Gases fugacity

Sulfur fugacity (/sj)- If electrum is in equilibrium with argentite, the equilibrium constant for the sulfidation reaction (K1.2), 

Barton and Toulmin (1964) have derived a relationship between fs2, temperature, and the Ag content of electrum in equilibrium with argentite, using the equation of White et al. (1957) for the chemical potential of Ag in electrum in combination with the equation 

Barton and Toulmin (1964) and Barton (1980) have derived the correction to equation (l)-(5) which is necessary due to the solubility of Au in argentite as a function of temperature and electrum eomposition. 

Based on this equation and N g, we can place a limit on /sj and temperature (Fig. 1.38). This application to ore fluids responsible for Kuroko deposits has been done by Sato (1969), Kajiwara (1970b) and Shikazono and Shimizu (1988a). 

Bomite-chalcopyrite—pyrite assemblage also defines /sj -temperature region. Combining the FeS content of sphalerite coexisting with bomite-chalcopyrite-pyrite, /s2-temperature can be determined (Kouda, 1977). 

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II The increment in the free energy, AF, in the reaction of forming the given substance in its standard state from its elements in their standard states. The standard states are for a gas, fugacity (approximately equal to the pressure) of 1 atm for a pure liquid or solid, the substance at a pressure of 1 atm for a substance in aqueous solution, the hyj)othetical solution of unit molahty, which has all the properties of the infinitely dilute solution except the property of concentration. 

A large number of geochemical studies on Kuroko deposits (fluid inclusions, gas fugacities, chemical and isotopic compositions of ore fluids etc.) have been carried out. These are summarized below. 

Based on the hydrothermal alteration mineral assemblages and the fluid inclusion, the probable range of gas fugacities (/s2, /o2 /H2S) and temperature can be seen in Figs. 1.81 and 1.82 these estimated fugaeities are quite different from those of the propylitic alteration. 

Numerous geochemical data (fluid inclusions, stable isotopes, minor elements) on the epithermal vein-type deposits in Japan are available and these data can be used to constrain geochemical environment of ore deposition (gas fugacity, temperature, chemical compositions of ore fluids, etc.) and origin of ore deposits. 

Garrels and Thompson s calculation, computed by hand, is the basis for a class of geochemical models that predict species distributions, mineral saturation states, and gas fugacities from chemical analyses. This class of models stems from the distinction between a chemical analysis, which reflects a solution s bulk composition, and the actual distribution of species in a solution. Such equilibrium models have become widely applied, thanks in part to the dissemination of reliable computer programs such as SOLMNEQ (Kharaka and Barnes, 1973) and WATEQ (Truesdell and Jones, 1974). 

The fugacities calculated in this way are those that would be found in a gas phase that is in equilibrium with the system, if such a gas phase were to exist. Whether a gas phase exists or is strictly hypothetical depends on how the modeler has defined the system, but not on the gas fugacities given by Equation 3.44. 

Here the aw and ak are the activities of water and minerals, and the fm are gas fugacities. We assume that each ak equals one, and that aw and the species activity coefficients y can be evaluated over the course of the iteration and thus can be treated as known values in posing the problem. 

Equation 4.6 can also be reserved because the gas fugacities fm are known. The nonlinear portion of the problem, then, consists of just two parts ... 

In this chapter we consider how to construct reactions paths that account for the effects of simple reactants, a name given to reactants that are added to or removed from a system at constant rates. We take on other types of mass transfer in later chapters. Chapter 14 treats the mass transfer implicit in setting a species activity or gas fugacity over a reaction path. In Chapter 16 we develop reaction models in which the rates of mineral precipitation and dissolution are governed by kinetic rate laws. 

In this chapter we consider how to construct reaction models that are somewhat more sophisticated than those discussed in the previous chapter, including reaction paths over which temperature varies and those in which species activities and gas fugacities are buffered. The latter cases involve the transfer of mass between the equilibrium system and an external buffer. Mass transfer in these cases occurs at rates implicit in solving the governing equations, rather than at rates set explicitly by the modeler. In Chapter 16 we consider the use of kinetic rate laws, a final method for defining mass transfer in reaction models. 

In a fixed activity path, the activity of an aqueous species (or those of several species) maintains a constant value over the course of the reaction path. A fixed fugacity path is similar, except that the model holds constant a gas fugacity instead of a species activity. Fixed activity paths are useful in modeling laboratory experiments in which an aspect of a fluid s chemistry is maintained mechanically. In studying reaction kinetics, for example, it is common practice to hold constant the pH of... 

In this chapter, we explore how we can use chemical analyses and pH determinations made at room temperature to deduce details about the origins of natural fluids. These same techniques are useful in interpreting laboratory experiments performed at high temperature, since analyses made at room temperature need to be projected to give pH, oxidation state, gas fugacity, saturation indices, and so on under experimental conditions. 

Standard state of Pure gas at unit fugacity for an ideal gas, fugacity is unity when... 

Then values of liquid fugacity and gas fugacity for each component are obtained from... 

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... 

The terms on the right-hand side of this equation are known (Fig. 3.11) or calculated by the model (gas fugacity = / (gi-Pfe)) (see previous discussions). If we assume an ideal solid solution (7ch4 6h2o = 7co2-6H2o)> then Eq. 3.55 simplifies to... 

Fig. 3.23. Gas fugacity coefficients for methane and carbon dioxide at 0°C as a function of pressure using the Duan et al. (1992b) model. Reprinted from Marion et al. (2006) with permission...

Table B.l lists all the chemical reactions and their temperature dependence. Table B.2 lists the Debye-Hiickel constants A,p and Av) as a function of temperature and pressure. Table B.3 lists the numerical arrays used for calculating unsymmetrical interactions (Equations 2.62 and 2.66). Table B.4 lists binary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.5 lists ternary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.6 lists binary and ternary Pitzer-equation parameters for soluble gases as a function of temperature. Table B.7 lists equations used to estimate the molar volume of liquid water and water ice as a function of temperature at 1.01 bar pressure and their compressibilities. Table B.8 lists equations for the molar volume and the compressibilities of soluble ions and gases as a function of temperature. Table B.9 lists the molar volumes of solid phases. Table B.10 lists volumetric Pitzer-equation parameters for ion interactions as a function of temperature. Table B.ll lists pressure-dependent coefficients for volumetric Pitzer-equation parameters. Table B.12 lists parameters used to estimate gas fugacities using the Duan et al. (1992b) model.

Table B.12. Parameters for Duan et al. (1992b) gas fugacity model (Eqs. 3.37-3.48). (Numbers are in computer scientific notation where e xx stands for 10 xx)...

The concentration of H2S gas in solution (C, mol kg-1) at equilibrium with various gas fugacities (fu2s)0311 be determined from... 

Chemical Potential, (realgas) for a Real (Non-Ideal) Gas. Fugacity, f... 

Our 2nd and 3rd law analysis of four sets of vapor pressure data produces the following results. The second virial coefficient determined by Osborne et al. (5) is used to convert all four vapor pressure data sets to ideal gas fugacity. 

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