The Born-Haber Thermochemical Cycle

The Born-Haber Thermoche mi cal Cycle. -The following cycle was devised by Born and Haber to relate the crystal energy to other thermochemical quantities  

A few years ago experimental values were available for Q, S, /, and Z), but not for E the procedure adopted in testing the equation was to use the equation with calculated values of Uq (Equation 13-5) to find E, and as a test of the method to examine the constancy of E for a series of alkali halogenides containing the same halogen. The values obtained in this way were found to be constant to within about 3 kcal/mole. However, later experimental determinations of the values of the electron affinities of the halogen atoms by direct methods have shown that Equation 13-5 for the crystal energy is in general reliable only to about 2 percent. 

Work on the direct determination of the electron affinities of halogen atoms was begun by Mayer,7 who, with his students, measured directly the equilibrium constant for dissociation of alkali halogenide gas molecules into ions or of gas halogenide ions into atoms and electrons. Other methods have also been used, especially some involving mass 

Verhandl. deut. pkysik. Ges. 21, 13 (1919) F. Haber, ibid. 750. 

We may illustrate the reliability of the Born equation by ar example. For NaF the values Q = 136.Q, S 26.0, I = 120.0, D 18.3, and E = 83.5 kcal/mole (all for 25°C) lead, with Equation 13-6, to 216.8 kcal/mole for U, the crystal enthalpy at 25°C. The value of Uo calculated by Equation 13-5 with R0 = 2.307 A and n = 7 is 215.5 kcal/mole. This value, with the pV correction 1,2 kcal/mole, leads to 216.7 kcal/mole for U, in excellent agreement with the experimental value. The mean deviation found for the alkali halogenides is 3 kcal/mole. 

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When the multiplicity of a complex is the same for ionic or ion-dipole bonds and for covalent bonds, the decision as to which extreme bond type is the more closely approached in any actual case must be made with the aid of less straightforward arguments. Sometimes theoretical energy diagrams can be constructed with sufficient accuracy to decide the question. A discussion of crystals based on the Born-Haber thermochemical cycle has been given by Rabinowitsch and Thilo3), and more accurate but less extensive studies have been made by Sherman and Mayer4). 

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