Born-Haber-Fayans Thermochemical Cycle

In calculating the lattice energy of a crystal, we adopt an arbitrary reference condition (two isolated ions in the gaseous state and at infinite distance) to which we assign a zero potential. It is worth stressing that this condition is not equivalent to the standard state commonly adopted in thermochemical calculations, which is normally that of element at stable state at reference P, T. 

The relationships between the two different states and between the enthalpy of formation from the elements at standard state (H°) and the lattice energy (U) are easily understood by referring to the Born-Haber-Fayans thermochemical cycle. In this cycle, the formation of a crystalline compound from isolated atoms in the gaseous state is visualized as a stepwise process connecting the various transformations. Let us follow the condensation process of a crystal MX formed from a metal M and a gaseous molecule X2  

First we transform metal M into a gaseous atom M(gas) and the gaseous molecule 5X2 into a gaseous atom X(gas)  

The energies required by these processes are composed of the sublimation energy of the metal (Es) and the dissociation energy of the gaseous molecule (fEjf). 

We now transform the gaseous atoms into gaseous ions  

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We have also seen (in chapter 1) that enthalpy and lattice energy are related through the Born-Haber-Fayans thermochemical cycle, on the basis of the energy additivity principle of Hess. The enthalpy or heat content of a phase H) is composed of the internal energy U at the T of interest and the PV product ... 

Table 5.37 Lattice energy terms for C2/c pyroxenes. Values in kJ/mole. bhf = energy of Born-Haber-Fayans thermochemical cycle U- = lattice energy Ec = coulombic energy = repulsive energy Edd = dipole-dipole interactions E q = dipole quadrupole interactions =...

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