Thermodynamic equilibria, dissolved

From the standpoint of thermodynamics, the dissolving process is the estabHsh-ment of an equilibrium between the phase of the solute and its saturated aqueous solution. Aqueous solubility is almost exclusively dependent on the intermolecular forces that exist between the solute molecules and the water molecules. The solute-solute, solute-water, and water-water adhesive interactions determine the amount of compound dissolving in water. Additional solute-solute interactions are associated with the lattice energy in the crystalline state. 

When an aqueous phase (noted w) is brought in contact with a second immiscible phase (noted o), the different species dissolved in one or the two phases spontaneously distribute depending on their hydrophilic-lipophilic balance until the thermodynamic equilibrium is reached. The distribution of the charged species generates an interfacial region, in which the electrical field strength differs from zero, so that an electrical Galvani potential difference, is established across the interface ... 

The effect of the medium (solvent) on the dissolved substance can best be expressed thermodynamically. Consider a solution of a given substance (subscript i) in solvent s and in another solvent r taken as a reference. Water (w) is usually used as a reference solvent. The two solutions are brought to equilibrium (saturated solutions are in equilibrium when each is in equilibrium with the same solid phase—the crystals of the dissolved substance solutions in completely immiscible solvents are simply brought into contact and distribution equilibrium is established). The thermodynamic equilibrium condition is expressed in terms of equality of the chemical potentials of the dissolved substance in both solutions, jU,(w) = jU/(j), whence... 

It is further interesting to observe that the behavior of a system approaching a thermodynamic equilibrium differs little from one approaching a steady state. According to the kinetic interpretation of equilibrium, as discussed in Chapter 16, a mineral is saturated in a fluid when it precipitates and dissolves at equal rates. At a steady state, similarly, the net rate at which a component is consumed by the precipitation reactions of two or more minerals balances with the net rate at which it is produced by the minerals dissolution reactions. Thermodynamic equilibrium viewed from the perspective of kinetic theory, therefore, is a special case of the steady state. 

A solution that is in thermodynamic equilibrium with the solid phase of its solute at a given temperature is a saturated solution, and a solution containing more dissolved solute than that given by the equilibrium saturation value is said to be supersaturated. The degree of supersaturation may be expressed by ... 

If two different polymers can be dissolved successfully in a common solvent, a molecular intermixing of the dissolved macromolecules should occur due to the fast establishment of the thermodynamic equilibrium. The difficulty with this procedure is due to the fact that very many polymers become incompatible above a certain concentration when their solutions in a common solvent are combined. This means that the originally homogeneous solutions of polymers A and B separate into two phases when being combined, whereby each of the phases contain different quantitative proportions A B [e.g., polystyrene and poly(vinyl acetate) in toluene]. But even when two polymers have been dissolved sue-... 

A photochemical process could use the energy of sunlight to split water into H2 and 02, the former then being used as a fuel which can be stored indefinitely. The splitting of water requires in principle a photoactivated catalyst dissolved or dispersed in water. The energy requirement for the overall reaction H20— H2 + 02 is 1.23 eV (per electron). In conditions of electrolysis it would however proceed extremely slowly at this potential difference which pertains to a thermodynamic equilibrium, and it is well known that a substantial overvoltage of the order of 0.5 V is required in practice to drive this reaction. 

The form in which chemical analyses of sea water are given records the history of our thought concerning the nature of salt solutions. Early analytical data were reported in terms of individual salts NaCl, CaSO/i, and so forth. After development of the concept of complete dissociation of strong electrolytes, chemical analyses of sea water were given in terms of individual ions Na+, Ca++, Cl-, and so forth, or in terms of known undissociated and partly dissociated species, e.g., HC03 , In recent years there has been an attempt to determine the thermodynamically stable dissolved species in sea water and to evaluate the relative distribution of these species at specified conditions. Table 1 lists the principal dissolved species in sea water deduced from a model of sea water that assumes the dissolved constituents are in homogeneous equilibrium, and (or) in equilibrium, or nearly so, with solid phases. 

The pronounced discrepancy between the measured dynamic 15 °C-elution curve and its extrapolated reversible-thermodynamic part, shown in Fig. 7, represents a direct proof of the inadequacy of the reversible Eq. (3) in the dynamic region of the column (PDC-effect). Moreover, the experiment shows immediately that the polymer of the mobile phase has to dissolve in the gel layer within the transport zone to a considerably higher extent than is allowed by the partition function (4) in a reversible-thermodynamic equilibrium between the gel and the sol at the same column temperature. As a consequence, a steady state, i.e. a flow-equilibrium, must be assumed in the system sol/gel within the considered transport zone, governing the polymer trans-... 

Eh is a measure of oxidation-reduction potential in the solution. The chemical reactions in the aqueous system depend on both the pH and the Eh. While pH measures the activity (or concentration) of hydrogen ions in the solution, Eh is a measure of the activity of all dissolved species. Aqueous solutions contain both oxidized and reduced species. For example, if iron is present in the solution, there is a thermodynamic equilibrium between its oxidized and reduced forms. Thus, at the redox equilibrium, the reaction is as follows ... 

