Standard thermodynamic functions

Since calcium carbonate and calcium oxide are pure phases iCcacOg == cao = 1 and (7.44) reduces to 

Two cases may arise. If the reaction is studied in the presence of a gas other than CO2 e.g. in air, then the equilibrium condition 4 = 0 gives  

We have already seen that the thermodynamic properties of a system are defined uniquely when we know the chemical potentials of the c components as a function of the independent variables T, p, Ui. .. n. In the particular case of an ideal system the chemical potentials are given by (7.1). 

We notice that the chemical potential may be written as the sum of two functions, the first of which pf (T, p) is a function of T and p only, while the second RT In depends upon the composition. 

In general an intensive thermodynamic quantity P in a uniform system  

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First, we shall explore a conceptual relation between kinetics and thermodynamics that allows one to draw certain conclusions about the kinetics of the reverse reaction, even when it has itself not been studied. Second, we shall show how the thermodynamic state functions for the transition state can be defined from kinetic data. These are the previously mentioned activation parameters. If their values for the reaction in one direction have been determined, then the values in the other can be calculated from them as well as the standard thermodynamic functions. The implications of this calculation will be explored. Third, we shall consider a fundamental principle that requires that the... 

Table 4.4 Standard thermodynamic functions of isomers in the ideal-gas...

By applying standard thermodynamic functions to the equilibrium, an expression for the rate constant in terms of AG, AH and AS can be given ... 

The standard thermodynamic functions of solvation defined as above indicated by superscript differ from the generally tabulated standard thermodynamic functions indicated by superscript0 due to the constraints of fixed positions. They therefore lack the changes in the translational degrees of freedom, due to the compression from the volume of the gaseous state to that in the solution, not relevant to the solvation of the solute. Thus, AH = AH0 + RT (1 - ap7), where ap is the isobaric expansibility of the solvent, AS = AS0 + R( - ap7), AV = AV° - (RT/P°) -1 + ktP°), where kt is the isothermal compressibility of the solvent, and so on. 

In calculations of thermodynamic functions, q is calculated at the appropriate temperature and volume. For example, for standard thermodynamic functions at 298 K, q is calculated at 298 K and 24.7 L. 

The analogous problem of determining changes in the standard thermodynamic functions associated with the ionization of weak acids from the relation between the equilibrium constant (K) and the temperature has received further attention within the last two years. Ives and Mardsen (1965) have expressed In A as a fonction of several orthogonal polynomials of the temperature. Their method has several advantages but... 

The calculated standard thermodynamic functions for carbonyl difluoride, Cj, S, (G - HjgjVT, (H - W gg), AHf, Gf and log,g(Xf), are listed in Table 13.9 for the extended temperature range 0-6000 K in the ideal gas state [359aa], and are illustrated over the more normal working temperature range [359aa] in Fig. 13.2. Earlier values for these thermodynamic properties have now been superseded [1171,1280,1360c,1587,1972,1973]. 

Kosmuiski, M., Matysiak, J., and Szczypa. J., Solvent effects on standard thermodynamic functions of surface dissociation of oxides, J. Colloid Interf. Sci., 164, 280, 1994. 

Table A-29 Standard thermodynamic functions of the aqueous species. ...

In the first case, the threshold equals the bond energy, D(AX —X). In the second case, the threshold equals the differences in the product and reactant heats of formation such that Z)(yf+ — B) = D BC) — Eq. When the threshold analysis is performed using Eq. (2), all sources of reactant energy are included, such that the bond energies so determined correspond to thermodynamic values at OK (Dalleska et al., 1993 Armentrout and Kickel, 1996). Conversion to 298-K values can be achieved using standard thermodynamic functions. In this work, 298-K heats of formation for ions are reported using the thermal electron convention. Values fi om the literature that use the stationary electron convention should be increased by 0.064 eV for comparison to these values. 

Note that all these abovementioned expressions for the standard affinity and the standard thermodynamic functions of micellisation were based on the definition of the CMC as an inflection point in the dependence ai(ctoti) given by Eqs. (5.53) and (5.54). If we use other definitions of the CMC, the corresponding relations will be different. 

The calculated standard thermodynamic functions according to this equation are in a reasonable agreement with experimental data. Moreover, the authors [14] used the quasichemical approach... 

The Gibbs free energies are calculated using standard thermodynamic tables which are easily usable by machine since they give the data in the form of polynomial coefficients. The data are sometimes limited to 6000 K and it is therefore necessary to make extrapolations or to carry out calculations of partition functions from spectroscopic data In the latter case, which is certainly more reliable, one can determine standard thermodynamic functions with the aid of the classical formulae of statistical thermodynamics. The results may then be fitted to polynomials so that they match the tabulated data . Furthermore the calculation of partition functions is necessary for spectroscopic diagnostics and for the calculations of reaction rate parameters. 

