Thermodynamic properties Gibbs energy

Explain why it is convenient to use the thermodynamic property Gibbs energy to determine pure species phase equilibrium. Discuss the balance between energetic and entropic effects at equilibrium. 

A. As we have just learned, the thermodynamic property Gibbs energy, g, characterizes the trade-off between enthalpy and entropy and teUs us which phase is more stable. Hence, we need to calculate the difference in Gibbs energy between the protein s... 

So far, we have examined specific cases to illustrate the effect of kinetics vs. thermodynamics upon reacting systems (butadiene) and how the thermodynamic property Gibbs energy allows us to calculate equilibrium compositions by quantifying the trade-off between energy and entropy (HCl). We now wish to develop a general approach so that we can analyze the chemical reaction equilibria for any system of interest. 

It turns out that as far as the thermodynamic calculations go, we do not need to pick the actual reactions that the real system undergoes we are free to choose any set of independent reactions we can think up. As we have seen many times, hypothetical paths can often be convenient for calculating thermodynamic properties. Since the chemical reaction equilibria calculation is based on a thermodynamic property—Gibbs energy— it should not surprise us that it does not depend on the specific reaction path used. 

For many species, thermochemical properties (Gibbs energy and enthalpy of formation, heat capacity) can be found in the NIST Chemistry Webbook [5]. A good written source, especially for small molecules, is the JANAF Tables [30]. The NBS Tables of Chemical Thermodynamic Properties... 

In thermodynamics, the Gibbs energy is a very important property, especially for the description of phase equilibria. To apply the Gibbs-Duhem equation to the Gibbs energy as a function of temperature, pressure, and composition G =f(T, P, Hi..., rin, its total differential is set up as... 

Keywords Aqueous systems bibliography biochemical systems enthalpy data entropy data equilibrium data excess properties Gibbs energy data heat capacHy data partial molar properties review articles thermochemistry thermodynamics. 

The thermodynamic data, Gibbs energies, enthalpies and entropies of formation of intermetallic compounds have been obtained from a literature search. We have also consulted the handbook Selected values of thermodynamic properties of binary alloys by Hultgren et al. (1973a) and a compilation of thermodynamic data on transition metal based alloys done by de Boer et al. in 1988. For the actinide-based alloys a literature search and a critical analysis of the data was done by Rand and Kubaschewski (1963) for uranium compounds, by Rand et al. (1966) for plutonium alloys, by Rand et al. (1975) for thorium alloys, and more recently by Chiotti et al. (1981) for binary actinide alloys. We have included in our review the data obtained from the original publications and also the assessed data of Chiotti et al. (1981) when they were different. 

Calculate the values of the thermodynamic properties, Gibbs free energy, enthalpy and entropy of micellization, for the following surfactants from the information below for T = 298 K. 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

The residual Gibbs energy and the fugacity coefficient are useful where experimental PVT data can be adequately correlated by equations of state. Indeed, if convenient treatment or all fluids by means of equations of state were possible, the thermodynamic-property relations already presented would suffice. However, liquid solutions are often more easily dealt with through properties that measure their deviations from ideal solution behavior, not from ideal gas behavior. Thus, the mathematical formahsm of excess properties is analogous to that of the residual properties. 

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

Thermodynamics gives limited information on each of the three coefficients which appear on the right-hand side of Eq. (1). The first term can be related to the partial molar enthalpy and the second to the partial molar volume the third term cannot be expressed in terms of any fundamental thermodynamic property, but it can be conveniently related to the excess Gibbs energy which, in turn, can be described by a solution model. For a complete description of phase behavior we must say something about each of these three coefficients for each component, in every phase. In high-pressure work, it is important to give particular attention to the second coefficient, which tells us how phase behavior is affected by pressure. 

R. C. Pemberton and C. J. Mash. "Thermodynamic Properties of Aqueous Non-Electrolyte Mixtures II. Vapour Pressures and Excess Gibbs Energies for Water-)- Ethanol at 303.15 to... 

What Are the Key Ideas Equilibrium between two phases is reached when the rates of conversion between the two phases are the same in each direction. The rates are equal when the molar Gibbs free energy of the substance is the same in each phase and therefore there is no tendency to change in either direction. The same concepts apply to the dissolving of a solute. The presence of a solute alters the entropy of a solvent and consequently affects its thermodynamic properties. 

Because osmosis is a thermodynamic property, we can expect it to be related to the effect of the solute on the enthalpy and entropy of the solution solvent flows until the molar Gibbs free energy of the solvent is the same on each side of the membrane We have already seen several times that a solute lowers the molar Gibbs free energy of the solution below that of the pure solvent, and solvent therefore has a tendency to pass into the solution (Fig. 8.33). 

Information on the thermodynamic properties (complexation constants, enthalpies of complexation, Gibbs energy of formation, and their relationships with structural and spectroscopic parameters) can be found in refs. 12, 23, and 24. 

In open systems consisting of several components the thermodynamic properties of each component depend on the overall composition in addition to T and p. Chemical thermodynamics in such systems relies on the partial molar properties of the components. The partial molar Gibbs energy at constantp, Tand rij (eq. 1.77) has been given a special name due to its great importance the chemical potential. The corresponding partial molar enthalpy, entropy and volume under the same conditions are defined as... 

Figure 3.3 Thermodynamic properties of an arbitrary ideal solution A-B at 1000 K. (a) The Gibbs energy, enthalpy and entropy, (b) The entropy of mixing and the partial entropy of mixing of component A. (c) The Gibbs energy of mixing and the partial Gibbs energy of mixing of component A.

The formalism shown above is in general easily extended to multi-component systems. All thermodynamic mixing properties may be derived from the integral Gibbs energy of mixing, which in general is expressed as... 

This type of defect equilibrium treatment has been used extensively to model the defect chemistry and non-stoichiometry of inorganic substances and has the great advantage that it easily takes several simultaneous defect equilibria into account [22], On the other hand, the way the mass action laws are normally used they are focused on partial thermodynamic properties and not on the integral Gibbs energy. The latter is often preferred in other types of thermodynamic analyses. In such cases the following solid solution approach is an alternative. 

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