The Biot theory of poroelasticity ([4, 2]) can be extended to account for the physico-chemical interactions taking place between the dissolved salt, pore fluid, and a chemically active shale ([8, 9]). For example, a sample of reactive shale surrounded by a fluid initially in thermodynamic equilibrium with the saturating fluid experiences a contraction (e < 0) accompanied by a decrease... 

In equilibrium sampling, the exposure time is sufficiently long to permit the establishment of thermodynamic equilibrium between the water and sorption phases. In this case the dissolved analyte concentration can be estimated using the sorption phase-water partition coefficient (Ksw) ... 

Mathematical models for mass transfer at the NAPL-water interface often adopt the assumption that thermodynamic equilibrium is instantaneously approached when mass transfer rates at the NAPL-water interface are much faster than the advective-dispersive transport of the dissolved NAPLs away from the interface [28,36]. Therefore, the solubility concentration is often employed as an appropriate concentration boundary condition specified at the interface. Several experimental column and field studies at typical groundwater velocities in homogeneous porous media justified the above equilibrium assumption for residual NAPL dissolution [9,37-39]. 

As mentioned earlier, the composition of natural groundwaters depends on the composition of the geological formations where they originate from they contain dissolved rock and soil components that were soluble under the conditions (such as temperature and pressure) of their formation. Their dissolution is governed by the law of thermodynamics that is, dissolution occurs when the solution is undersaturated with respect to components such as rocks and soils. Provided that the solid components are present in sufficient quantity and there is no kinetic barrier, this process may lead to a thermodynamic equilibrium. The reversed process of dissolution is precipitation, that is, the formation of a solid phase from the dissolved components of a supersaturated solution. The composition of the... 

The thermodynamic equilibrium models, including surface complexation models, require the solution of a complex mathematical equation system. For this reason, many computer programs (e.g., CHEAQC, CHEMEQL, CHESS, EQ3/6, F1TEQL, Geochemist s Workbench, H ARPHRQ, JESS, MINTEQ and its versions, NETPATH, PHREEQC, PHRQPITZ, WHAM, etc.) have been developed to calculate the concentration and activity of chemical species, estimate the type and amount of minerals formed or dissolved, and the type and amount of sorbed complexes. 

The theoretical solubility profile of a pure monoprotic base, B, provides a simple yet powerful illustration of equilibrium solubility. A saturated solution of B at relatively high pH values will contain dissolved compound, in thermodynamic equilibrium with pure solid base, B ... 

At low concentration (x 1) hydrogen first dissolves in the metal lattice and forms a solid solution phase (a phase). Hydrogen is then randomly distributed in the metal host lattice and the concentration varies slowly with temperature. The a phase has the same crystal structure as the bare metal. The condition for thermodynamic equilibrium is given by ... 

Steels become more susceptible to hydrogen embrittlement as the materials are exposed to higher gas pressures. Thermodynamic equilibrium between hydrogen gas and dissolved atomic hydrogen is expressed by the general form of Sievert s law ... 

An SI index of zero indicates that a mineral is in thermodynamic equilibrium with the solution. If the SI is less than zero, the solution is undersaturated with respect to the mineral and that mineral may dissolve. Conversely, an SI greater than zero indicates the solution is oversaturated with respect to the mineral and that the mineral may precipitate. These considerations are useful in constraining the kinds of reactions that are possible in groundwater systems. 

The situation i.s similar at solid-liquid interfaces. Again, at a given temperature, only a certain amount of solid can be dissolved in a liquid, and the sol-ubiUly of the solid in the liquid is determined from the requirement that thermodynamic equilibrium exists between the solid and the solution at the interface. The solubility represents the maximum amoiiitl of solid that can be dissolved in a liquid at a specified temperature and is widely available in chemistry handbooks. In Table 14-5 we present sample solubility data for sodium chloride (NaCl) and calcium bicarbonate [Ca(HC03)2] at various temperatures. For example, the solubility of salt (NaCl) in water at 310 K is 36.5 kg per 100 kg of water. Therefore, the mass fraction of salt in the brine at the interface is simply... 

The term speciation is used to describe the reactions that take place when an electrolyte is dissolved in water. Water dissociates, sour gases hydrolyze, some ions dissociate, and other ions associate until thermodynamic equilibrium is attained. The liquid phase of the ternary H2O-NH3-CO2 system contains at least the following nine species HjO, NH3(aq), COjiaq), H", OH, NH4, HCOj, COj , and NHjCOO. (aq) indicates that the species is in aqueous solution to avoid ambiguity. In order to adequately model this system, interaction parameters for the interaction between each pair of species need to be determined thus, speciation calculations are performed simultaneously with the parameter estimation, and the calculated amount of each species is compared with experimental data. Some models also require ternary parameters and consequently an additional amount of data to determine these parameters. 

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