ESTIMATION OF THERMODYNAMIC QUANTITIES

In this chapter we shall review some empirical and theoretical methods of estimation of thermodynamic quantities associated with chemical transformations. 

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Standard electrode potentials of the elements and their temperature coefficients in water at 298.15 K were listed for nearly 1700 half-reactions at pH = 0.000 and pH =13.996. General and specific methods of estimation of thermodynamic quantities were described, but the original papers, from which the individual entries were derived, have not been cited. 

Mesmer, R.E., 1985, A model for estimation of thermodynamic quantities for reactions— uncertainties from such predictions Paper presented at Second International Symposium on Hydrothermal Reactions at The Pennsylvania State University. 

D. R. Stull, E. F. Westrum, Jr. and G. C. Sinke, The Chemical Thermodynamics of Organic Compounds (SWS), Krieger Publ. Co., Malabar, Florida, 1987. The first 200 pages include a review of basic thermodynamic concepts and thermochemistry, the evaluation of entropy, the estimation of thermodynamic quantities and applications to industrial problems. The bulk of the volume consists of ideal gas tables [including C , S -(G° - and logXf for 298 < T (K) < 1000] for... 

Integral equation theories of g(r) do in general yield only an approximate estimate of this quantity, and hence they are, to more or less extent, thermodynamically inconsistent. In practice, instead of Eq. (16), one prefers to apply the pressure-compressibility (P — %T) condition expressed by... 

Why should one bother with these thermodynamic quantities when the overall aim of this chapter is to determine the structure of liquids near ions The answer is the same as it would be to the generalized question What is the utility of thermodynamic quantities They are the quantities at the base of most physicochemical investigations. They are fully real, no speculations or estimates are made on the way (at least as far as the quantities for salts are concerned). Their numerical modeling is the challenge that the theoretical approaches must face. However, such theoretical approaches must assume some kind of structure in the solution and only a correct assumption is going to lead to a theoretical result that agrees with experimental results. Thus, such agreement indirectly indicates the structure of the molecules. 

The existence of the zirconium selenides ZrSe(cr), ZrSe 5(cr), ZrSe2(cr), and ZrSc3(cr) have been reported. No experimental thermodynamic data are available except for ZrSesCcr) for which the heat capacity has been measured in the temperature range 8 to 200 K [86PRO/AYA]. These temperatures are too low for a derivation of thermodynamic quantities at 298.15 K. Mills [74MIL] has estimated some thermodynamic values by comparison with the corresponding sulphides and tellurides. 

Evidently, then, there is no point in collecting the required averages to make direct estimates [Eq. (2.13)] of thermodynamic quantities in TDSMC investigation we require only, averages of the type appearing in... 

In Chapter 14, Roux and Temprado have provided a detailed survey of the many facets of thermochemistry, including the history of the subject, methods of measurement of thermodynamic quantities, calibration of instruments, estimation of accuracy and the application of correction factors. Reference materials are discussed and data bases of thermodynamic properties are described, including an introduction to computation thermochemistry. The chapter concludes with some examples of the solving of thermochemical problems. 

The usefulness of any theory is directly proportional to its ability correctly to describe systems for which no data are available. One would hope that the correlations of the data and theoretical considerations presented in previous sections would make it possible to estimate accurately thermodynamic quantities for systems which are experimentally difficult to measure. To some extent this appears to be possible. However, the systems are extremely complex and there is a wide variety of phenomena involved, which makes extrapolation of ideas to experimentally virgin areas subject to question. As mentioned previously, ionic entropies and volumes are physically more meaningful therefore, they should present the best opportunities for successful estimations. 

In addition to the ambiguities inherent to the physical concept, the determination of thermodynamic quantities such as the latent heat and the volume change at the transition is often hampered by the fact that the crystalline state of chain molecules is quite complex. The polymer crystals are usually polycrystalline and coexist with the disordered amorphous domain. An accurate estimation of the equilibrium melting temperature defined for a perfectly aligned crystal requires great effort [5,18,19]. At the melting temperature, equilibrium usually exists between the liquid and somewhat imperfect crystalline phases. 

