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How is lattice energy estimated using a Born Haber cycle Estimating lattice energy using the Born Haber cycle has been discussed in Ionic Solids For a quick review the following is an example that illustrate the estimate of the energy of crystallization of NaCl Hsub of Na 108 kJ mol Heat of sublimation D of Cl2 244 Bond dissociation energy IP of Na g 496 Ionization potential or energy EA of Cl g 349 Electron affinity of Cl Hf of NaCl 411 Enthalpy of formation The Born Haber cycle to evaluate Elattice is shown below Na Cl g 349 496 244 2 Na g Cl g Na g 0 5Cl2 g 108 Ecryst 788 Na s 0 5Cl2 l 411 NaCl s Ecryst 411 108 496 244 2 349 kJ mol 788 kJ mol Discussion The value calculated for U depends on the data used Data from various sources differ slightly and so is the result The lattice energies for NaCl most often quoted in other texts is about 765 kJ mol Compare with the method shown below Hf Na s 0 5 Cl2 l NaCl s 411 108 Hsub Na g Na s 496 IP Na g e Na g 0 5 244 0 5 D Cl g 0 5 Cl2 g 349 EA Cl g Cl g 2 e Add all the above equations leading to Na g Cl g NaCl s 788 kJ mol Ecryst The bond between ions of opposite charge is strongest when the ions are small The lattice energies for the alkali metal halides is therefore largest for LiF and smallest for CsI as shown in the table below Lattice Energies of Alkali Metals Halides kJ mol FLi Na Br I 1036 853 807 757 K 923 787 747 704 821 715 682 649 785 689 660 630 740 659 631 604 Rb Cs Cl The ionic bond should also become stronger as the charge on the ions becomes larger The data in the table below show that the lattice energies for salts of the OH and O2 ions increase rapidly as the charge on the ion becomes larger Lattice Energies of Salts of the OH and O2 Ions kJ mol Na Mg 2 Al3 OH O2 900 2481 3006 3791 5627 15 916 Here is an additional explanation Why Does Sodium Form NaCl Sodium reacts with chlorine to form Na ions and Cl ions in spite of the fact that the first ionization energy of sodium is larger than the electron affinity of chlorine To explain this we need to divide the reaction between sodium and chlorine into a number of hypothetical steps for which we know the amount of energy given off or absorbed The starting materials for this reaction are solid sodium metal and chlorine molecules in the gas phase and the product of the reaction is solid sodium chloride 2 Na s Cl2 g 2 NaCl s Let s imagine that the reaction takes place by the following sequence of



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