The lattice enthalpy cannot be determined directly. We calculate it indirectly by making use of changes for which data are available and link them together in an enthalpy cycle the Born Haber cycle N Goalby chemrevise.org 2 MgCl2 (s) Mg (s) + Cl2 (g) Mg (g) + Cl2 (g) 2 xEaH(Cl) atH (Mg) 2x atH (Cl) LEH fH (MgCl2 ) + 2Cl- Mg (g) 2+ (g) Mg + 2Cl (g) 2+ (g) + 2e- Mg2+ (g) + 2e- + Cl2 (g) Mg+ (g) + e- + Cl2 (g) IE 1H(Mg) IE 2H (Mg) NaCl (s) Na (s) + ½ Cl2 (g) Na (g) + ½ Cl2 (g) EaH (Cl) atH (Na) atH (Cl) LE H (NaCl) fH (NaCl) + Cl- Na (g) + (g) Na + Cl (g) + (g) + eNa+ (g) + e- + ½ Cl2 (g) IE 1H(Na) Born Haber cycle: sodium Chloride By applying Hess’s law the heat of formation equals to the sum of everything else fH =atH (Na) + IEH(Na)+ atH(Cl) + EaH(Cl) + LEH Rearrange to give LEH = fH – (atH (Na) + IEH(Na)+ atH (Cl) EaH(Cl) ) Pay attention to state symbols and direction of arrows. Usually all pieces of data are given except the one that needs to be calculated LEH =-411 – (+107 + 496 + 122 + -349) = -787 kJmol-1 Born Haber cycle: magnesium Chloride The data for the at H (Cl) could also be given as the bond energy for E(Cl-Cl ) bond. Remember : E(Cl-Cl ) = 2 x at H (Cl) Note in this example the first and second ionisation energies of magnesium are needed as Mg is a +2 ion Careful This Born Haber cycle has been constructed using a lattice enthalpy of formation. Sometimes questions will give the enthalpy of lattice dissociation which has the opposite sign and the arrow points in the opposite direction. This changes the calculation. Notice the second electron affinity for oxygen is endothermic because it take energy to overcome the repulsive force between the negative ion and the electron
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3.1.8.1 Born–Haber cycles (A-level only)
Students should be able to:
• construct Born–Haber cycles to calculate lattice enthalpies using these enthalpy changes
• construct Born–Haber cycles to calculate one of the other enthalpy changes
Cycles are used to calculate enthalpies of solution for ionic compounds from lattice enthalpies and enthalpies of hydration.
Students should be able to:
• perform calculations of an enthalpy change using these cycles.