Born-Haber cycle bonding

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 ... 

Fig. 7. Born-Haber cycle for the formation of ions by heterolytie fission of a covalent bond. I ionization potential of M, E electron affinity of X...

The number of electrons available for empirical evaluation of metal-metal bonding has been taken as the Pauling metallic valence less the number of H ions per metal. In this connection the valence numbers of Borelius (6) give somewhat better correlations—e.g., in differentiating Pd from Ag (valences 7 and 1, respectively). Heats of formation calculated from the lattice energies by the Born-Haber cycle are not yet sufficiently accurate to be useful numerically, but they provide an interesting rationalization of the formation of many hydrides. This is the principal reason for considering such a naive model. 

In the sulphides, selenides, tellurides and arsenides, all types of bond, ionic, covalent and metallic occur. The compounds of the alkali metals with sulphur, selenium and tellurium form an ionic lattice with an anti-fluorite structure and the sulphides of the alkaline earth metals form ionic lattices with a sodium chloride structure. If in MgS, GaS, SrS and BaS, the bond is assumed to be entirely ionic, the lattice energies may be calculated from equation 13.18 and from these values the affinity of sulphur for two electrons obtained by the Born-Haber cycle. The values obtained vary from —- 71 to — 80 kcals and if van der Waal s forces are considered, from 83 to -- 102 kcals. 

The electron affinity of ClOt has been estimated from a Born—Haber cycle, employing a lattice energy calculation, to be 134 kcal mof (V. I. Medeoeyev, L. V. Gurvich, V. N. Kondrat yev, V. A. Medvedev, and Ye, L Frankevich, "Bond Energies, Ionization Potentials and Electron Affinities," St. Martin s Press, New York, N. Y., 1966), whereas the electron affinity of the P atom has been determined spectroscopically to be 79.5 d 0.1 kcal mol (R. S. Berry and C. W. Reimann, J. Ckem. Pkys., 18, 1540 (1963)). 

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. 

Figure 2. Born-Haber cycle for the single-electron transfer (SET) response of the carbon-metal bond, incorporating the Blicke-Powers hypothesis.

It has been studied by IR spectroscopy (when trapped in a low-temperature matrix) and by mass spectrometric studies on the vapor. Isotopic studies ( C1/ C1 and 0/ 0) allow the 0-P-Cl bond angle to be calculated from the IR spectra at ca. 105° (i.e. close to the bond angle of CH2PCI). From the observed appearance potential (20.9 eV) of P+ [AP(P+)] in the mass spectrum of OPCl, it is possible to estimate the enthalpy of atomization of OPCl(g) via the Born-Haber cycle (Scheme 6). Hence, since the standard enthalpies of formation of P(g), 0(g), and Cl(g) are all known, the standard enthalpy of formation of OPCl(g) [A//f°2gg(OPCl)] may be estimated as -250.7 kJmol-L... 

Born-Haber cycle. The cycle that relates lattice energies of ionic compounds to ionization energies, electron affinities, heats of sublimation and formation, and bond enthalpies. (9.3)... 

The ionic bond results from the Coulomb attraction of oppositely charged ions. Its strength is characterised by the electrostatic energy in MX ionic crystals it is the crystal lattice energy C/(MX), which can be determined experimentally from the Born-Haber cycle or calculated theoretically from the known net charges of ions (Z, not to be confused with nuclear charges ) and inter-ionic distances d), as... 

Enthalpy changes of atomization are always positive, because energy must be absorbed to pull the atoms apart and break the chemical bonds. Enthalpy changes of atomization are usually found indirectly by calculation from other enthalpy changes, using Hess s law. Enthalpy changes of atomization are used in Born-Haber cycle calculations. 

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