Thermodynamics lattice energy calculation

The dissociation energy determination and lattice energy calculation for C102" BF4"(c), with other thermodynamic data given in Table VIII, provide the enthalpy change... 

One problem which is of great interest and which has not been tackled directly because of the great instability of the obvious substrate is the electron affinity of the hydroxyl radical. Lattice energy calculations, and thermodynamic cycles, can be made consistent with any value between 40 and 70 kcal., as can the electron transfer spectra. Some years ago the author interpreted a number of microwave studies of flames as indicating an electron affinity of hydroxyl of 62... 

Lattice energies and thermodynamic parameters have been calculated and tabulated for AlCL and GaCL- ... 

Fuger (1979) and Fuger et al. (1983) reviewed experimental thermodynamic data on complex halides of the f elements, almost all of which were limited to ternary An chlorides. Jenkins and Pratt (1979) used an ionic model for lattice-energy calculation to place the energetics of formation of complex halides of d and f transition elements (from binary halides)... 

Born-Haber cycle A thermodynamic cycle derived by application of Hess s law. Commonly used to calculate lattice energies of ionic solids and average bond energies of covalent compounds. E.g. NaCl ... 

There is another use of the Kapustinskii equation that is perhaps even more important. For many crystals, it is possible to determine a value for the lattice energy from other thermodynamic data or the Bom-Lande equation. When that is done, it is possible to solve the Kapustinskii equation for the sum of the ionic radii, ra + rc. When the radius of one ion is known, carrying out the calculations for a series of compounds that contain that ion enables the radii of the counterions to be determined. In other words, if we know the radius of Na+ from other measurements or calculations, it is possible to determine the radii of F, Cl, and Br if the lattice energies of NaF, NaCl, and NaBr are known. In fact, a radius could be determined for the N( )3 ion if the lattice energy of NaNOa were known. Using this approach, which is based on thermochemical data, to determine ionic radii yields values that are known as thermochemical radii. For a planar ion such as N03 or C032, it is a sort of average or effective radius, but it is still a very useful quantity. For many of the ions shown in Table 7.4, the radii were obtained by precisely this approach. 

However, the obscure choice of frequencies in the visible and UV regions in the original calculations may have been guided by a desire to fit experimental heats. In fact, the Debye rotational and translational crystal frequencies relate to sublimation energies of the lattice, and, together with internal molecular vibrations, can be used to calculate thermodynamic functions (16). An indirect connection between maximum lattice frequencies (vm) and heats of formation may hold because the former is inversely related to interatomic dimensions (see Section IV,D,1) ... 

Calculate a value for the lattice energy of potassium chloride using Equation (1.15). Compare this with the value you calculate from the thermodynamic data in Table 1.20. 

We first look at the fluorides of barium. Only BaF2 is known, a typically ionic solid having the fluorite (8 4) structure. From Table 5.2, we see that the calculated lattice energy is very close to the experimental value in other words, we can calculate the enthalpy of formation of BaF2(s) almost within the limits of experimental uncertainty. Why have BaF3 and BaF not been prepared Presumably they are thermodynamically unstable with respect to other species. In order to verify this supposition, let us estimate the enthalpies of formation AHf of BaF(s) and BaF3(s), assuming these to be ionic. 

The lattice energy U of an ionic compound is defined as the energy required to convert one mole of crystalline solid into its component cations and anions in their thermodynamic standard states (non-interacting gaseous ions at standard temperature and pressure). It can be calculated using either the Born-Land6 equation... 

Numerous organic species are known to lead to the crystallization of the MFI-type structure (7). but the tetrapropylammonium cations can be considered to be the most specific. To our knowledge no thermodynamic data such as standard formation enthalpies (AfH°) and stabilization energies attributed to the organic species have been published to corroborate this experimental observation. The published thermodynamic data (AfG°, AfH°, AfS°. Cp) are for natural zeolites (8-11) or for organic-free synthetic zeolites. However. some data have been obtained by calculations using lattice energy minimization and extended Hiickel theory (1 2) or by semi-empirical methods based on addition of the thermodynamic functions of the oxide compo-... 

Potentially therefore we may be able to generate an unlimited number of possible zeolitic frameworks. Of these, only a portion is likely to be of interest as having desirable properties, with an even smaller fraction being amenable to synthesis in any given composition. It is this last problem, the feasibility of hypothetical frameworks, which is the key question in any analysis of such structures. The answer is not a simple one, since the factors that govern the synthesis of such materials are not fully understood. Zeolites are metastable materials, as shown by the calculated lattice energies reported in Table 1. Aside from this thermodynamic constraint, the precise identity... 

Quite apart from its theoretical calculation, by the use of one of the expressions developed above, it is possible to relate the lattice energy of an ionic crystal to various measurable thermodynamic quantities by means of a simple Hess s law cycle. This cycle was first proposed and used by Bom 15) and represented in its familiar graphical form by Haber (45). It is now usually referred to as the Born-Haber cycle. The cycle is given below for a uni-univalent salt in terms of enthalpies. 

One generally finds, therefore, that absolute values for thermodynamic parameters are less important than are relationships that predict the relative stability of the various phases of a polymorphic system. Although it is possible to calculate such energy differences from considerations of the lattice energies of the different structures,most workers instead employ the time-honored empirical rules that have been developed over time. For instance, since Gmetastabie > G tabie, then the vapor pressure of the stable form must be less than the vapor pressure of the metastable form. 

Born-Haber cycle - A thermodynamic cycle in which a crystalline solid is converted to gaseous ions and then reconverted to the solid. The cycle permits calculation of the lattice energy of the crystal. 

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