Formation, thermodynamic functions compounds

The enthalpy of formation of a compound is a so-called thermodynamic state function, which means that the value depends only on the initial and final states of the system. When the formation of crystalline NaCl from the elements is considered, it is possible to consider the process as if it occurred in a series of steps that can be summarized in a thermochemical cycle known as a Born-Haber cycle. In this cycle, the overall heat change is the same regardless of the pathway that is followed between the initial and final states. Although the rate of a reaction depends on the pathway, the enthalpy change is a function of initial and final states only, not the pathway between them. The Born-Haber cycle for the formation of sodium chloride is shown as follows ... 

As the Gibbs function is a thermodynamic property, values of AG do not depend on the intermediate chemical reactions that have been used to transform a set of reactants, under specified conditions, to a series of products. Thus, one can add known values of a Gibbs function to obtain values for reactions for which direct data are not available. The most convenient values to use are the functions for the formation of a compound in its standard state from the elements in their standard states, as given in Tables 7.2... 

Here, AH(A-B) is the partial molar net adsorption enthalpy associated with the transformation of 1 mol of the pure metal A in its standard state into the state of zero coverage on the surface of the electrode material B, ASVjbr is the difference in the vibrational entropies in the above states, n is the number of electrons involved in the electrode process, F the Faraday constant, and Am the surface of 1 mol of A as a mono layer on the electrode metal B [70]. For the calculation of the thermodynamic functions in (12), a number of models were used in [70] and calculations were performed for Ni-, Cu-, Pd-, Ag-, Pt-, and Au-electrodes and the micro components Hg, Tl, Pb, Bi, and Po, confirming the decisive influence of the choice of the electrode material on the deposition potential. For Pd and Pt, particularly large, positive values of E5o% were calculated, larger than the standard electrode potentials tabulated for these elements. This makes these electrode materials the prime choice for practical applications. An application of the same model to the superheavy elements still needs to be done, but one can anticipate that the preference for Pd and Pt will persist. The latter are metals in which, due to the formation of the metallic bond, almost or completely filled d orbitals are broken up, such that these metals tend in an extreme way towards the formation of intermetallic compounds with sp-metals. The perspective is to make use of the Pd or Pt in form of a tape on which the tracer activities are electrodeposited and the deposition zone is subsequently stepped between pairs of Si detectors for a-spectroscopy and SF measurements. 

Dielectric polarizabilities are useful for prediction of dielectric constants of new materials and compounds whose dielectric constants have not been measured, and in calculations of energies of the formation and migration of defects. In addition, deviations from the polarizability additivity rule are useful in understanding certain physical properties such as thermodynamic functions and ionic and electronic conductivity." ... 

Comparison of the solubility of iron hydroxides and goethite according to the data of Lengweiler et al. (1961) and Schindler et al. (1963) showed that there is a functional relationship between the variation in isobaric potential (AAG) during aging of the precipitate and aging time (Mel nik, 1972b). This made it possible to calculate the isobaric potentials of formation of the compounds—from thermodynamically stable a-FeOOH to metastable freshly precipitated Fe(OH)3-I (AC°298, kcal/mol) ... 

Bondi and Simkin presented a similar calculation for liquids, using the heat of vaporization (AHv) (241, 242). The purpose was to obtain an estimate of but in the process a value of the H bond increment, 5(OH) is derived. This increment is .. . a measure of (but not identical with) the heat of formation of the H bond,. . Values for 5(OH) are very similar to enthalpy values, though they are not intended as thermodynamic functions. Bondi gives an extensive discussion of their use with simple and polyhydric alcohols and a few other compound classes. Table 7-V compares 6(OH) and AH values. 

Values of thermodynamic functions (heats of formation and entropies) are known for many compounds, typically at 298.15° K = 25° C (see e.g. [17]). However, for even more compounds these values are not known and must be estimated. 

Phenomenological, theoretical and practical aspects of the double-double effect are presented on the basis of the review of original papers concerning the variation with Z of thermodynamic functions of complex formation, lattice parameters, and several other properties of lanthanide and actinide compounds. 

