Solubility hydrate calculations

Given gas partial pressures (Fig. 3.10), a model to calculate solubility product (Eq. 3.36) can be calculated for gas hydrates (Fig. 3.11). The actual solubility product calculations are made at the experimental gas partial pressures, which vary widely (Fig. 3.10). Equation 2.29 was used to adjust all these pressure-dependent estimates (Kp) to a hypothetical 1.0 atm total pressure (iTP0), which is what is presented in Fig. 3.11. 

In a wet atmosphere, iron and steel corrode producing first hydrated ferrous ions at the anodic site and hydrated hydroxide ions, OHaq, at the cathodic site where air-oxygen is reduced into OHaq ions. The presence of salts such as NaCl is known to enhance corrosion. Hydrated ferrous ions occur in the form of Fe2+, Fe(OH)+, Fe(OH) aq, and Fe(OH) aq. Gel-like hydroxide of Fe(OH)2,solid precipitates when the concentration of hydrated ferrous ions exceeds its solubility. Thermodynamic calculation gives the proton level to be pH 9.31 and 1.27 x 10 5 mol dm 3 of solubility at which the equilibrium is established between gel-like Fe(OH)2,soiid and hydrated OHaq ions when Fe(OH)2solid is put in pure water [90]. 

In almost all theoretical studies of AGf , it is postulated or tacitly understood that when an ion is transferred across the 0/W interface, it strips off solvated molecules completely, and hence the crystal ionic radius is usually employed for the calculation of AGfr°. Although Abraham and Liszi [17], in considering the transfer between mutually saturated solvents, were aware of the effects of hydration of ions in organic solvents in which water is quite soluble (e.g., 1-octanol, 1-pentanol, and methylisobutyl ketone), they concluded that in solvents such as NB andl,2-DCE, the solubility of water is rather small and most ions in the water-saturated solvent exist as unhydrated entities. However, even a water-immiscible organic solvent such as NB dissolves a considerable amount of water (e.g., ca. 170mM H2O in NB). In such a medium, hydrophilic ions such as Li, Na, Ca, Ba, CH, and Br are selectively solvated by water. This phenomenon has become apparent since at least 1968 by solvent extraction studies with the Karl-Fischer method [35 5]. Rais et al. [35] and Iwachido and coworkers [36-39] determined hydration numbers, i.e., the number of coextracted water molecules, for alkali and alkaline earth metal... 

In principle, Gibbs free energies of transfer for trihalides can be obtained from solubilities in water and in nonaqueous or mixed aqueous solutions. However, there are two major obstacles here. The first is the prevalence of hydrates and solvates. This may complicate the calculation of AGtr(LnX3) values, for application of the standard formula connecting AGt, with solubilities requires that the composition of the solid phase be the same in equilibrium with the two solvent media in question. The other major hurdle is that solubilities of the trichlorides, tribromides, and triiodides in water are so high that knowledge of activity coefficients, which indeed are known to be far from unity 4b), is essential (201). These can, indeed, be measured, but such measurements require much time, care, and patience. 

In Investigation 9-A, you will collect solubility data and use these data to determine a Ksp for calcium hydroxide, Ca(OH)2. When you calculate Ksp, you assume that the dissolved ionic compound exists as independent hydrated ions that do not affect one another. This assumption simplifies the investigation, but it is not entirely accurate. Ions do interfere with one another. As a result, the value of Ksp that you calculate will be just an approximation. iCp values that are calculated from data obtained from experiments such as Investgation 9-A are generally higher than the actual values. 

If A+aq and B"aq were in their standard states, the accurate value of AG would be available from the solubility product. However, in pulverizing and hydrating, we had to avoid any dilution. We can therefore only estimate that the activities of A+aq and B"aq are less than 1 if expressed in terms of mole fractions and equal to or greater than 1 if expressed in terms of molarities. Since mole fraction and molarity are related by a factor of about 55, the uncertainty of the calculated AG is, in our present example, about 2 RT In 55. This term becomes comparatively small if In Ks0 is large. From Equations 3 and 4 we obtain ... 

F. Martin gave 174° for the temp, of explosion. According to L. Wohler and W. Krupko, basic cupric azide, cupric oxyazide, CuO.CuNg, is formed as a yellow hydrated substance when water with normal cupric azide in suspension is heated to 70°-80° in a current of air freed from carbon dioxide until the calculated quantity of hydrazoic acid has been evolved. It inflames at 245°. L. M. Dennis and H. Isham obtained cupric amminoazide,Cu(NHg)Ns,by shaking freshly precipitated black cupric hydroxide, while still moist, with an excess of hydrazoic acid and washed the precipitate. A soln. of the precipitate in aq. ammonia deposits crystals of the salt. It explodes when heated or struck. It is insoluble in water, and soluble in dil. acids,... 

