Lattice energies thermodynamics

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 ... 

From the standpoint of thermodynamics, the dissolving process is the estabHsh-ment of an equilibrium between the phase of the solute and its saturated aqueous solution. Aqueous solubility is almost exclusively dependent on the intermolecular forces that exist between the solute molecules and the water molecules. The solute-solute, solute-water, and water-water adhesive interactions determine the amount of compound dissolving in water. Additional solute-solute interactions are associated with the lattice energy in the crystalline state. 

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. 

With respect to the sharpness of the top metal/molecule interface, thermodynamically, given the vastly different lattice energies of the soft-condensed matter SAM and the hard metal layer, one would expect the interface to be near the limit of no interfacial mixing (essentially a large chi mixing parameter, x l) the interface to approach an infinitely sharp condition. An example of the complexity that can be introduced in this simple picture is illustrated by considering the case of... 

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. 

The lattice energy U is defined as the energy released (U is therefore negative by thermodynamic convention) when a mole of the requisite free gaseous ions comes together from infinite interionic separation to make up the crystal. If N is Avogadro s number (6.0221 x 1023), we have the Bom-Lande formula ... 

Physical Properties. Of the three modifications of TiOz, rutile is the most thermodynamically stable. Nevertheless, the lattice energies of the other phases are similar and hence are stable over long periods. Above 700 °C, the monotropic conversion of anatase to rutile takes place rapidly. Brookite is difficult to produce, and therefore has no value in the TiOz pigment industry. 

An important property of an ionic crystal is the energy required to break the crystal apart into individual ions, this is the crystal lattice energy. It can be measured by a thermodynamic cycle, called the Born-Haber cycle. 

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 weakness of F-O bonds compared with the bond in the 02 molecule is clearly important, as for F03(0H). But an additional factor is likely to be the high lattice energy of NaF compared with NaF04 the thermochemical radius of F04 is expected to be larger than the crystal radius of F. Note, however, that NaC104 - a well-known substance - is likewise thermodynamically unstable. For the decomposition ... 

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... 

One of the most successful applications of crystal field theory to transition metal chemistry, and the one that heralded the re-discovery of the theory by Orgel in 1952, has been the rationalization of observed thermodynamic properties of transition metal ions. Examples include explanations of trends in heats of hydration and lattice energies of transition metal compounds. These and other thermodynamic properties which are influenced by crystal field stabilization energies, including ideal solid-solution behaviour and distribution coefficients of transition metals between coexisting phases, are described in this chapter. 

Almost all elements form thermodynamically stable halides. The normal stability sequence is F > Cl > Br >1, which in covalent compounds follows the expected order of bond strengths, and in ionic compounds that of the lattice energies. The thermodynamic stability of fluorides (and the kinetic reactivity of F2) is... 

These disproportionations are thermodynamically driven by the very high lattice energy (stability) of LiF and its insolubility in nonaqueous solvents. The insolu-... 

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