1. Born-Haber Cycle Section 15.2 (AHL)

2. Lattice Enthalpy Of an ionic crystal: the heat energy absorbed (at constant pressure) when 1 mol of solid ionic compound is decomposed to form gaseous ions separated to an infinite distance from each other The reverse of lattice enthalpy is the heat energy released when 1 mol of an ionic solid is formed from gaseous ions

3. More Lattice energies are a measure of the stability of a crystal The greater the lattice energy, the more stable the lattice, the higher the melting point and boiling point

4. Electron Affinity The first electron affinity ( Δ H θ EA(1) ) is the energy released when 1 mol of gaseous atoms accepts 1 mol of electrons to form singly charged negative ions 2 nd electron affinity, ( Δ H θ EA(2) ) is the energy absorbed when 1 mol of gaseous ions with a single negative charge accept 1 mol of electrons

5. Example Cl (g) + e - → Cl - (g) Δ H θ EA(1) = -364 kJ mol -1 O - (g) + e - → O 2- (g) Δ H θ EA(2) = +844 kJ mol - 1 The 2 nd electron affinity is always endothermic because energy is required to overcome the mutual repulsion between negatively charged oxygen ion and the electron

6. Enthalpy Change of Atomization Standard enthalpy change of atomization is the enthalpy change required to produce one mole of gaseous atoms of an element from the element in the standard state Na (s) → Na (g) Δ H θ at = +103 kJ mol -1

7. Lattice Enthalpies of Ionic Compounds Magnitude of the lattice enthalpy depends upon the nature of the ions involved The greater the charge on the ions, the greater the electrostatic attraction, the greater the lattice enthalpy and vice versa The larger the ions, the greater the separation of charges, and the lower the lattice enthalpy and vice versa

8. Example

9. Born-Haber Cycle An indirect way to measure lattice enthalpies

10. Example of Na (s) + ½Cl 2(g) → NaCl Enthalpy of formation of NaCl = -411 kJ mol -1 Enthalpy of atomization of Na = + 103 kJ mol -1 Enthalpy of atomization of Cl = + 121 kJ mol -1 Electron affinity of Cl = -364 kJ mol -1 Ionization energy of Na = + 500 kJ mol -1 Enthalpies of atomization + electron affinity + ionization energy = enthalpy of formation + lattice enthalpy

12. Calculations 103 + (+121) + (-364) + (+500) = (-411) + L.E. 360 = -411 + L.E. 771 = L.E. Lattice enthalpy is +771 kJ mol -1

13. Example 2 Use a Born-Haber cycle to calculate the value of the lattice enthalpy for MgCl 2 Enthalpy of atomization of Mg = + 147 kJ mol -1 Enthalpy of atomization for Cl = 2 x +121 kJ mol -1 1 st ionization energy for Mg = +736 kJ mol -1 2 nd ionization energy for Mg = +1451 kJ mol -1 Electron affinity for Cl = 2 x -364 kJ mol -1

14. Continued Enthalpy of formation of MgCl 2 = -641 kJ mol -1 Enthalpies of atomization + electron affinity + ionization energies = enthalpy of formation + lattice energy + 147 + 2(121) + 736 + 1451 + 2 (-364) = -641 + L.E. 1848 = -641 + L.E. Lattice enthalpy is +2489 kJ mol -1

15. Experimental vs Theoretical Lattice Enthalpies The Born-Haber cycle provides a way to indirectly measure through experimental techniques An ionic model can be used to calculate theoretical lattice enthalpies The electrostatic attractive and repulsive forces between the ions can be summed Sometimes it works and sometimes it doesn't

16. Comparison

17. Explanation The more “purely” ionic, the closer the values are to each other When the bond is partially covalent, this strengthens the bond and the actual lattice enthalpy is higher The closer the EN values, the lower the difference between the two values, which indicates covalent character will occur in the bonding. NaCl has an electronegativity difference of 2.1 while AgI is 0.6, hence NaCl values of calculated and actual lattice enthalpies are close, while the values for AgI are not as similar.