The calculation of two-phase (hydrate and one other fluid phase) equilibrium is discussed in Section 4.5. The question, To what degree should hydrocarbon gas or liquid be dried in order to prevent hydrate formation is addressed through these equilibria. Another question addressed in Section 4.5 is, What mixture solubility in water is needed to form hydrates ... 

There are only few data sets of aqueous solubility for systems with hydrates (1) methane and ethane solubility in water as a function of temperature ramping rate (Song et al. 1997), (2) carbon dioxide solubility in water by Yamane and Aya (1995), (3) methane in water and in seawater (Besnard et al., 1997), (4) methane in water in Lw-H region [see Servio and Englezos (2002) and Chou and Burruss, Personal Communication, December 18,2006, Chapter 6], As a standard for comparison, Handa s (1990) calculations for aqueous methane solubility are reported in Table 4.3. 

While Table 4.3 shows solubility both above and below the hydrate point, at the three-phase hydrate condition Handa s predictions show a sharp maximum in solubility with pressure at constant temperature. In Holder s laboratory, Toplak (1989) measured the solubility of gas in liquid water around the hydrate point, both in water that had formed hydrates and in water with no residual structure his results show no dramatic change in pure component solubility at the three-phase (Lw-H-V) condition. Kobayashi and coworkers (Besnard et al., 1997) measured a significant solubility increase at the hydrate point beyond that calculated using Henry s law. However, comprehensive solubility measurements around the hydrate point await further experiments. 

Calculations of Methane Solubility in Water and Seawater, at Conditions Above and Below the Hydrate Point... 

From Chapters 4, 5 and 6 thermodynamic data and predictions, the maximum methane concentration (solubility) occurs in the aqueous liquid at equilibrium with hydrates. In order for methane to exsolve the liquid, the solubility must change rapidly as the water rises with corresponding decreases in pressure and temperature. Solubility calculations (Handa, 1990) indicate a change in methane concentration too gradual to account for a significant hydrate amount. Solubility data are needed at conditions of hydrate formation, in order to confirm this model. Preliminary solubility data are available from Besnard et al. (1997). 

If we calculated with the idealized co-operative model by the content of spectroscopic determined Op values the number Nei of H-bonded water molecules we would get — with different 1 molar salt solutions — the result of Fig. 11. The values Nei with salt additions depend strongly on the salt concentrations because of the disturbance of the big H-bonded system3At small concentrations the Nel-N0 numbers (7V0 association number in pure water) of structure-makers are in size of the order of Debye-Sack s or Azzam s calculations. They are of the same size of order as the secondary hydration numbers calculated by solubility measurements of organic substances in water (Chapter b) or as the hydration numbers of hydrophilic organic molecules (Chapter lld-e) or biopolymers (Chapter III). 

To estimate a gas hydrate solubility product requires knowing g, Pg, and aw (Eq. 3.36). The gas partial pressure, Pg, is experimentally measured. The activity of water, aw, is calculated by the FREZCHEM model (Eq. 2.37), as is the gas fugacity coefficient (g) using a model developed by Duan et al. (1992b). The equation used to calculate gas fugacity coefficients is given by... 

There is an abundance of experimental gas partial pressures for gas hydrate equilibria across a broad range of temperatures (Fig. 3.10 Sloan 1998). The lower temperature limit in our model database for these systems is 180 K (Fig. 3.10) because this is the lower limit of our model s ability to estimate aw (Fig. 3.1, Eq. 3.11), which is needed to calculate the solubility product of gas hydrates (Eq. 3.36). In our model, the upper temperature limit for methane hydrate is at 298 K (25 °C), which is the upper temperature limit for FREZCHEM the upper temperature limit for carbon dioxide hydrate is at 283K (10 °C), which is the temperature where liquid C02(l) becomes the thermodynamically stable phase. 

W. Swope, H. Andersen, A molecular dynamics method for calculating the solubility of gases in liquids and the hydrophobic hydration of inert-gas atoms in aqueous solution. J. Phys. Chem. 88, 6548 (1984)... 

From the free-energy considerations, one can calculate the reversible potentials for a metal that is in equilibrium with its simple hydrated ions or with its soluble product of hydrolysis or with its insoluble oxide. Under the given conditions, the... 

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