Thermodynamic functions for

A thermodynamic function for systems at constant temperature and pressure that indicates whether or not a reaction is favorable (AG < 0), unfavorable (AG > 0), or at equilibrium (AG = 0). 

Table 19.1 Stability constants and thermodynamic functions for some complexes of Cd at 25°C...

P10.5 The thermodynamic functions for solid, liquid, and gaseous carbonyl chloride (COCL) obtained from Third Law and statistical calculations... 

Vapor pressures and vapor compositions in equilibrium with a hypostoichiometric plutonium dioxide condensed phase have been calculated for the temperature range 1500 I H 4000 K. Thermodynamic functions for the condensed phase and for each of the gaseous species were combined with an oxygen-potential model, which we extended from the solid into the liquid region to obtain the partial pressures of O2, 0, Pu, PuO and Pu02 as functions of temperature and of condensed phase composition. The calculated oxygen pressures increase rapidly as stoichiometry is approached. At least part of this increase is a consequence of the exclusion of Pu +... 

The process we have followed Is Identical with the one we used previously for the uranium/oxygen (U/0) system (1-2) and Is summarized by the procedure that Is shown In Figure 1. Thermodynamic functions for the gas-phase molecules were obtained previously (3) from experimental spectroscopic data and estimates of molecular parameters. The functions for the condensed phase have been calculated from an assessment of the available data, Including the heat capacity as a function of temperature (4). The oxygen potential Is found from extension Into the liquid phase of a model that was derived for the solid phase. Thus, we have all the Information needed to apply the procedure outlined In Figure 1. 

Thermodynamic Functions of the Condensed Phases. Tabulated thermodynamic functions for the condensed phases of plutonium dioxide and a detailed description of their calculation are given elsewhere (21). The AG (Pu02 c) is represented by the equation given in Table I. The AGf values were calculated using standard thermodynamic relations and the data given below. 

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

In summary, Eq. (86) is a general expression for the number of particles in a given quantum state. If t = 1, this result is appropriate to Fenni-rDirac statistics, or to Bose-Einstein statistics, respectively. However, if i is equated torero, the result corresponds to the Maxwell -Boltzmann distribution. In many cases the last is a good approximation to quantum systems, which is furthermore, a correct description of classical ones - those in which the energy levels fotm a continuum. From these results the partition functions can be calculated, leading to expressions for the various thermodynamic functions for a given system. In many cases these values, as obtained from spectroscopic observations, are more accurate than those obtained by direct thermodynamic measurements. 

TABLE 10.6 Thermodynamic Functions for Reversible Attachment-Detachment Reactions in Hydrocarbon Liquids... 

Thermodynamic Functions for the Formation of Hydrolyzed Beryllium(II) Species ... 

Fig. 11. Thermodynamic functions for the formation of hydroxospecies as a function of the number of contained hydroxide groups (—) least-squares regression. Reproduced with permission from Ref. (85). Copyright 1998, Wiley-VCH Veriag GmbH.

Pa being the total pressure of the solvent in the reaction chamber. Values for AHn-i, n, and ASZ-i, . can eventually be obtained from the temperature dependence of AG%-, n- Known values for the individual steps (n — 1, n) can be combined to give the thermodynamic functions for any reaction (m,n). The total build-up of a solvated complex, characterized by m = 0, is of particular interest and corresponds to Eq. (38). 

It is this last characteristic that is used most frequently in testing thermodynamic functions for exactness. If the differential li/ of a thermodynamic quantity J is exact, then J is called a thermodynamic property or a state function. 

An alternative approach that is particularly applicable to binary solutions of nonelectrolytes is that of excess thermodynamic functions for the solution instead of activities for the components. That approach is most useful in treatments of phase equihbria and separation processes [1], and it will be discussed in Section 16.7. 

Therefore, the physical meaning of the solubility curve of a surfactant is different from that of ordinary substances. Above the critical micelle concentration the thermodynamic functions, for example, the partial molar free energy, the activity, the enthalpy, remain more or less constant. For that reason, micelle formation can be considered as the formation of a new phase. Therefore, the Krafft Point depends on a complicated three phase equilibrium. 

The development of other methods with less computing requirements and free of such limitations seems to be necessary in order to understand better the processes that take place in the liquid phase, understand their molecular mechanism, predict the influence of various factors on their equilibria and kinetics, and evaluate correctly the thermodynamic functions for the whole process and its particular steps. 

Table 9 Thermodynamic functions for 1,2,4-trioxolane calculated from experimental structural parameters.

More recently, Pound and co-workers compared both the classical theory and their own modified proposal to the exact results obtained by a Monte-Carlo simulation study of small clusters [65] thermodynamic functions for such clusters (size from 13 to 87 entities) were calculated, showing a better agreement between the Monte-Carlo calculations and the authors theory. 

Excess thermodynamic functions for four mixtures with increasingly negative HB, (References in the text.)... 

We will now present some of the results of the recent Monte Carlo computations of the chain partition function and the related thermodynamic functions for some three-dimensional lattices performed recently by McCrackin and Mazur.2... 

The recognition that AH - T AS = 0 for a system at equilibrium led J. W. Gibbs to realize that the proper thermodynamic function for determining the spontaneity of a reaction is what is now known as the Gibbs energy or Gibbs function G (Eq. 6-14). 

Binding Constants of Protons to Dianions of Dicarboxylic Acids Thermodynamic Functions for Oxygenation of Hemoglobin A Few Well-Known Structural Domains... 

The transformation can be influenced by an applied stress. As seen in Fig. 24.13, the stress-free transformation to martensite results in a decrease in specimen length. Data in Figs. 24.14 and 24.15 were obtained by applying a series of constant uniaxial stresses at constant ambient pressure, P. The data show that the transformation temperature increases approximately linearly with applied uniaxial compressive stress. This dependence of transformation temperature on stress state follows from minimization of the appropriate thermodynamic function. For a material under... 

Soptrajanov142 calculated thermodynamic functions for oxadiazole over the range 298.16-1000° K, based on the infrared spectral assignments of Zecchina and co-workers,143 with which he agreed ex-... 

Thermodynamics. By correlating thermochemical and electrochemical data for liquid ammonia, it has been possible to estimate thermodynamic functions for a wide variety of ionic species in liquid ammonia at 25 ° C. (22,24). The heats and free energies of formation and entropies (relative to H+) for a few species are given in Table I. These values have been calculated from the data of references 6,19, 20, and 24. 

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