Mixtures, thermodynamic fundamental

Thermodynamic Fundamentals of Mixtures 2.1.3.3.1 Equilibria, ideal - nonideal... 

It is perhaps surprising that thermodynamics can tell us anything about chemical reactions, for when we encounter a reaction, we naturally think of rates, and we know that thermodynamics cannot be applied to problems posed by reaction rates or mechanisms. However, a chemical reaction is a change, so whenever the initial and final states of a reaction process are well-defined, differences in thermodynamic state functions can be evaluated, just as they can be evaluated for other kinds of processes. In particular, the laws of thermodynamics impose limitations on the directions and magnitudes (extents) of reactions, just as they impose limitations on other processes. For example, thermodynamics can tell us the direction of a proposed reaction it can tell us what the equilibrium composition of a reaction mixture should be and it can help us decide how to adjust operating variables to improve the yields of desired products. These kinds of issues can be addressed using equations derived in this and the next section moreover, these equations are derived without introducing any new thermodynamic fundamentals or assumptions. 

The thermodynamic fundamentals of rectification are best explained by considering binary mixtures first. 

For future reference, note that the term 7i(x3/3)ln (X3/3) in Eq. (5.4.22b) represents the negentropy of trimers assembled from n ebbs. This identification follows from a comparison with Eq. (2.5.10) for the entropy of mixtures more fundamentally, it is the standard formulation for the entropy of X3/3 units provided by statistical thermodynamics, as shown in Chapter 10. As a result, the remaining term G3 in Eq. (5.4.22b) is equivalent to the enthalpy for nl3 trimers generated from n ebb units. On multiplying by three, one obtains the molar enthalpy of trimers = 3m, a result used later. 

Pyrotechnics is based on the estabflshed principles of thermochemistry and the more general science of thermodynamics. There has been Httle work done on the kinetics of pyrotechnic reactions, largely due to the numerous chemical and nonchemical factors that affect the bum rate of a pyrotechnic mixture. Information on the fundamentals of pyrotechnics have been pubflshed in Russian (1) and English (2—6). Thermochemical data that ate useful in determining the energy outputs anticipated from pyrotechnic mixtures are contained in general chemical handbooks and more specialized pubHcations (7-9). 

Chromatographic separations rely on fundamental differences in the affinity of the components of a mixture for the phases of a chromatographic system. Thus chromatographic parameters contain information on the fundamental quantities describing these interactions and these parameters may be used to deduce stabiUty constants, vapor pressures, and other thermodynamic data appropriate to the processes occurring in the chromatograph. 

The phase rule specifies the number of intensive properties of a system that must be set to estabUsh all other intensive properties at fixed values (3), without providing information about how to calculate values for these properties. The field of appHed engineering thermodynamics has grown out of the need to assign numerical values to thermodynamic properties within the constraints of the phase rule and fundamental laws. In the engineering disciplines there is a particular demand for physical properties, both for pure fluids and mixtures, and for phase equiUbrium data (4,5). 

Perhaps the most significant of the partial molar properties, because of its appHcation to equiHbrium thermodynamics, is the chemical potential, ]1. This fundamental property, and related properties such as fugacity and activity, are essential to mathematical solutions of phase equihbrium problems. The natural logarithm of the Hquid-phase activity coefficient, Iny, is also defined as a partial molar quantity. For Hquid mixtures, the activity coefficient, y, describes nonideal Hquid-phase behavior. 

The use of visible and UV spectrometry for quantitative analysis by comparing the absorbance of standards and samples at a selected wavelength is one of the most widespread of all analytical techniques. It is also one of the most sensitive. The analysis of mixtures of two or more components is facilitated by the additivity of absorbances. This has been discussed earlier (p. 356). Other applications include measurement of the absorption of complexes as a function of solution conditions or time to establish their composition, and to determine thermodynamic and kinetic stability for analytical purposes or for more fundamental studies. 

LS measurements on binary liquid mixtures have been directed primarily as a means of obtaining fundamental thermodynamic information such as chemical potentials and the excess mixing functions. Although molecular weights could in fact be derived from some published data, this has largely not been done by the authors, since such an exercise on substances of known molecular weight would have been subsidiary to the main purpose of their studies. 

In the previous chapters, the fundamental areas of thermodynamics and chemical kinetics were reviewed. These areas provide the background for the study of very fast reacting systems, termed explosions. In order for flames (deflagrations) or detonations to propagate, the reaction kinetics must be fast—that is, the mixture must be explosive. 

It is also quite reasonable to treat a reactive medium as a two-component material.140,141 The initial state of the reactive mixture is a low-viscosity liquid, which passes into a uniform solid material as a result of chemical reactions. The ratio of solid-to-liquid components is determined by the degree of chemical conversion. This ratio is an important property of a reactive mixture, and can range from 0 to 1. The fundamental characteristic of such a two-component material is its specific free energy. This thermodynamic function is assumed to be the sum of the free energies of both components calculated from the degree of conversion ... 

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