Equilibrium activity diagrams

Bowers T.S., Jackson K.J., and Helgeson H.C. (1984) Equilibrium Activity Diagrams (for Coexisting Minerals and Aqueous Solutions at Pressures and Temperatures of 5 KB and 600°C). Springer-Verlag, Berlin, 397 pp. 

Bowers, T. S., K, J. Jackson, and H. C. Helgeson. 1984. Equilibrium activity diagrams. New York Springer-Vcrlag. 

Fig. 19.5. Equilibrium activity diagram for the system K20-Al203-Si02-H20 at 25°C, 1 bar (after Helgeson, 1979). The reaction path ABCDG represents successive stages in the hydrolysis of K-feldspar, which correspond to stages ABCDG in Figure 19.6.

Pourbaix has evaluated all possible equilibria between a metal M and HjO (see Table 1.7) and has consolidated the data into a single potential-pH diagram, which provides a pictorial summary of the anions and cations (nature and activity) and solid oxides (hydroxides, hydrated oxides and oxides) that are at equilibrium at any given pH and potential a similar approach has been adopted for certain M-H2O-X systems where A" is a non-metal, e.g. Cr, CN , CO, SOj , POj", etc. at a defined concentration. These diagrams give the activities of the metal cations and anions at any specified E and pH, and in order to define corrosion in terms of an equilibrium activity, Pourbaix has selected the arbitrary value of 10 ° g ion/1, i.e. corrosion of a metal is defined in terms of the pH and potential that give an equilibrium activity of metal cations or anions > 10 g ion/1 conversely, passivity and immunity are defined in terms of an equilibrium activity of < 10 g ion/1. (Note that g ion/1 is used here because this is the unit used by Pourbaix in the S.I, the relative activity is dimensionless.)... 

Helgeson (1967) constructed an activity diagram depicting chemical equilibrium points (albite-sericite-K-feldspar and albite-sericite-Na-montmorillonite) of NazO-K20-Si02-Al203-H20 system at elevated temperatures. At these points,... 

Table 8.25 Equilibrium constants used for construction of figure 8.31 (activity diagram). ...

Fig. 2. Logarithmic activity diagram depicting equilibrium phase relations among aluminosilicates and sea water in an idealized nine-component model of tire ocean system at the noted temperatures, one atmosphere total pressure, and unit activity of H20. The shaded area represents (lie composition range of sea water at the specified temperature, and the dot-dash lines indicate the composition of sea water saturated with quartz, amotphous silica, and sepiolite, respectively. The scale to the left of the diagram refers to calcite saturation foi different fugacities of CO2. The dashed contours designate the composition (in % illite) of a mixed-layer illitcmontmorillonitc solid solution phase in equilibrium with sea water (from Helgesun, H, C. and Mackenzie, F T.. 1970. Silicate-sea water equilibria in the ocean system Deep Sea Res.).

Solid-liquid equilibrium phase diagrams play an important role in the design of industrial crystallization processes. The calculation of phase diagrams can be used to validate the activity coefficient model used for process simulation. 

Helgeson, H.C., Brown, T.H. and Leeper, R.H., 1969a. Handbook of Theoretical Activity Diagrams Depicting Chemical Equilibrium in Geologic Systems Involving an Aqueous Phase at One Atmosphere and 0—300 C. Freeman and Cooper, San Francisco, Calif., 253 pp. 

The method developed in this book is also used to provide input parameters for composite models which can be used to predict the thermoelastic and transport properties of multiphase materials. The prediction of the morphologies and properties of such materials is a very active area of research at the frontiers of materials modeling. The prediction of morphology will be discussed in Chapter 19, with emphasis on the rapidly improving advanced methods to predict thermodynamic equilibrium phase diagrams (such as self-consistent mean field theory) and to predict the dynamic pathway by which the morphology evolves (such as mesoscale simulation methods). Chapter 20 will focus on both analytical (closed-form) equations and numerical simulation methods to predict the thermoelastic properties, mechanical properties under large deformation, and transport properties of multiphase polymeric systems. 

Table V summarizes the experimental results of the tests with low oxygen content in the matte i.e., tests 1-5,9and 10. The matte conqxrsititMi and nramalized zinc solubility at Pzn=0.1 atm and 1350°C as reported Table III are repeated here. The zinc solubility has been converted into mole fractions to calculate the activity coefficient. The sulfur potentials at 1450 and 1200°C are taken from the reported activity diagrams for Fe-S-O matte (9), from which the sulfur potentials at 1350°C are estimated. The activities of ZnS in the matte were calculated from azns = K Pzn (Ps2), where K is the equilibrium constant for reaction Zn(g)+V2S2(g)=ZnS(l) and was estimated to be 64 at 1350 C. The activity coefficient of ZnS in the matte was estimated (Table IV). Although the estimated activity coefficient of ZnS varied from 7 to 22, it has an average value of 12.6 and is very close to the reported value, 10 (8). Considering the many possible sources of aror in the tests, it is not surprising that there is a large scatta in the estimated ZnS activity coefficient Nevertheless, the experimental data wae in close agreement with the theoretical predictions.

