Look up the lattice energies in table and calculate the energy change in kilojou

Question

Look up the lattice energies in table and calculate the energy change in kilojoules per mole for the formation of the following substances from their elements: (a) LiF(s) [the sublimation energy for Li(s) is +159.4kj/mol, the Ei for Li(g) is 250kj/mol, the Ea for F(g) is -328kj/mol, and the bond dissociation energy of F2(g) is +159kj/mol] (b) CaF2(s) [the sublimation energy for Ca(s) is +178.2kj/mol, Ei1 = +589.8kj/mol, and Ei2=+1145kj/mol.]

Explanation / Answer

Lattice energies, U(latt), cannot be measured directly, however they can be claculated by realising:- = all of which can be determined by other means. 1. Sublimation of Mg Mg(s) + Cl2(g) ==> Mg(g) + Cl2(g) .....?H°(sub) = 148 kJ mol¯¹ 2. Ionisations of Mg Mg(g) + Cl2(g) ==> Mg+(g) + e- + Cl2(g) .....IE(1) = 738 kJ mol¯¹ Mg+(g) + e- + Cl2(g) ==> Mg2+(g) + 2e- + Cl2(g) .....IE(2) = 1450 kJ mol¯¹ 3. Dissociation of Cl2 Mg2+(g) + 2e- + Cl2(g) ==> Mg2+(g) + 2e- + 2Cl(g) .....BD = 243 kJ mol¯¹ 4. Electron Affinities of Cl's Mg2+(g) + 2e- + 2Cl(g) ==> Mg2+(g) + e- + Cl¯(g) + Cl(g) .....EA = -349 kJ mol¯¹ Mg2+(g) + e- + Cl¯(g) + Cl(g) ==> Mg2+(g) + 2Cl¯(g) .....EA = -349 kJ mol¯¹ 5. Lattice Energy of MgCl2 Mg2+(g) + 2Cl¯(g) ==> MgCl2(s) .....U(latt) = your unknown 6. Formation of MgCl2 Mg(s) + Cl2(g) ==> MgCl2(s) .....?Hf° = -614.6 kJ mol¯¹ You should notice that overall equation #6 is the same as going stepwise from #1 through to #5. So in terms of energies (thermodynamics): ?Hf = ?H(sub) + IE(1) + IE(2) + BD + 2EA + U(latt) ==> U(latt) = ?Hf° - ?H°(sub) - IE(1) - IE(2) - BD - 2EA = -614.6 - 148 - 738 - 1450 - 243 + 2(349) kJ mol¯¹ = -2495.6 kJ mol¯¹ So the lattice engery of magnesium chloride is found to be -2495.6 kJ mol¯¹. This above is the Born-Haber cycle, an application of Hess' Law - look up these for more information.

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