Gibbs-Duhem theory

A theory of stability that is based on the positivity of entropy production in spontaneous processes is more general than the classical Gibbs—Duhem theory of stability [1, 2], which is limited to the constraints expressed in (14.1.1) to (14.1.3) and the associated thermodynamic potentials. In addition, stability... 

In theory, once the activity of an electrolyte in solution is known, the activity of the solvent can be determined by the Gibbs-Duhem integration (see section 2.11). In practice, the calculation is prohibitive, because of the chemical complexity of most aqueous solutions of geochemical interest. Semiempirical approximations are therefore preferred, such as that proposed by Helgeson (1969), consisting of a simulation of the properties of the H20-NaCl system up to a solute... 

In this section, we wish to derive the Gibbs-Duhem equation, the fundamental relationship between the allowed variations dRt of the intensive properties of a homogeneous (singlephase) system. Paradoxically, this relationship (which underlies the entire theory of phase equilibria to be developed in Chapter 7) is discovered by considering the fundamental nature of extensive properties Xu as well as the intrinsic scaling property of the fundamental equation U = U(S, V, n, n2,. .., nc) that derives from the extensive nature of U and its Gibbs-space arguments. 

Another problem is the use of the relationship aw — 1 — Vwap. Here Vw is the degree of hydration, ap is the NMR-derived protein activity and aw the water activity. This underived expression is analogous to a stoichiometric population expression but is inappropriate for activities whose relationships are determined by the Gibbs-Duhem equation. Despite these shortcomings the Kumosinski-Pessen theory has been extensively used in the food literature.37,38,40-43... 

Therefore, for such primed thermodynamic quantities, we have not only all the results of our theory of primed thermodynamic quantities but also the Gibbs-Duhem equations for all of them are valid. 

This set of simultaneous equations, coupled with the Gibbs-Duhem equation at constant T, are all we need to derive the most common forms of the basic theory providing a range of relationships between fluctuating quantities and thermodynamic... 

Surface solution theories should be consistent with the Gibbs adsorption equation (Equation 1.24), just as the bulk solution theories should be consistent with the Gibbs-Duhem equation. It is readily shown that ideal surface solution theory, as discussed above, satisfies this criterion (see Problem 1.15). However, regular surface solution theory does not, owing to the limitations of modeling the interfacial region by a single composition. This matter is discussed in some detail by Defay et al. (1966). 

The thermodynamic theory of the ideally polarised electrode has been extensively reviewed in the past few decades [1-5], and the relationship with the ideally non-polarisable interface has been derived in an elegant treatment by Parsons [6]. The starting point in all derivations is the Gibbs-Duhem equation which defines the relationship between the extensive thermodynamic variables. For a bulk phase this has the form ... 

The essentials of the constitutive theory are that the experimental results are reproduced after satisfying the requirements of thermodynamics such as the Clausius-Duhem inequality and the Gibbs-Duhem relation. The constitutive theory that includes chemical processes is complex because all the conservation laws for mass, linear momentum/moment of momentum and energy are involved, and experiments to determine the parameters are extremely difficult to conduct. 

It should be pointed out that Overb k critidzed the Sogami theory and contended that, if solvent ccmtribution is taken into account, the attraction in the Sogami theory disappears [52], This ccmdusirMi canimt be correct, however, because his argument violated the Gibbs-Duhem relation, as was discussed recently by us [31]. 

For a nonvolatile substance we must find a way to determine its activity coefficient that does not depend on measuring its vapor pressure. We will discuss three different methods. The first is through integration of the Gibbs-Duhem equation. The second is through a theory due to Debye and Hiickel, which can be applied to electrolyte solutes. The third method for electrolyte solutes is an electrochemical method, which we will discuss in Chapter 8. Published data are available for common electrolytes, and some values are included in Table A. 11 in Appendix A. 

The most important personality in thermodynamic history was credibly Gibbs who discriminated that a system of r coexistent phases, each of which having the same independently variable components, n, is capable of ( + 2 - r) variations of phase, known until now as the famous phase rule , that factually unveiled that the whole is simpler than its parts. It followed that for temperature, pressure and chemical equivalents ( potentials later specified as chemical potentials by Ostwald) the actual components bear the same values in the different phases and the variation of these quantities are subject to as many conditions as there are different phases (introduction of partial derivatives). This important work on the theory of phase equilibria was published in the period 1873 to 1878 in an almost unknown journal Transaction of Connecticut Academy and its insufficient publicity was fortunately compensated by the proper recognition of renowned scientists [135,146-151], such as Maxwell, Duhem, Ostwald or Le Chatelier, also mentioning the Dutch school of thermodynamics, that must be particularly credited with the broader application attempts aimed at the problems of general chemistry and technology. 

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