Plyasunova et al. critically evaluated the standard thermodynamic quantities of Ni, its hydrolysis reactions and hydroxo-complex formation on the basis of published experimental studies and the specific interaction theory (SIT) for activity coefficient modelling [97GRE/PLY2]. Recommended thermodynamic functions and interaction coefficients relevant for the present review and its compounds were presented, see Table A-... 

The IR spectra of 3-oxo-l-thioxo-2,3-dihydro-17/-pyrrolo[l,2-c]imidazole in the solid form and in solution have been measured as a function of temperature, and a direct correlation has been obtained between the two phases and the type and extent of hydrogen bonding. It was suggested that the compound exists as cyclic dimer (103) in the solid state (below 310 K) and in dilute solution by formation of two equivalent hydrogen bonds. At transition temperature, the cyclic dimer changes to the noncyclic dimer (104) and persists in this structure till 410 K. In addition, thermodynamic functions AG°, AH", and AS" have been estimated using spectral data in solution <84CJC1845>. 

The thermodynamic properties are needed in the selection of suitable conditions for the synthesis of this compound and of elements which can be used to dope it. Therefore, we determined the principal thermodynamic functions associated with the formation of gallium phosphide. This was done using the emf method and a liquid electrolyte. 

A different but still empirical approach to the problem of the connection between thermodynamic properties in water and molecular structure of the solutes considers the thermodynamic functions of hydration of the saturated organic compounds AX as a sum of terms arising from the formation of a cavity where the molecule of the solute is lodged, the interaction water-hydrocarbon part of... 

The thermodynamic data of the RBei3 and AnBeis compounds are reported in table 2. The enthalpies of formation of these compounds are presented in fig. 15 as a function of the atomic number of the rare-earth element or of the actinide. The values obtained by Ivanov and Tumbakov (1959) and Pyatkov et al. (1971) for the enthalpy of formation of UBei3 intermetallic compound are rather different. The values given for LaBe and CeBei3 are partial Gibbs energy of Be in the compound. The only conclusion which can be drawn is that the enthalpies of formation of UBe and PuBe arc less exothermic than that of YBe. ... 

The calculation scheme for the enthalpies of formation of lanthanide dihalides proposed by Kim and Oishi (1979) is based on the assumption that the formation of these compounds, except for europium and ytterbium, is accompanied by an electronic transition 4f 5d 6s 4f + 5d°6s in the lanthanide atom. This results in the observation of an irregularity in the variation of the thermodynamic parameters, including the enthalpies of formation, as a function of the lanthanide atomic nmnber. 

But it is still not enough if we use this method only. Thermodynamic method cannot make prediction of new phase formation because the thermodynamic function of unknown intermediate compound is not available. 

In considering phase transformations or chemical reactions, only changes in thermodynamic functions are of interest Consequently, H can be measured relative to any reference level. This is usually done by defining = 0 for a pure element in its most stable modification at 298 K (25 °C). For a compound, is taken as the standard heat of formation of one mole of this compound from its elemental constituents in their standard states. 

Thermodynamic and transport properties of pure substances includes the various thermodynamic functions (//, S, G, Cp, etc.), density, vapor pressure, viscosity, thermal conductivity, and many others. These properties are functions of temperature and pressure, but an important subset consists of values defined under standard conditions, such as Af//°, the standard state enthalpy of formation of a compound from its elements. 

The final class of polymers containing carboranyl units to be mentioned here is the polyphosphazenes. These polymers comprise a backbone of alternating phosphorous and nitrogen atoms with a high degree of torsional mobility that accounts for their low glass-transition temperatures (-60°C to -80°C). The introduction of phenyl-carboranyl units into a polyphosphazene polymer results in a substantial improvement in their overall thermal stability. This is believed to be due to the steric hindrance offered by the phenyl-carborane functionality that inhibits coil formation, thereby retarding the preferred thermodynamic pathway of cyclic compound formation (see scheme 12). 

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