General Thermodynamic Correlations

Lee, B. I. and Kesler, M. G. (1975) AIChemEJL 21, 510. A generalized thermodynamic correlation based on three-parameter corresponding states. 

The Lee/Kesler tables are adapted and published by permission from "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States," by Byungik Lee and Michael G. Kesler, AIChE J.,21,510-527 (1975). The numbers printed in italic type are liquid-phase properties. 

The PvT behavior of a pure substance can be described by so-called equations of state (EOS). In general, an equation of state is a relationship between P. v, and T. They can be formulated in diflferent ways, for example, volume-explicit (v=f(T,P)) or, most commonly, pressure-explicit (P = /(T, v)). An equation of state combined with the general thermodynamic correlations offers the possibility to calculate all thermodynamic properties of the substance. The simplest equation of state for describing the PvT behavior of gases is the ideal gas law ... 

Mathematical Consistency Requirements. Theoretical equations provide a method by which a data set s internal consistency can be tested or missing data can be derived from known values of related properties. The abiUty of data to fit a proven model may also provide insight into whether that data behaves correctiy and follows expected trends. For example, poor fit of vapor pressure versus temperature data to a generally accepted correlating equation could indicate systematic data error or bias. A simple sermlogarithmic form, (eg, the Antoine equation, eq. 8), has been shown to apply to most organic Hquids, so substantial deviation from this model might indicate a problem. Many other simple thermodynamics relations can provide useful data tests (1—5,18,21). 

GENERAL CHEMISTRY, Linus Pauling. Revised 3rd edition of classic first-year text by Nobel laureate. Atomic and molecular structure, quantum mechanics, statistical mechanics, thermodynamics correlated with descriptive chemistry. Problems. 992pp. 54 x 84. 65622-5 Pa. 18.95... 

Figure 3.17 Generalized density correlation for liquids. (Bated on A. L Lydersen, R. A Greenkom, and O. A Hougen, Generalized Thermodynamic Properties of Pure Fluids, Univ. Wisconsin, Eng. Expt. Sta. Rept. 4, 1955.)...

Throughout this book, we have seen that when more than one species is involved in a process or when energy balances are required, several balance equations must be derived and solved simultaneously. For steady-state systems the equations are algebraic, but when the systems are transient, simultaneous differential equations must be solved. For the simplest systems, analytical solutions may be obtained by hand, but more commonly numerical solutions are required. Software packages that solve general systems of ordinary differential equations— such as Mathematica , Maple , Matlab , TK-Solver , Polymath , and EZ-Solve —are readily obtained for most computers. Other software packages have been designed specifically to simulate transient chemical processes. Some of these dynamic process simulators run in conjunction with the steady-state flowsheet simulators mentioned in Chapter 10 (e.g.. SPEEDUP, which runs with Aspen Plus, and a dynamic component of HYSYS ) and so have access to physical property databases and thermodynamic correlations. 

Using the general thermodynamical relations expressing the enthalpy H and the volume Fas a function of the free enthalpy G, H = d([iG)/d[i and V — dG/dP, one can deduce the following informations from the correlation time. At constant pressure, the slope of lnxc as a function of /i = 1 //cBT is the activation enthalpy. Similarly, at constant temperature, a study as a function of pressure gives the activation volume as A Fa — knTdln(xc)/dP. A more complete discussion may be found in ref. 88. 

From the results summarized in Table I, apparently the Brpnsted relationship will hold for all combinations of nucleophiles and electrophiles. Because, as pointed out previously, the Hammett equation is really a special case of the Brpnsted relationship, all the legion of nucleophile-electrophile, rate-equilibrium Hammett correlations that have been studied also fall under the scope of the Brpnsted relationship. For example, nucleophilicities of ArO , ArS , ArC(CN)2 , and the other families listed in footnote c of Table I have generally been correlated by the Hammett equation, where the acidities of benzoic acids in water are used as a model for substituent interactions with the reaction site (a), and the variable parameter p is used to define the sensitivity of the rate constants to these substituent effects. The Brpnsted equation (equation 3) offers a much more precise relationship of the same kind, because this equation does not depend on an arbitrary model and allows rate and equilibrium constants to be measured in the same solvent. Furthermore, the Brpnsted relationship is also applicable to families of aliphatic bases such as carboxylate ions (GCH2C02 ), alkoxide ions (GCH20 ), and amines (GCH2NH2). In addition, other correlations of a kinetic parameter (log fc, AGf, Ea, etc.) can be included with various thermodynamic parameters (pKfl, AG°, Eox, etc.) under the Brpnsted label. 

The exponent can be related to the other exponents through a general thermodynamic theorem connecting the space integral of the correlation function to the susceptibility ... 

The ideal adsorption solution theory described in Section IVA is the simplest approach to multicomponent adsorption from the point of view of the general thermodynamic theory of the surface phase. The lAST is comparable with potential adsorption theory by predictability. Both theories need the correlation of experimental data for pure components in order to estimate adsorption of mixtures. However, in general, the predictions of the two theories are different, as illustrated in Section IVD. Let us analyze assumptions on which the two theories may become similar. 

The great generality of thermodynamics is a consequence of its minimal use of specific and detailed models on the other hand, it is the absence of such models that prevents thermodynamics from providing insight into molecular mechanisms. The combination of detailed models with the concepts of thermodynamics is called the extrathermodynamic approach. Because it involves model building, the technique lacks the rigor of thermodynamics, but it can provide information not otherwise accessible. Extrathermodynamic relationships often take the form of correlations among rates and equilibria, and the models used to account for these... 

In fluid mechanics the principles of conservation of mass, conservation of momentum, the first and second laws of thermodynamics, and empirically developed correlations are used to predict the behavior of gases and liquids at rest or in motion. The field is generally divided into fluid statics and fluid dynamics and further subdivided on the basis of compressibility. Liquids can usually be considered as incompressible, while gases are usually assumed to be compressible. 

For nonideal solutions, the thermodynamic equilibrium constant, as given by Equation (7.29), is fundamental and Ei mettc should be reconciled to it even though the exponents in Equation (7.28) may be different than the stoichiometric coefficients. As a practical matter, the equilibrium composition of nonideal solutions is usually found by running reactions to completion rather than by thermodynamic calculations, but they can also be predicted using generalized correlations. 

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