Stoichiometric saturation states

Field or laboratory observations of miscibility gaps, spinodal gaps, critical mixing points or distribution coefficients can be used to estimate solid-solution excess-free-energies, when experimental measurements of thermodynamic equilibrium or stoichiometric saturation states are not available. As an example, a database of excess-free-energy parameters is presented for the calcite, aragonite, barite, anhydrite, melanterite and epsomite mineral groups, based on their reported compositions in natural environments. 

Several thermodynamic states are of interest in the study of SSAS systems. The following sections discuss the concepts of thermodynamic equilibrium, primary saturation and stoichiometric saturation states. 

Applying the law of mass action then gives the defining condition for stoichiometric saturation states ... 

Stoichiometric saturation states can be represented on Lippmann phase diagrams (figure 1) by relating the total solubility product variable Ellgg (defined specifically at stoichiometric saturation with respect to a solid Ex. CxA) to the Kgg constant (equation 12) and to the aqueous activity fractions and c,aq-... 

As shown in figure 1, stoichiometric saturation states never plot below the solutus curve. This is consistent with the fact that stoichiometric saturation can never be reached before primary saturation in a solid-solution dissolution experiment. The unique point at which a stoichiometric saturation curve (for a given solid Bj.xCxA) joins the Lippmann solutus represents the composition of an aqueous solution at thermodynamic equilibrium with respect to a solid Bx xCxA. 

The final solid solution-aqueous solution compositions of Table I will fall into one of three catagories (1) they will either be at equilibrium, (2) at stoichiometric saturation, or (3) correspond to some non-equilibrium state. 

One of the primary concerns in a study of the geochemistry of carbonates in marine waters is the calculation of the saturation state of the seawater with respect to carbonate minerals. The saturation state of a solution with respect to a given mineral is simply the ratio of the ion activity or concentration product to the thermodynamic or stoichiometric solubility product. In seawater the latter is generally used and Qmjneral is the symbol used to represent the ratio. For example ... 

Note that the value of KdSiSs depends on the mole fraction x, and therefore will vary with the composition of the mixed solid. Unlike Kdis for a pure solid phase, Kd must be measured as a function of mixed solid composition in order to apply Eq. 3.29 to all possible states of stoichiometric saturation. 

Because of difficulties in precisely calculating the total ion activity coefficient (y) of calcium and carbonate ions in seawater, and the effects of temperature and pressure on the activity coefficients, a semi-empirical approach has been generally adopted by chemical oceanographers for calculating saturation states. This approach utilizes the apparent (stoichiometric) solubility constant (K ), which is the equilibrium ion molal (m) product. Values of K are directly determined in seawater (as ionic medium) at various temperatures, pressures and salinities. In this approach ... 

The interest in the carbonate system is related to attempts to understand the uptake of fossil fuel produced CO2 by the oceans. The carbonate system can be studied by measuring pH, total alkalinity (TA), total inorganic carbon (TCO2), and the fugacity of CO2 (fco )- At least two of these variables are needed (Park, 1969) to characterize the CO2 system in the oceans. Reliable stoichiometric constants (K ) for the carbonate system are needed to determine the concentration, mol (kg solution) of the components of the CO2 system ([HCOa"], [CO2], [COa ]) and the saturation state of CaCOa as a function of salinity, temperature, and pressure (Culberson and Pytkowicz, 1968 Ingle, 1975 Millero, 1995, 2001). This includes constants for the solubility of CO2 in seawater (Weiss, 1974)... 

This result indicates that the velocity of the solute front is inversely proportional to the slope of the isotherm. We can illustrate this result using a Type I isotherm (Figure 7.6). During the adsorption step, the direction is from the lower left to upper right portion of the curve. So, dg/dT is largest V is slowest) during the initial portion of sorption. This is the rate-limiting step so the entire front moves as a discontinuous wave (stoichiometric front). A balance across this wave shows that Aq/AY reduces to Aq/AY, the chord from the initial state to the saturated state in the column. 

Figure 1. Lippmann diagram (with stoichiometric and pure-phase saturation curves) for the Ag(Cl,Br) - H2O system at 30° C. Calculated ao and ai values are 0.30 and -0.18 respectively. pK gci = 9.55 (16J. pK gBr = 12.05 (12). T1 and T2 give the aqueous and solid phase compositions, respectively, of a system at thermodynamic equilibrium with respect to an AgCl.sBr 5 solid. PI and P2 describe the state of a system at primary saturation with respect to the same solid. MSI gives the composition of an aqueous phase at congruent stoichiometric saturation with respect to that solid.

Stoichiometric saturation was formally defined by Thorstenson and Plummer (1). These authors argued that solid-solution compositions typically remain invariant during solid aqueous-phase reactions in low-temperature geological environments, thereby preventing attainment of thermodynamic equilibrium. Thorstenson and Plummer defined stoichiometric saturation as the pseudoequilibrium state which may occur between an aqueous-phase and a multi-component solid-solution, "in situations where the composition of the solid phase remains invariant, owing to kinetic restrictions, even though the solid phase may be a part of a continuous compositional scries". 

