Lattice energy and chemical prediction: Use of the Kapustinskii equations and the Born-Haber cycle

Abstract

The chemist is fascinated to see the realizat'ion of chemical behavior previously predicted by t'heoretical reasoning. Mendeleev established the reasoning by the basic idea that "there must be some bond of union between mass and the chemical elements" ( I ) . In order that chemical analogies should be preserved, he left gaps in his periodic classification and predicted the properties of these missing elements with remarkable accuracy.More recently, crystal chemistry has provided a more quantitative basis for predicting chemical syntheses. An early example of this is provided by the work of Grimm and Herzfield (8) where use was made of latatice energies of neighboring stable compounds in the periodic table and, for some compounds, values calculated from the Born-Lande equation (3):where U is the lattice energy, N is Avogadro's number, M is the Madelung constant, z+ and z-are the valencies of the ions, e is the charge on the electron, r is the interionic distance, and n is the electronic shells repulsion exponent.The various lattice energies were used to predict the stability of a number of hypothetical compounds. For example, it was predicted that the monohalides of the noble gases would be unstable in an ionic lattice and would decompose into the constituent elements (8).The Born-Lande equation is dependent on an exact lcnowlcdge of crystal structure and hence of the Madelung constant. The same is also true of certain other equations employed for the calculation of lattice energies of compounds. One such equation is that of Born-R l a~e r (41, an improved version of equation ( I ) , where p characterizes the quantum-mechanical repulsion forces acting between the electronic shells of the ions and has the di~nensions of length. For most crystals p may be regarded as practically constant a t 0.345 A. The Kapustinskii EquationsFor hitherto unknown conlpounds, it is imperative that a certain crystal structure be assumed before equat,ions of the type of (1) and (2) can be used. Kapustinskii (5) regarded such an assumption as unsatisfactory and proposed an equation with which it was possible to ext,end the sphere of calculations of lattice energies.The development of this equation may be traced by making a slight modification in equations ( 1 ) and (2) (6, 7) to give equat,ions (3) and (4). respectively.In both equations, v is the number of ions in the molecule and cr = [ M / ( v / 2 ) ] . The Rfadelung constant, M, is independent of cr, since it is proportional to the number of ions in the chemical molecule. However, or is not identical for different lattice types and Kapustinskii (5) found, empirically, that in passing from one lattice type to another, the change in u was proportional to the change in interionic distance.With these modifications and by taking the Goldschmidt ionic radii referred to the coordination number 6, giving (r+ + r -) for r , and the structural coefficient, u = 1.745, for roclr-salt type lattices, the same value is obtained for the lattice energy as by calculating it with the aid of r, derived...

Stability of Naturally Relevant Ternary Phases in the Cu–Sn–S System in Contact with an Aqueous Solution

“…Since thermodynamic properties of crystals are strongly structure-dependent [41,42], we established a Born-Haber cycle including a close structural control on the mineral phases. This cycle is based on the thermodynamic properties of kesterite, Cu 2 ZnSnS 4 [43], and kuramite.…”

A Simplified Mathematical Model for Calculating the Lattice Energies of Binary Group I and II Ionic Compounds: Using Solver to Estimate the Empirical Constants

“…These calculated values are physically reasonable, as the radius of the free ion has been calculated to be 2.08 Å, and the radius of the H ᎑ ion varies from 1.30 in LiH to 1.54 Å in RbH (1). These experimental values are smaller than the value found from the use of eqs 11 and 14, but the exercise is illustrative of a general method (4)(5)(6)(10)(11)(12) for estimating thermochemical radii of ions known to be nonspherical.…”

“…Equation 11 gives more reliable values for lattice energies than the Kapustiskii equation, and eq 11 or 14 could be used instead of it for determining self-consistent thermochemical radii, electron and proton affinities, and the calculation of the enthalpy of formation of hypothetical compounds (4,5,(9)(10)(11).…”

Superior electrochemical performance of alkali metal anodes enabled by milder Lewis acidity

“…Lattice energy primarily hinges on the Coulombic interaction between cations and anions and typically follows the order Li > Na > K according to the Kapustinskii equation. 49–51 For the same anions, it generally holds that smaller lattice energy and greater solvation energy result in a substantial negative energy change, favoring salt dissolution. In contrast, solvation energy is determined by the interaction between ions and solvents and exhibits the following sequence: Li > Na > K ( vide infra ).…”