molecule) average molecular areas. This may be taken as direct evidence of headgroup ionization effects. The surface... 

Thus, contributions include accounting for adsorbent heterogeneity [Valenzuela et al., AIChE J., 34, 397 (1988)] and excluded pore-volume effects [Myers, in Rodrigues et al., gen. refs.]. Several activity coefficient models have been developed to account for nonideal adsorbate-adsorbate interactions including a spreading pressure-dependent activity coefficient model [e.g., Talu and Zwiebel, AIChE h 32> 1263 (1986)] and a vacancy solution theory [Suwanayuen and Danner, AIChE J., 26, 68, 76 (1980)]. 

Temperature modification of an aqueous solution can also be used to maintain constant relative humidity in the headspace [14]. This technique maintains the solid at one temperature and an aqueous solution connected to the system at another temperature. Due to the strong vapor pressure dependence on temperature, very tight temperature control of the aqueous solution and the solid are required to maintain constant relative humidity in the vicinity of the solid. 

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>... 

As a result of these experiments Smith concludes that (a) the simple Helmholtz theory of the double layer is insufficient to account for all the observed facts. The potential difference mercury-electrolyte is not purely electrostatic, but depends on the nature of the ions, as, according to Nemst s theory, it should do. This theory, it will be remembered, involves the " solution pressure of the ions, which varies with their chemical nature. (6) The potential difference mercury-electrolyte is not necessarily zero when the interfacial tension is a maximum, although in the particular case of dilute KC1 this condition is very nearly fulfilled. 

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), =... 

Since osmotic pressure depends upon the number of particles of solute(s) in solution, the osmotic pressure of an electrolyte is directly proportional to the degree (or extent) of dissociation. The dissociation factor, symbolized by the letter i, can be calculated by dividing the total number of particles (which include undissociated molecules and ions) in a solution by the number of particles before dissociation, i.e.,... 

Colligative properties are those properties of solutions that depend on the number of solute particles present and not their identity. Colligative properties include vapor pressure lowering, freezing point depression, boiling point elevation, and osmotic pressure. Colloids are homogeneous mixtures, in which the solute particles are intermediate in size between suspensions and true solutions. We can distinguish colloids from true solutions by the Tyndall effect. 

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