Solubility Gibbs energy

Solubility, Gibbs Energy, and Entropy of Transfer of Hydrocarbons from the Uquid Phase to Water ... 

A relative scale of the standard Gibbs energies of ion transfer or the standard ion transfer potentials can be established based on partition and solubility measurements. The partition eqnilibrium of the electrolyte can be characterized by a measnrable parameter, the partition coefficient P x-... 

Table III gives values of the changes in Gibbs energy, enthalpy, entropy, and heat capacity of the solution process as calculated from the equations of Table I. Figure 1 shows the recommended noble gas mole fraction solubilities at unit gas partial pressure (atm) as a function of temperature. The temperature of minimum solubility is marked.

The mutual solubility of two liquids A and B depends, in general, on how much the molecules of each liquid tend to attract those of its own kind, relative to their tendency to attract those of the other. This tendency is measured by the excess Gibbs energy of mixing of the two liquids (see section 2.4), Am gL, which is related to the partial vapor pressures p/ and of the two liquids A and B in the mixture. If the composition of the system is given by and Wb moles of the respective components in a given phase, their mole fractions in this phase are... 

The differences in the solvation abilities of ions by various solvents are seen, in principle, when the corresponding values of As ivG° of the ions are compared. However, such differences are brought out better by a consideration of the standard molar Gibbs energies of transfer, AtG° of the ions from a reference solvent into the solvents in question (see further section 2.6.1). In view of the extensive information shown in Table 2.4, it is natural that water is selected as the reference solvent. The TATB reference electrolyte is again employed to split experimental values of AtG° of electrolytes into the values for individual ions. Tables of such values have been published [5-7], but are outside the scope of this text. The notion of the standard molar Gibbs energy of transfer is not limited to electrolytes or ions and can be applied to other kinds of solutes as well. This is further discussed in connection with solubilities in section 2.7. 

The solubility of an ionic solute, Sca, may be expressed in terms of its solubility product, The equilibrium between a pure solid salt, Cv+Av and its saturated solution in a solvent where it is completely dissociated to ions (generally having e > 40 see section 2.6) is governed by its standard molar Gibbs energy of dissolution... 

Solubility products can be derived indirectly from standard electrode potentials and other thermochemical data, and directly from tabulated standard Gibbs energies of formation, AfG°, of the ions in aqueous solution [12]. Thus, the use of... 

When solubility products in nonaqueous solvents are desired, tables [5-7] of the Gibbs energies of transfer of the ions from water to the desired solvent, org, must be consulted. For any ion... 

In many cases the CALPHAD method is applied to systems where there is solubility between the various components which make up the system, whether it is in the solid, liquid or gaseous state. Such a system is called a solution, and the separate elements (i.e., Al, Fe...) and/or molecules (i.e., NaCl, CuS...) which make up the solution are defined as the components. The model description of solutions (or solution phases) is absolutely fundamental to the CALPHAD process and is dealt with in more detail in chapter S. The present chapter will discuss concepts such as ideal mixing energies, excess Gibbs energies, activities, etc. 

Box 3.1 Relationship between Solubility and Gibb Energy Change for Solution... 

If activity coefficients arc iunorcd la-Mimcd lo bo unity a gro s approximation responsible lor the noii-quantitative connection between chances in Gibbs energy ol solution and actual salt solubilities), it is possible to draw up a table of values of the change in (iibbs energy for the solution of a compound in water that might be expected for various solubilities. Table. Tin contains the calculations of A , (/ for various solubilities of I I ionic compounds. The calculations arc based on the approximate relationship ... 

As described in Section 2.1, the solubility of a crystalline electrolyte is detennined by the difference between the lattice Gibbs energy and the solvation energy of the electrolyte. For a given electrolyte, the solubility increases with the increase in the... 

To obtain the Gibbs energy of formation in aqueous solution, we must have solubility data as well as activity coefficients of acetic acid at various concentrations. From these data the change in Gibbs energy for solution of the liquid acetic acid in water to give aqueous acetic acid in the hypothetical 1 molal standard state (Eq. 6-39) can be obtained. 

Although the difference in solubility (and Gibbs energy) may be rather large, it is often observed that some metastable solids show a high inertia in that their rate of conversion to stable solids may be extremely small. We shall return to this later. 

Next, let us consider the fact that a given solid of known crystal structure has at least two additional degrees of freedom which may change its behavior. The presence of lattice defects, such as dislocations, and any alteration of particle size or specific surface will change its Gibbs energy. Since our present knowledge of the influence of lattice defects on solubility is rather limited, we shall restrict ourselves to a discussion of the particle size effect only. 

It should be noted that either the insertion or annihilation of the particle can be used to calculate the Gibbs energy of solvation, and both are related by a change of sign. With an appropriate method for solving the solubility calculations in aqueous solution, such as the one presented here, one can parameterize a model of C02 for a particular water model to reproduce these values over an extended thermodynamic window, such as over a desired temperature range that would encompass any type of brine aquifer. 

To finalize the development of the aqueous CO2 force field parameters, the C02 model was used in free energy perturbation Monte Carlo (FEP/MC) simulations to determine the solubility of C02 in water. The solubility of C02 in water is calculated as a function of temperature in the development process to maintain transferability of the C02 model to different simulation techniques and to quantify the robustness of the technique used in the solubility calculations. It is also noted that the calculated solubility is based upon the change in the Gibbs energy of the system and that parameter development must account for the entropy/enthalpy balance that contributes to the overall structure of the solute and solvent over the temperature range being modeled [17]. 

Analytical representation of the excess Gibbs energy of a system impll knowledge of the standard-state fugacities ft and of the frv. -xt relationshi Since an equation expressing /, as a function of x, cannot recognize a solubili limit, it implies an extrapolation of the /i-vs.-X[ curve from the solubility I to X) = 1, at which point /, = This provides a fictitious or hypothetical va for the fugadty of pure species 1 that serves to establish a Lewis/ Randall 1 for this species, as shown by Fig. 12.21. ft is also the basis for calculation of activity coefficient of species 1 ... 

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