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Born–Haber cycles are used primarily as a means of calculating lattice energy (or more precisely enthalpy [note 1]), which cannot otherwise be measured directly. The lattice enthalpy is the enthalpy change involved in the formation of an ionic compound from gaseous ions (an exothermic process ), or sometimes defined as the energy to break the ...
The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound.In 1918 [1] Max Born and Alfred Landé proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice and a repulsive potential energy term.
The concept of lattice energy was originally applied to the formation of compounds with structures like rocksalt and sphalerite where the ions occupy high-symmetry crystal lattice sites. In the case of NaCl, lattice energy is the energy change of the reaction Na + (g) + Cl − (g) → NaCl (s) which amounts to −786 kJ/mol. [2]
The calculated lattice energy gives a good estimation for the Born–Landé equation; the real value differs in most cases by less than 5%. Furthermore, one is able to determine the ionic radii (or more properly, the thermochemical radius) using the Kapustinskii equation when the lattice energy is known.
The Born–Mayer equation is an equation that is used to calculate the lattice energy of a crystalline ionic compound.It is a refinement of the Born–Landé equation by using an improved repulsion term.
For many substances, the formation reaction may be considered as the sum of a number of simpler reactions, either real or fictitious. The enthalpy of reaction can then be analyzed by applying Hess' law, which states that the sum of the enthalpy changes for a number of individual reaction steps equals the enthalpy change of the overall reaction.
Such a calculation in the Gaussian and Spartan programs also give the MP2 and MP4 energies which are also used. The effect of polarization functions is assessed using an MP4 calculation with the 6-311G(2df,p) basis set. The effect of diffuse functions is assessed using an MP4 calculation with the 6-311+G(d, p) basis set.
The law states that the total enthalpy change during the complete course of a chemical reaction is independent of the sequence of steps taken. [2] [3] Hess's law is now understood as an expression of the fact that the enthalpy of a chemical process is independent of the path taken from the initial to the final state (i.e. enthalpy is a state ...