Property excess

Refs. 208 and 209 hot—wet properties and light stabiUty inferior to nylon-6 and nylon-6,6. Refs. 209 and 210 excessive property loss when wet. 

Liquid solutions are often most easily dealt with through properties that measure their deviations, not from ideal gas behavior, but from ideal solution behavior. Thus the mathematical formaUsm of excess properties is analogous to that of the residual properties. 

If M represents the molar value of any extensive thermodynamic property, an excess property is defined as the difference between the actual property value of a solution and the value it would have as an ideal solution at the same temperature, pressure, and composition. Thus,... 

Excess properties have no meaning for pure species, but for species in solution. 

This is the fundamental excess property relation, analogous to the fundamental residual property relation (eq. 169). 

Whereas the fundamental residual property relation derives its usefulness from its direct relation to experimental PVT data and equations of state, the excess property formulation is useful because and are all experimentally accessible. Activity coefficients are found from vapor—Hquid... 

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. 

This definition is analogous to the definition of a residual property as given by Eq. (4-67). However, excess properties have no meaning for pure species, whereas residual properties exist for pure species as well as for mixtures. In addition, analogous to Eq. (4-99) is the partial-property relation,... 

All three quantities are for the same T, P, and physical state. Eq. (4-126) defines a partial molar property change of mixing, and Eq. (4-125) is the summability relation for these properties. Each of Eqs. (4-93) through (4-96) is an expression for an ideal solution property, and each may be combined with the defining equation for an excess property (Eq. [4-99]), yielding ... 

Property changes of mixing and excess properties find greatest application in the description of hqnid mixtures at low reduced tempera-... 

The heat of mixing (excess enthalpy) and the excess Gibbs energy are also experimentally accessible, the heat of mixing by direcl measurement and G (or In Yi) indirectly as a prodiicl of the reduction of vapor/hqiiid eqiiihbriiim data. Knowledge of H and G allows calculation of by Eq. (4-13) written for excess properties. 

Figure 4-2 displays plots of AH, AS, and AG as functions of composition for 6 binary solutions at 50°C. The corresponding excess properties are shown in Fig. 4-3 the activity coefficients, derived from Eq. (4-119), appear in Fig. 4-4. The properties shown here are insensitive to pressnre, and for practical pnrposes represent sohition properties at 50°C (122°F) and low pressnre (P 1 bar [14.5 psi]).

In principle, equation-of-state procedures can be used for the calculation of hquid-phase as well as gas-phase properties, and much has been acconmlished in the development of PVT equations of state suitable for both phases. However, a widely used alternative for the hquid phase is application of excess properties. 

A vast store of liquid-phase excess-property data for binary systems at temperatures near 30°C and somewhat higher is available in the literature. Effective use of these data to extend correlations to higher... 

Vanderzee, C. E. and W. W. Rodenburg, 1970, Gas Imperfections and Thermodynamic Excess Properties of Gaseous Hydrogen Fluoride, Journal of Chemical Thermodynamics, Vol. 2, pp. 461-478,. 

D. A. Palmer and B. D. Smith, Thermodynamic Excess Property Measurements for Acetonitrile-Benzene-n-Heptane System at 45 C". J. Client. Eng. Data, 17. 71-76 (1972). 

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 ... 

It follows that the surface excess properties are macroscopic parameters only. 

In the derivation of the regular solution model the vibrational contribution to the excess properties has been neglected. However, as a first approximation the vibrational contribution can be taken as independent of the interaction between the different atoms, and this contribution can be factored out of the exponential and taken into account explicitly. The partition function of the solution is then given as... 

Evolved gas analysis (ega), 14 234 Ewens-Bassett numbers, 17 391, 392 Examiners citations, 18 237, 238 Exanta, 4 100t, 102 Excess properties, ideal mixture and,... 

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 ... 

In order to calculate explicitly the excess properties of a mixture A + B from the formulas of Section II, we need the values of the six quantities ... 

It has been stressed in Section I that it is essentially these four parameters d, p, 0, and a which determine the values of the excess properties of the mixture A + B should all these parameters be equal to zero then all excess functions vanish. 

In the following sections we shall discuss some of the excess properties of the following mixtures ... 

The situation is quite different for the excess properties of one particular mixture A + B, where it is now — ( bb/ aa) 1 and p = (r B/r A) — 1 which are required (and not simply bb/ aa and Tbb/ aa) it is essential here to get values which are as accurate as possible for these quantities. We shall therefore deduce 8 and p (or alternatively bb/ aa and bbAaa) from different source data, see how far these values agree with each other, and finally select from them an average value. The following experimental data were used ... 

This latter expression allows us to compute all the excess properties of dilute electrolytic solutions for instance, the excess osmotic pressure is determined by Eq. (138). The most remarkable result is of course that all these thermodynamic properties are non-anaiytic functions of the concentration ... 

---