Lattice energy importance

In the case of ionic solid substances, an important quantity is the free lattice energy AGS, i.e., the energy liberated when one type of crystalline substance is formed from its ionic constituents in the gas phase. This definition implies that this magnitude for a simple 1 1 solid electrolyte is a sum of the real potentials of cation and anion ... 

For crystalline compounds, they noted that an important factor to consider is the crystal lattice energy. From theoretical considerations and subsequent empirical studies, they discovered that melting point (mp) serves as an excellent proxy for this factor. While this is a significant advance in our understanding of water solubility, it falls short as a means to predict solubility from the chemical structure alone a compound must be made and a mp determined experimentally. 

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. 

By means of appropriate thermochemical cycles, it is possible to calculate proton affinities for species for which experimental values are not available. For example, using the procedure illustrated by the two foregoing examples, the proton affinities ofions such as HC03-(g) (1318 k J mol-1) and C032-(g) (2261 kj mol-1) have been evaluated. Studies of this type show that lattice energies are important in determining other chemical data and that the Kapustinskii equation is a very useful tool. 

It is also interesting to note that metal ions having low polarizability (Al3+ Be2+ etc.) are those that are acidic (as shown in Eq. (9.17)). Also, in Chapter 7 we discussed how the polarization of ions leads to a lattice energy that is higher than that predicted on the basis of electrostatic interactions alone. The polarizability data shown in the table make it easy to see that certain ions are much more polarizable than others. Although we will not visit again all of the ramifications of electronic polarizability, it is a very useful and important property of molecules and ions that relates to both chemical and physical behavior. 

The hydrated cation Ca2+aq is of prime importance to the aqueous solution chemistry of calcium, and to most of its various roles in biological systems. The relation between lattice energy and hydration energies of the constituent ions determine solubilities, the size of the hydrated cation controls selectivity and the passage of ions through channels, and the work required to remove some or all of the water of hydration is relevant both to... 

The extent of the ionization produced by a Lewis acid is dependent on the nature of the more inert solvent component as well as on the Lewis acid. A trityl bromide-stannic bromide complex of one to one stoichiometry exists in the form of orange-red crystals, obviously ionic. But as is. always the case with crystalline substances, lattice energy is a very important factor in determining the stability and no quantitative predictions can be made about the behaviour of the same substance in solution. Thus the trityl bromide-stannic bromide system dilute in benzene solution seems to consist largely of free trityl bromide, free stannic bromide, and only a small amount of ion pairs.187 There is not even any very considerable fraction of covalent tfityl bromide-stannic bromide complex in solution. The extent of ion pair and ion formation roughly parallels the dielectric constant of the solvents used (Table V). The more polar solvent either provides a... 

Two factors, other than structure, are important here. The two compounds with the highest lattice energies contain divalent ions (+2 or -2) while NaF contains... 

The moments of a charge distribution provide a concise summary of the nature of that distribution. They are suitable for quantitative comparison of experimental charge densities with theoretical results. As many of the moments can be obtained by spectroscopic and dielectric methods, the comparison between techniques can serve as a calibration of experimental and theoretical charge densities. Conversely, since the full charge density is not accessible by the other experimental methods, the comparison provides an interpretation of the results of the complementary physical techniques. The electrostatic moments are of practical importance, as they occur in the expressions for intermolecular interactions and the lattice energies of crystals. 

As the electrostatic potential is of importance in the study of intermolecular interactions, it has received considerable attention during the past two decades (see, e.g., articles on the molecular potential of biomolecules in Politzer and Truhlar 1981). It plays a key role in the process of molecular recognition, including drug-receptor interactions, and is an important function in the evaluation of the lattice energy, not only of ionic crystals. 

In molecular crystals, the relative importance of the electrostatic, repulsive, and van de Waals interactions is strongly dependent on the nature of the molecule. Nevertheless, in many studies the lattice energy of molecular crystals is simply evaluated with the exp-6 model of Eq. (9.45), which in principle accounts for the van der Waals and repulsive interaction only. As underlined by Desiraju (1989), this formalism may give an approximate description, but it ignores many structure-defining interactions which are electrostatic in nature. The electrostatic interactions have a much more complex angular dependence than the pairwise atom-atom potential functions, and are thus important in defining the structure that actually occurs. 

In typical organic crystals, molecular pairs are easily sorted out and ab initio methods that work for gas-phase dimers can be applied to the analysis of molecular dimers in the crystal coordination sphere. The entire lattice energy can then be approximated as a sum of pairwise molecule-molecule interactions examples are crystals of benzene [40], alloxan [41], and of more complex aziridine molecules [42]. This obviously neglects cooperative and, in general, many-body effects, which seem less important in hard closed-shell systems. The positive side of this approach is that molecular coordination spheres in crystals can be dissected and bonding factors can be better analyzed, as examples in the next few sections will show. 

It is important to note that the good agreement achieved between the Born-Haber and calculated values for lattice energy, do not in any way prove that the ionic model is valid. This is because the equations possess a self-compensating feature in that they use formal charges on the ions, but take experimental internuclear distances. 

The concepts required for a quantitative treatment of the reactivity of solids were now clear, except for one important issue. According to the foregoing, point defect energies should be on the same order as lattice energies. Since the distribution of point defects in the crystal conforms to Boltzmann statistics, one was able to estimate their concentrations. It was found that the calculated defect concentrations were orders of magnitude too small and therefore could not explain the experimentally observed effects which depended on defect concentrations (e.g., conductivity, excess volume, optical absorption). Jost [W. Jost (1933)] provided the correct solution to this problem. Analogous to the fact that NaCl can be dissolved in H20... 

A dislocation line may only terminate al the surface of the crystal. The energy of a dislocation is largely stored as strain in the surrounding lattice. The important property of a dislocation is its ability to move quite easily... 

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