So far in this section the practical applications of thermodynamics in chemistry and in industry have been considered, but an extremely important use of thermodynamics is in the systematic understanding of chemistry. There is of course no clear demarcation between the practical and theoretical interest of thermodynamics. Indeed, many estimation procedures designed to obtain values of thermodynamic quantities required for practical applications depend on the understanding, in depth, of chemistry. 

An example of a strong acid is hydrochloric acid, HCl, which has a pATa value, estimated from thermodynamic quantities, of-9.3 in water. The concentration of undissociated acid in a 1 mol-dm solution will be less than 0.01% of the concentrations of the products of dissociation. Hydrochloric acid is said to be "fully dissociated" in aqueous solution because the amount of undissociated acid is imperceptible. When the pATa and analytical concentration of the acid are known, the extent of dissociation and pH of a solution of a monoprotic acid can be easily calculated using an ICE table. 

Since the experimental determination of thermodynamic quantities is usually a rather tedious work, and up to now the known thermodynamic data are far from complete, it is desirable to have some semi-empirical methods for the estimation of unknown thermodynamic quantities of chemical substances. Because the thermodynamic quantities of a compound or a mixture should be related to the microscopic structure of this compound or this mixture, and the microscopic structure of this compound or this mixture can be approximately described by its atomic parameters or molecular descriptors, it is possible to estimate these thermodynamic quantities by some functions of the atomic parameters or molecular descriptors of this compound or this mixture. So we can have a semi-empirical method for the prediction of unknown thermodynamic data by transduction, i.e., to find the mathematical model describing the relationship between the thermodynamic quantities and the atomic parameters or molecular descriptors based on the SVM computation of the known data firstly, and then use this mathematical model obtained to predict the unknown thermodynamic quantities of some target substances. 

A number of methods have been described in earlier sections whereby the surface free energy or total energy could be estimated. Generally, it was necessary to assume that the surface area was known by some other means conversely, if some estimate of the specific thermodynamic quantity is available, the application may be reversed to give a surface area determination. This is true if the heat of solution of a powder (Section VII-5B), its heat of immersion (Section X-3A), or its solubility increase (Section X-2) are known. 

In order to ensure thermodynamic consistency, in almost all cases these properties are calculated from Tr. and the vapor pressure and liquid density correlation coefficients listed in those tables. This means that there will be slight differences between the values listed here and those in the DIPPR tables. Most of the differences are less than 1%, and almost all the rest are less than the estimated accuracy of the quantity in question. 

A more interesting possibility, one that has attracted much attention, is that the activation parameters may be temperature dependent. In Chapter 5 we saw that theoiy predicts that the preexponential factor contains the quantity T", where n = 5 according to collision theory, and n = 1 according to the transition state theory. In view of the uncertainty associated with estimation of the preexponential factor, it is not possible to distinguish between these theories on the basis of the observed temperature dependence, yet we have the possibility of a source of curvature. Nevertheless, the exponential term in the Arrhenius equation dominates the temperature behavior. From Eq. (6-4), we may examine this in terms either of or A//. By analogy with equilibrium thermodynamics, we write... 

From a practical point of view, it would be very desirable to have reliable rules, even if only empirical, which could provide estimates of barrier heights in the absence of experimental data. This would be of obvious use in predicting thermodynamic quantities for stable molecules and would also be most valuable in testing and applying theories of reaction rates. Furthermore, any empirical regularities observed could be helpful in the development of a theoretical treatment of barriers. 

The molecular mechanics method is usually limited to the determination of molecular geometry and thermodynamic quantities. However, it is sometimes employed to estimate vibrational frequencies - at least in those cases in which 7r electrons are not involved in the determination of the molecular geometry. It should be emphasized that this method, as well as those presented in Chapter 12, are applicable only to isolated molecules, as intermolecular forces are not included in the model. 

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