Excess properties entropy

T, may become positive or negative, depending on the particular interface in question. Other surface excess properties, such as the surface internal energy and surface entropy, are defined similarly ... 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

The main excess properties are the free energy gE, enthalpy hB, entropy sE, and volume v (per molecule) data on other excess properties (specific heat, thermal expansion or compressibility) are rather scarce. In most cases gE, hE, sE, and vE have been determined at low pressures (<1 atm) so that for practical calculations p may be equated to zero their theoretical expressions deduced from Eqs. (33) and (34) are then as follows ... 

Peculiarities of liquid-mixture behavior are dramatically revealed in the excess properties. Those of primary interest are G , H, and. The excess Gibbs energy comes from experiment tluough reduction of vaporAiquid equilibrium data, and is detenuinedby mixing experiments (Chap. 12). The excess entropy is not measured directly, but is found from... 

All other thermodynamic relations can be written with excess quantities in this manner, simply substituting the excess property for the usual variable. As with all thermodynamic variables, this permits us to completely determine all excess properties simply by measuring a necessary minimum number of properties. Therefore if excess volumes, free energies, and enthalpies are known for a solution at different temperatures and compositions, then all other properties can be calculated for a range of T, P, and composition. Similarly, if we have measured excess free energies over a range of temperatures, it is not necessary to measure the excess entropy it is already known from... 

Excess properties are just anotlier way of representing the activity coefficient and are used because they tend to simplify notation. We now derive the relationships between the activity coefficient and excess free energy, enthalpy, entropy, and volume. 

The Margules equations such as those in Table 15.1 can be fitted by standard least-squares regression analysis to data for real solutions. For example, if data for the total free energy of a binary asymmetric solution is available over a range of compositions at different T and P, you could fit equation (15.41) for Greai (or the equation for in Table 15.1) and obtain Wq, and ITcj as regression parameters. The same could be done with the equations for excess enthalpy, entropy, and so on. This permits construction of phase diagrams and determination of thermodynamic properties based... 

Most of the excess properties are available experimentally. While the g -values can be obtained from VLE measurements (see Example 5.3), the excess enthalpies are obtained from calorimetric and the excess volumes from density measurements. When the excess properties mentioned before are known, other excess properties, for example the excess entropy s, can directly be derived, as shown in the next example. 

The different equations are represented in detail in the literature. To derive a reliable g - resp. activity coefficient model using Eq. (4.85) the different excess properties (h . s, v ) should be taken into account Flory [16] and Huggins [17,18] independently derived an expression for g starting from the excess entropy... 

Definitions of excess properties of entropy, volume, and enthalpy in terms of the excess Gibbs energy are... 

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 scope of the present work remains essentially that of Special Publication 454, The general aim 1 to assist the reader in locating those publications which contain thermochemical data which can best serve his needs. Equilibrium data Is taken in its most general sense and includes equilibrium constants, enthalpies, entropies, heat capacities, volumes, and partial molar and excess property data. To a much lesser extent, transport and other properties have been included. Unfortunately, much of the data on biochemical systems is scattered throughout much of the literature and there is a need for... 

We have seen that when two pure liquids mix to form an ideal liqiud mixture at the same T and p, the total volume and internal energy do not change. A simple molecular model of a binary liquid mixture will elucidate the energetic molecular properties that are consistent with this macroscopic behavior. The model assumes the excess molar entropy, but not necessarily the excess molar internal energy, is zero. The model is of the type sometimes called the qmsicrystalline lattice model, and the mixture it describes is sometimes called a simple mixture. Of course, a molecular model like this is outside the realm of classical thermodynamics. 

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