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Born-Haber cycle Crystals

Fig. 1. Born-Haber cycle for the formation of solvated ions from an ionic crystal [M+X ]w. U lattice energy, Affsoiv. enthalpy of ion solvation... Fig. 1. Born-Haber cycle for the formation of solvated ions from an ionic crystal [M+X ]w. U lattice energy, Affsoiv. enthalpy of ion solvation...
It is quite remarkable that electrostatic calculations based on a simple model of integral point charges at the nuclear positions of ionic crystals have produced good agreement with values of the cohesive energy as determined experimentally with use of the Born-Haber cycle. The point-charge model is a purely electrostatic model, which expresses the energy of a crystal relative to the assembly of isolated ions in terms of the Coulombic interactions between the ions. [Pg.195]

E. A. Hylleraas, Z. Physik 63, 771 (1930). The calculated value of the crystal energy is 219 kcal/mole, and the Born-Haber cycle value is 218 kcal/mole, using for the electron affinity of hydrogen the reliable quantum-mechanical value 16.480 kcal/mole (see Introduction to Quantum Mechanics, Sec. 29c). The calculated value for the lattice constant, 4.42 A, is less reliable than the value... [Pg.511]

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. [Pg.53]

D is the dissociation enthalpy of Cl2,1 is the ionization potential of Na, E is the electron addition enthalpy of Cl (which is the negative of the electron affinity), and U is the lattice energy. The Born-Haber cycle shows that the lattice energy corresponds to the energy required to separate a mole of crystal into the gaseous ions, and forming the crystal from the ions represents -U. [Pg.64]

The initial step (S3.1 l-2a) is highly endothermic, corresponding to the cohesive energy of the crystal as evaluated by the Born-Haber cycle (Sidebar 3.10) ... [Pg.111]

Hess s law states that the enthalpy of a reaction is the same whether the reaction takes place in one or several steps it is a necessary consequence of the first law of thermodynamics concerning the conservation of energy. If this were not true, one could manufacture energy by an appropriate cyclic la-ocess. Bom and Haber applied Hess s law to the enthalpy of formation of an ionic soHd. For the formation of an ionic crystal from the elements, the Born-Haber cycle may most simply be depicted as... [Pg.64]

The oxides of the alkaline earth metals crystallize in a sodium chloride lattice although in SrO and BaO the radius ratio is greater than 0 732. It has been proposed that the crystals are constructed from the ions M + and the electron affinity of the oxygen atom calculated on this assumption by the Born-Haber cycle for the different oxides give rather... [Pg.329]

Use the Born-Haber cycle to calculate the enthalpy of formation of MgO, which crystallizes in the mtile lattice. Use these data in the calculation O2 bond energy = 247 kJ/mol AHj ji,(Mg) = 37 kJ/mol. Second ionization energy of Mg = 1451 kJ/mol second electron affinity of O = —744 kJ/inol. [Pg.238]

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. [Pg.160]

Sherman (114) and other workers have compared crystal energies obtained by the Born-Haber cycle from experimental thermochemical data with theoretical values calculated assuming strict ionic character. The differences obtained have been used to indicate deviations from strict heteropolarity. Sherman 114) in his review gives results for 50 crystals, the computations being made with the Born-Lande equation. [Pg.206]

Most of the enthalpies associated with steps in the cycle can be estimated, to a greater or less accuracy, by experimental methods. The lattice energy, however, is almost always obtained theoretically rather than from experimental measurement. It might be supposed that the enthalpy of dissociation of a lattice could be measured in the same way as the enthalpy of atomization of the metal and nonmctal, that is, by heating the crystal and determining how much energy is necessary to dissociate it into ions. Unfortunately, this is experimentally very difTicull. When a crystal sublimes (AHj), the result is not isolated gaseous ions but ion pairs and other clusters. For this reason it is necessary to use Eq. 4.13 or some more accurate version of it. We can then use the Born-Haber cycle to check the accuracy of our predictions if we can obtain accurate data on every other step in the cycle. Values computed from the Bom-Haber cycle are compared with those predicted by Eq. 4.13 and its modifications in Table 4.3. [Pg.65]

A slightly different problem arises when we consider the lower oxidation states of metals. We know that CaFj is stable. Why not CaF as well Assuming that CaF would crystallize in the same geometry as KF and that the internuclear distance would be about the same, we can calculate a lattice energy for CaF, Uq = — 795 kJ mol h The terms in the Born-Haber cycle are... [Pg.66]

The adequacy of a purely electrostatic picture of simple ionic crystals A, X is demonstrated by the agreement between the values of the lattice energy resulting from direct calculation, from the Born-Haber cycle, and in a few cases from direct measurement. [Pg.255]

Indirect determinations of the lattice energies of many ionic crystals have been made using the Born-Haber cycle, which relates the following quantities ... [Pg.257]

J5 Crystal Lattice Energy 245-1 Born-Haber Cycle... [Pg.53]

Assuming NeCl crystallizes in the NaCl structure and, using the Born-Haber cycle, show why NeCl does not exist. Make any necessary assumptions. [Pg.49]


See other pages where Born-Haber cycle Crystals is mentioned: [Pg.74]    [Pg.74]    [Pg.7]    [Pg.91]    [Pg.64]    [Pg.213]    [Pg.184]    [Pg.795]    [Pg.118]    [Pg.40]    [Pg.318]    [Pg.324]    [Pg.329]    [Pg.330]    [Pg.523]    [Pg.238]    [Pg.238]    [Pg.1133]    [Pg.64]    [Pg.4]    [Pg.91]    [Pg.40]    [Pg.318]    [Pg.324]    [Pg.329]    [Pg.330]   


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