NaCl lattice energy

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 ... 

To date there is no evidence that sodium forms any chloride other than NaCl indeed the electronic theory of valency predicts that Na" and CU, with their noble gas configurations, are likely to be the most stable ionic species. However, since some noble gas atoms can lose electrons to form cations (p. 354) we cannot rely fully on this theory. We therefore need to examine the evidence provided by energetic data. Let us consider the formation of a number of possible ionic compounds and first, the formation of sodium dichloride , NaCl2. The energy diagram for the formation of this hypothetical compound follows the pattern of that for NaCl but an additional endothermic step is added for the second ionisation energy of sodium. The lattice energy is calculated on the assumption that the compound is ionic and that Na is comparable in size with Mg ". The data are summarised below (standard enthalpies in kJ) ... 

There is a lively controversy concerning the interpretation of these and other properties, and cogent arguments have been advanced both for the presence of hydride ions H" and for the presence of protons H+ in the d-block and f-block hydride phases.These difficulties emphasize again the problems attending any classification based on presumed bond type, and a phenomenological approach which describes the observed properties is a sounder initial basis for discussion. Thus the predominantly ionic nature of a phase cannot safely be inferred either from crystal structure or from calculated lattice energies since many metallic alloys adopt the NaCl-type or CsCl-type structures (e.g. LaBi, )S-brass) and enthalpy calculations are notoriously insensitive to bond type. 

Determination of Lattice Breakup Energies from Experimental Data The process of lattice breakup can be split into individual steps for which the energies can be measured. Thus, breaking up the NaCl lattice to form free ions in the gas phase can be described (with a Born-Haber cycle) as... 

Calculation of the Electrostatic Energy of Lattice Breakup In 1919, Max Bom proposed a method for calculating the energy necessary to draw apart a pair of ions from a crystal lattice to infinite distance against electrostatic attraction forces. The equation derived by Bom gives for the lattice energy of a NaCl crystal the value -762kJ/mol (i.e., a value close to the experimental value of the heat of breakup that we had mentioned). 

The electrostatic part of the lattice energy for chlorides crystallizing in the CsCl, NaCl and zinc blende type as a function of the radius ratio... 

Sometimes, the unknown quantity in the cycle is the lattice energy, U. From the cycle just shown, we know that the heat change is the same regardless of the pathway by which NaCl(s) is formed. Therefore, we see that... 

Therefore, a value of 8 can be used in calculations for NaCl. When the repulsion is included, the lattice energy, U, is expressed as... 

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. 

Whether or not enthalpies of sublimation of the alkali metals are approximately the same, lattice energies of a series such as LiCl(s), NaCl(s), KCl(s), RbCl(s), and CsCl(s) will vary approximately with the size of the cation. A smaller cation will produce a more exothermic lattice energy. Thus, the lattice energy for LiCl(s) should be the most exothermic and CsCl(s) the least in this series, with NaCl(s) falling in the middle of the series. 

Equation (1.4) is an expression for the lattice energy of an ionic solid like NaCl, first derived by Born and Mayer. The equation can be used directly for the calculation of cohesive energy of ionic solids provided we know A and p. 

As long as we only assume coulomb forces and repulsive forces of the type discussed, this contraction leads to the surprising result that the CsCl lattice can never be formed. It can only exist if the lattice energy of the CsCl lattice is smaller, or at least equal to that of the NaCl lattice. The conditions for the stability of the CsCl lattice are... 

For solution in organic media, therefore, the experimental quantity of significance is not the lattice energy of the crystalline solid, but its heat of sublimation. Thus, the heat of sublimation (to monomeric gas molecules) of NaCl is given (Table 1) as 54.3 kcal/mole. Therefore, any solution process must produce an energy evolution of the order of 50 to 60 kcal/mole for the process which we shall write as... 

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... 

Sodium fluoride and sodium chloride both crystallize into the same type of structure. Which do you predict to have the higher lattice energy, NaF or NaCl ... 

Since Na+ is smaller than Cs+ and Cl- is smaller than I-, the distance between ions is smaller in NaCl than in Csl. Thus, NaCl has the larger lattice energy. 

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