2 Born Haber cycles

BORN HABER CYCLES 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 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. Born Haber cycle: calcium oxide CaO (s) Ca (s) + ½ O2 (g) Ca (g) + ½ O2 (g) ∆Ea1H (O) ∆atH(Ca) ∆atH(O) ∆LEH ∆fH (CaO) + e- + O- Ca (g) 2+ (g) Ca + O (g) 2+ (g) + 2eCa2+ (g) + 2e- + ½ O2 (g) Ca + (g) + e- + ½ O2 (g)) ∆IE1H(Ca) ∆IE2H (Ca) Ca2+ (g) + O2- (g) ∆Ea1H(O) 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