When rainwater interacts with a rock that contains potassium feldspar, the feldspar dissolves and new minerals grow until the aqueous solution comes to equilibrium with the potassium feldspar. The reactions add K and H4Si04 to the solution and consume H. This reaction path model tracks the changing solution composition on an activity diagram (Figure 8.6) to show how the solution composition traverses the stability fields of gibbsite (gib), kaolinite (kaol), and muscovite (mu) until it reaches equilibrium with potassium feldspar (KJ). The phase boundaries are defined by five reactions. 

The equilibrium phase diagram of RDX has been determined to 7.0 GPa and 573K. Three solid phases, a, p and 7, have been found and their stability fields delineated. The pressure dependence of the melting point has also been defined. The ot and P phases were found to thermally decompose in the P, T regime of concern here. Pressure enhances the rate of decomposition of the a phase and probably reacts through a bimolecular-type mechanism. The activation volume, AV, for the reaction is -5.6 cm /mole and is temperature independent. The... 

Fig. 3. Potential-pH diagrams drawn at the equilibrium activities of Cu2+ aquo ion at pH 9 and (a) 298, (b) 323, and (c) 353 K considering the species Cu2+, CuO, CU2O, and Cu. Oxyanions of copper, HCUO2" and Cu022 , or hydroxyanions of copper, Cu(OH)3" and Cu(OH)42, are not considered for simplicity. These potential-pH diagrams are only valid at the vertical line of pH 9 because the equilibrium activity of Cu2+ aquo ion changes with pH in this system.

FIGURE 8.9 (a) Partial and total pressure of acetone-chloroform at 60°C. (b) Activity coefficients for acetone and chloroform at 1.00 atm. (c) Vapor-liquid equilibrium diagram for acetone-chloroform solutions at 1.00 atm. (d) Vapor-liquid equilibrium phase diagram for acetone-chloroform at 1.00 atm. 

FIGURE 8.10 Activity coefficients for water-sulfuric acid at 200°C [8, p. 2-83]. Observe that the least volatile species, sulfuric acid, is chosen as species a. This is contrary to the standard convention, but the normal way of showing water-sulfuric acid diagrams. This equilibrium is complicated by the formation of several weak intermolecular compounds and by the presence of free SO3 in the equilibrium vapor. Nonetheless, it shows that for species that form such weakly-bonded quasi-compounds, the equilibrium activity coefficients can be quite small. 

The equilibrium constants for oxidation [Eq. (3)] and for decarboxylation [Eq. (4)] have been calculatd by Shock (1988, 1989) for conditions of 100°C and 300 bar and were then used to generate the activity diagrams given in Figs. 2 and 3. This information provides a framework for assessing the relative importance of oxidation and decarboxylation reactions in determining the stability of acetic acid in basin brines. These data show that. 

Fig. 4. Activity diagram for the equilibrium between acetic and propionic acids, as given in Eq. (23), at 100 °C and 300 bar (Shock 1989), showing log(acH3CH2CooH) versus log(flcH3CooH) The solid lines are contours of log(/o2)- oth open and solid symbols represent activities calculated from reported concentrations of acetic and propionic acids in natural brine samples from the San Joaquin and Gulf Coast Basins (Carothers and Kharaka 1978). Solid symbols indicate values for which a correlation with iodide is shown in Fig. 7. (With permission by E.L. Shock and The Geological Society of America)...

Charge diagrams suggest that the 2-amino-5-halothiazoles are less sensitive to nucleophilic attack on 5-position than their thiazole counterpart. Recent kinetic data on this reactivity however, show, that this expectation is not fulfilled (67) the ratio fc.. bron.c.-2-am.noih.azoie/ -biomoth.azoie O"" (reaction with sodium methoxide) emphasizes the very unusual amino activation to nucleophilic substitution. The reason of this activation could lie in the protomeric equilibrium, the reactive species being either under protomeric form 2 or 3 (General Introduction to Protomeric Thiazoles). The reactivity of halothiazoles should, however, be reinvestigated under the point of view of the mechanism (1690). 

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