The choice of the appropriate concentration scale for standard thermodynamic functions of transfer was extensively discussed by Ben-Naim who showed that the molarity scale has a number of advantages over the others. 

Whereas in that field it is (or was) possible to foresee the time when tables of standard thermodynamic functions would be complete, and be kept up to date as new substances were prepared, in the field of thermodynamic properties of mixtures it is scarcely possible even to contemplate our ever having a reasonably complete set of properties even for mixtures of only two substances. 

Both kinds of quantity are needed if the yield of a chemical reaction is to be calculated under any particular conditons. Standard thermodynamic functions lead to standard equilibrium constants. Except at infinite dilution for gases or solutions, a condition of little importance in chemical industry, the properties of real mixtures are needed to calculate the yield from the standard equilibrium constant. No Haber-process chemist would keep his job for long who calculated the yield at 50 or 100 MPa from the standard equilibrium constant. Nor do we have even for mixtures of nitrogen + hydrogen + ammonia measured values of the properties needed. 

FIGURE 9.7 Experimental (symbols) and fitted (lines) results for Henry s constants (H21) for Hydrogen sulfide (2) in water (1) from Equation 9.37 through Equation 9.41. (Reprinted with permission from A. Plyasunov, J. P. O Connell, R. H. Wood, and E. L. Shock, 2000, Infinite Dilution Partial Molar Properties of Aqueous Solutions of Nonelectrolytes. II. Equations for the Standard Thermodynamic Functions of Hydration of Volatile Nonelectrolytes over Wide Ranges of Conditions Including Subcritical Temperatures, Geochimica Et Cosmochimica Acta, 64, 2779, With permission from Elsevier.)... 

Plyasunov, A. V., J. P. O Connell, and R. H. Wood. 2000. Infinite dilution partial molar properties of aqueous solutions of nonelectrolytes. I. Equations for partial molar volumes at infinite dilution and standard thermodynamic functions of hydration of volatile nonelectrolytes over wide ranges of conditions. Geochimica et Cosmochimica Acta. 64,495. 

A comment This was quite a problem, wasn t it If you understand most of the steps we went through you should feel confident about the questions, riddles - and real-life problems - involving concentrations, equilibrium constants, and standard thermodynamic functions, G, H, S of chemical reactions. And this is probably the major area of physical chemistry. I am proud of you - you have been a good companion on a long and difficult journey. Now I would like to see you becoming more of a guide than a tourist on this journey. 

The standard thermodynamic functions of dissolution and excess functions are connected by the equation ... 

TABLE XII. Standard Thermodynamic Functions Expressed in kcal/mole for Micellization of NaTC and NaTDC in Water at Three Temperatures (44)... 

Phase equilibria, particularly the solubility of sparingly soluble ionic solids can be calculated if the standard thermodynamic functions for aqueous species, the constants of... 

The results of measurements and calculations of these kinds are made available in thermodynamic tables. Such thermodynamic tables can conveniently be divided into two classes. Primary thermodynamic tables contain values of the standard equilibrium constant K (T), which depends only on thermodynamic temperature r, or of other standard thermodynamic functions from which these can be calculated, and when is given for only one value of T (commonly 298.15 K), of standard thermodynamic functions which can be used to estimate it at other values of T. The yield of a reaction under specified conditions can be calculated from the standard equilibrium constant only when the specified conditions are such that... 

The quantities listed in primary thermodynamic tables are the standard thermodynamic functions of substances, and sums and differences of these, leading to the standard equilibrium constants of chemical reactions. 

The definition of a standard ( ) thermodynamic function of a substance B often involves an arbitrarily chosen standard value p of pressure and an arbitrarily chosen standard value of molality.f The value assigned to p (usually, though not necessarily, 101.325 kPa) and the value assigned to (usually, though not necessarily, 1 mol kg ) must be specified. ... 

Values having been specified where necessary for and m , the standard chemical potential / of a substance B, and hence any other standard thermodynamic function of the substance B, depends only on the thermodynamic temperature T. The definition of the standard chemical potential Pb of ia substance B is given for a component of a gas mixture in Section 4, for a component of a liquid or solid (one-phase) mixture in Section 5, and for a solute in a solution and for the solvent (which may be a mixed one) in Section 6.t... 

Once the standard chemical potential fif has been defined, formulae follow for all the other standard thermodynamic functions obtained by differentiation of ju, with respect to temperature. In particular,... 

The standard thermodynamic functions of a substance are often described as relating to the substance in its standard state. Any difficulties associated with a verbal description of such a standard state disappear when an algebraic definition of the standard chemical potential is given. 

Standard Thermodynamic Functions of a Substance in a Liquid or Solid Mixture... 

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