Born Haber Cycle Born Haber Cycle The Born–Haber cycle is an approach to analyzing reaction energies. It was named after and developed by the two German scientists Max Born and Fritz Haber. The cycle is concerned with the formation of an ionic compound from the reaction of a metal (often a Group I or Group II element) with a non-metal. Born–Haber cycles are used primarily as a means of calculating lattice energies (or more precisely enthalpies[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. Some chemists define it as the energy to break the ionic compound into gaseous ions. The former definition is invariably exothermic and the latter is endothermic. A Born–Haber cycle applies Hess' Law to calculate the lattice enthalpy by comparing the standard enthalpy change of formation of the ionic compound (from the elements) to the enthalpy required to make gaseous ions from the elements. This latter calculation is complex. To make gaseous ions from elements it is necessary to atomise the elements (turn each into gaseous atoms) and then to ionise the atoms. If the element is normally a molecule then we first have to consider its bond dissociation enthalpy (see also bond energy).
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The energy required to remove one or more electrons to make a cation is a sum of successive ionization energies; for example the energy needed to form Mg2+ is the first plus the second ionization energies of Mg. The energy changes when successive electrons are added to an atom to make it an anion are called the electron affinities. Born Haber Cycle NaCl The energy change during the formation of sodium chloride crystal from metallic sodium and chlorine gas can be used to calculate lattice enthalpy of NaCl(s). The net enthalpy change for the formation of NaCl ( ΔfH° ) is 411.2 kj/mol. Νa(s) +1/2Cl2(g) → NaCl(s) ΔfH° = -411.2 kj/mol The overall process can be explained in following steps. Formation of sodium chloride: The formation of one mole of sodium chloride from its elements under standard conditions releases 411 kj/mol of heat. This is known as standard enthalpy of formation and represented by ∆fH°. Na(s) + ½ Cl2 (g) → NaCl(s) ∆Hf°(NaCl) = - 411 kJ/mol Standard enthalpy of atomization of chlorine (∆Ha°): The energy required to atomize one mole of gaseous chlorine molecules into one mole of gaseous chlorine atoms is known as standard enthalpy of atomization of chlorine. It’s an endothermic step as the bonds between Cl-Cl atoms are being broken. ½ Cl2 (g) → Cl (g) ∆Ha° (Cl2) = +121 kJ/mol Standard enthalpy of electron affinity of chlorine (∆Hea°): The energy released when one mole of gaseous chlorine atoms gains one mole of electrons to form chloride ion. The electron affinity of chlorine atom is 349 kj/mol. Cl (g) + e- → Cl-(g) ∆Hea° (Cl) = -349 kJ/mol
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Sublimation energy of sodium (∆Hs°): This is the energy required to change one mole of solid sodium atoms into one mole of gaseous atoms. Sublimation of sodium is an endothermic process and requires energy to change the state from a solid to a gas. Na (s) → Na (g) ∆Hs° (Na) = +107 kJ/mol Ionization energy of sodium (∆HIE° (Na): Removal of one mole of electron from a gaseous metal atom involve some energy change, known as ionization energy. Endothermic, energy needs to be absorbed to remove the electron. Na (g) → Na+(g)+ e- (∆HIE° (Na) = +496 kJ/mol)
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