Chemical standard state

This is done by starting with equation (6.84), which relates the chemical potential of a solute in solution with activity to the standard state chemical potential... 

Note, in using Equations 50 and 53 above, that tabulations of thermodynamic data for electrolytes tend to employ a 1 molar ess concentration for all species in solution. For situations defined to have a standard-state pH value different from 0 (which corresponds to a 1 molar concentration of solvated protons), the standard-state chemical potentials for anions and cations are determined as... 

Here a°(c) is the standard state chemical potential of condensed fluid in equilibrium with the vapor at the vapor pressure P, and the temperature of the measurement. 

The algebraic formulation of the relationship among chemical potential p,, standard state chemical potential and thermodynamic activity a, is... 

Table 5.51 Energy terms relating standard state chemical potentials of pnre components (p,°o.) to lictive potentials in the host phase (p-Js) in the Will and Powell (1992) application of Darken s Quadratic Formalism to amphiboles. 

Figure 10,1 (A) Activity-molar concentration plot. Trace element concentration range is shown as a zone of constant slope where Henry s law is obeyed. Dashed lines and question marks at high dilution in some circumstances Henry s law has a limit also toward inhnite dilution. The intercept of Henry s law slope with ordinate axis defines Henry s law standard state chemical potential. (B) Deviations from Nernst s law behavior in a logarithmic plot of normalized trace/carrier distribution between solid phase s and ideal aqueous solution aq. Reproduced with modifications from liyama (1974), Bullettin de la Societee Francaise de Mineralogie et Cristallographie, 97, 143-151, by permission from Masson S.A., Paris, France. A in part A and log A in part B have the same significance, because both represent the result of deviations from Henry s law behavior in solid.

However, the term in braces (a numerical constant) must be merely the standard state chemical potential for the liquid phase (where we choose pure A as standard state for liquid at the chosen T and P),... 

If P- = RT In standard-state chemical potential, then by construction,... 

Here C is the concentration of component i in grams per liter, and t/ is the activity coefficient of component i on this concentration scale. The quantity m° is the standard state chemical potential of component i and is a function of temperature only. The standard state of solute component i is chosen so that In t/ — 1 as c, — 0. In Equation 4, R is the universal gas constant, 8.314 X 107 ergs/(deg mole), and T is the absolute temperature. The quantity In t/ is a function of the concentration of all q solutes thus... 

In equations 27-29, P(j is the partial distribution coefficient of component ij, Tij is the ratio of activity coefficients, 0 is the reduced standard-state chemical potential difference, xiop is the standard-state chemical potential of component i in phase p, and yf and yxjp are the activity coefficients of components i and ij, respectively, in phase p. The working equations (equations 23-26) describing phase equilibria, along with the equation defining a mole fraction, are implicitly complex relations for T, P, x, y, xAC, xA, xc, and xD but involve only two thermodynamic quantities, 0 and Tiy Equations 23-25 are implicit in composition only through the term, which is itself only a weak function of composition. 

The thermodynamic quantity 0y is a reduced standard-state chemical potential difference and is a function only of T, P, and the choice of standard state. The principal temperature dependence of the liquidus and solidus surfaces is contained in 0 j. The term is the ratio of the deviation from ideal-solution behavior in the liquid phase to that in the solid phase. This term is consistent with the notion that only the difference between the values of the Gibbs energy for the solid and liquid phases determines which equilibrium phases are present. Expressions for the limits of the quaternary phase diagram are easily obtained (e.g., for a ternary AJB C system, y = 1 and xD = 0 for a pseudobinary section, y = 1, xD = 0, and xc = 1/2 and for a binary AC system, x = y = xAC = 1 and xB = xD = 0). 

Reduced Standard-State Chemical Potential Difference. The... 

From a Solution Model. Calculation of the difference in reduced standard-state chemical potentials by methods I or III in the absence of experimental thermodynamic properties for the liquid phase necessitates the imposition of a solution model to represent the activity coefficients of the stoichiometric liquid. Method I is equivalent to the equation of Vieland (106) and has been used almost exclusively in the literature. The principal difference between methods I and III is in the evaluation of the activity coefficients... 

By using the procedures just outlined, the reduced standard-state chemical potential can be estimated for all compounds. This value of Gy is valid for any solid-liquid phase equilibrium problem that contains the compound... 

If the standard state chemical potential of species i is denoted by p", then the chemical potentials of the species i satisfy [55]... 

Iquaiion sl. 8 applies to any substance, in any phase, in any kind of mixture at equilibrium. It expresses the idea that the chemical potential of a substance always may be written as equal to the Standard-State chemical potential plus a... 

The Standard-State chemical potentials of substances in the gas, liquid, and .olul phases, as well as of solutes in aqueous solution, can be determined by a v.uiely of experimental methods, among them spectroscopic, colorimetric, mi 11 ib i lily, colligative-property, and electrochemical techniques.817 The accepted values of these fundamental thermodynamic properties are and should be undergoing constant revision under the critical eyes of specialists. It is not the puipose of this book lo discuss the practice of determining values of /i° for all < (impounds of interest in soils. This is best left lo. specialized works on... 

Because of the continual revision in pP values, no attempt will be made to present a list of critically compiled data, even for the compounds of principal interest in soils. In this and subsequent chapters, Standard-State chemical potentials for gases, liquids, solids, and solutes usually will be taken from data in the following critical compilations. 

As an example of the use of Eq. si. 16, the equilibrium constant for the C02 hydration reaction in Eq. 1.16 will be calculated at 298 K. The Standard-State chemical potentials that contribute to ArG° for this reaction are, together with their reported uncertainties,... 

In soil solutions the most important chemical elements that undergo redox reactions are C, N, O, S, Mn, and Fe. For contaminated soils the elements As, Se, Cr, Hg, and Pb could be added. Table 2.4 lists reduction half-reactions (most of which are heterogeneous) and their equilibrium constants at 298.15 K under 1 atm pressure for the six principal elements involved in soil redox phenomena. Although the reactions listed in the table are not full redox reactions, their equilibrium constants have thermodynamic significance and may he calculated with the help of Standard-State chemical potentials in the manner... 

If Standard-State chemical potentials are used to calculate equilibrium constants (with Eqs. si.6 and si.8), these concerns become paramount.33,34 Consider, for example, the complex, AIF 1T whose kinetics of formation was... 

Values of llio Standard State chemical potentials in liq. 2.58 are available from... 

The value of Kdis can be calculated with Standard-State chemical potentials according to the relationships in Eqs. sl.12-sl.14 1... 

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