3.091 – Introduction to Solid State Chemistry Lecture Notes No. 2 ...

LN–2E +* e 2o(Coul)) e 24pe o r o n4pe o r oE o(Coul)+* e 21 * 1 4pe o r onFor a “molar” crystal with ionic charges Q 1 and Q 2 , the molar ΔE o(Coul) is thus given as:+* MN AQ 1Q 2eDE 2 * 1 cryst1 4pe o r onHere M and N A stand, as indicated above, for the conventional terms, the Madelungconstant and Avogadro’s number.]For the present system (NaCl):ΔE cryst = –777 kJ/mole.Now considering reactions (1) through (5):ΔH Total = –414 kJ/molewhich is identical with the value experimentally determined and given for the reaction:Na (metal) + Cl 2 (gas) ! NaCl (solid)ΔH Reaction = –414 kJ/moleIn the Haber-Born cycle, the reaction energy (ΔH) associated with the formation of NaClfrom Na + Cl 2 may be summarized as:ΔH = E.I. + E.A. + ΔH V + 1/2 E.D. + ΔH crystΔH, the heat of reaction, may thus be obtained from the energetics of the steps leadingto the end product. In most instances, however, the reaction energy (ΔH) is determinedexperimentally in a calorimeter and the Haber-Born cycle is used to obtain the value ofΔE cryst or E.A., which are both extremely hard to come by.11