The composition of a SSAS system at primary saturation or at stoichiometric saturation will be generally independent of the initial solid to aqueous-solution ratio, but will depend on the initial aqueous-solution composition existing prior to the dissolution of the solid. In contrast, the final thermodynamic equilibrium state of a SSAS system attained after a dissolution or recrystallisation process will generally depend not only on the initial composition of the system but also on the initial solid to aqueous-solution ratio (Glynn et al, submitted to Gcochim, Cosmochim. Acta). 

Lippmann phase diagrams can be used to describe and compare thermodynamic equilibrium (equations 3, 4), primary saturation (equations 9, 10), stoichiometric saturation (equation 13) and pure end-member saturation states (equations 14, 15) in binary SSAS systems. 

The construction of the structural kinetic model proceeds as described in Section VIII.E. Note that in contrast to previous work [84], no simplifying assumptions were used the model is a full implementation of the model described in Refs. [113, 331]. The model consists of m = 18 metabolites and r = 20 reactions. The rank of the stoichiometric matrix is rank (N) = 16, owing to the conservation of ATP and total inorganic phosphate. The steady-state flux distribution is fully characterized by four parameters, chosen to be triosephosphate export reactions and starch synthesis. Following the models of Petterson and Ryde-Petterson [113] and Poolman et al. [124, 125, 331], 11 of the 20 reactions were modeled as rapid equilibrium reactions assuming bilinear mass-action kinetics (see Table VIII) and saturation parameters O1 1. 

A general treatment of a diffusion-controlled growth of a stoichiometric intermetallic in reaction between two two-phase alloys has been introduced by Paul et al. (2006). A reaction couple in which a layer of Co2Si is formed during inter-diffusion from its adjacent saturated phases was used as a model system. In the discussion it has been emphasized that the diffusion couple is undoubtedly one of the most efficient and versatile techniques in solid-state science it is therefore desirable to have alternative theories that enable us to deduce the highest possible amount of information from the data that are relatively easily attainable in this type of experiments. 

Using one liter of subsurface site material (containing 0.33 L of water and 0.67 L of solids Altoluene(1 = 0.1 L-kg-1) in an enclosed column in the laboratory, you flush it with water containing 100 /tM toluene and 02 (added as H202) in stoichiometric excess. You find the steady-state dry biomass is 10 mg biomass. L- (i.e., 30 mg biomass - L 1 of water). By varying the influent toluene concentration, you find the pmax on this substrate is 1 d l, the die-off coefficient is 0.15 d l, the half-saturation constant with respect to dissolved toluene is 10 fjM, and the dry biomass yield from toluene is 8 x 104 mg biomass.mor1 toluene. 

The results demonstrate that for liquid mass fluxes, which do not lead into the direct proximity of the state of saturation of air, a stoichiometric relationship does not play an unimportant role. Rather, the mass transfer area of the fluidized bed is the limiting factor of the absorption. Over-stoichiometric operation does not lead to any improved separation of the SO2 (Figs. 16.14 and 16.15), the reason being the permanent destruction of the liquid film by particle-particle collisions and the consequent production of inactive reactants. 

Hydrosilylation of Generic Ketones. All other hydrosilylation reactions were performed in a similar fashion to that stated previously. Thus, the desired ketone and catalyst (5000 1 mol ratio ketone catalyst) were dissolved in CH2C12 and a stoichiometric amount of the appropriate disubstituted silane was added to the rapidly stirred solution. After addition of the silane, stirring was continued for two hours at room temperature. Evaporation of the solvent and hydrolysis of the resulting silyl ether in 10% HC1 (2 hr room temperature) followed by addition of a saturated Na C solution and extraction with diethyl ether gave the expected chiral alcohol. Isolated yields are reported for the alcohols following purification by distillation or column chromatography. 

It is also useful to consider the luminescence from metallated oligonucleotides in the presence of noncovalent metallointercalator. Adding one equivalent of free [Ru(phen)2(dppz)]2+ to the ruthenium-modified duplex doubles the intensity in luminescence, consistent with independent intercalation by the two species. As described earlier, steady-state luminescence reaches saturation at approximately three times the luminescence of the ruthenium-modified duplex when two equivalents of [Ru(phen)2(dppz)]2+ have been added. It is not surprising, then, that addition of a stoichiometric amount of [Rh(phi)2(phen)]3+ to the ruthenium-modified duplex leads to substantial but not complete quenching of the ruthenium emission. Statistically, some duplexes will accommodate two rhodium(III) complexes, leaving a few ruthenium-modified duplexes unoccupied and therefore unquenched. Thus, complete quenching is observed only when the acceptor is covalently bound to the same duplex as the donor. 

The inventor proposes an alternate process in claim 1 in which the oxides are dissolved into an unspecified supercritical fluid at unspecified conditions but at 1 to 25 wt% below the solubility of the least soluble cranponent, rapidly expanding the fluid to precipitate a uniform and stoichiometrically accurate mixture, and thermally treating the powder. We wonder how this patent was allowed since the patent by Sievers and Hansen (U.S. 4,970,093) reviewed in this edition of the book, states explicitly the process and conditions neededlo dissolve metal complexes for superconductor fabrication. Sievers and Hansen are not quoted by the inventor nor is their quantitative data quoted. We also wonder if the inventor has ever tried to dissolve some of the materials that are listed in the claims section since the instant patent teaches to operate at 1 to 25 wt% less than the saturation amount of the least soluble component. Can we expect compounds such as yttrium to have solubilities at weight percent levels We do not believe so. 

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