Thermochemistry : 9.3 Born-Haber Cycle

• First Ionization Energy (IE₁)
  • Energy required for 1 mol of gaseous atom to lose 1 mol of electrons.
    
    
• Affinity Electron (EA) 
  • Energy change that occurs when 1 mol of gaseous atom gains 1 mol of electrons.
    
    
• Lattice Energy
  • Energy change when 1 mol of solid ionic compound formed from its gaseous ions
    
    
• Magnitude Lattice Energy
  • Indicates the strength of ionic bonding
  • The more negative lattice energy, the stronger ionic bonding
  • It influences : 
    • Melting point
    • Hardness
    • Solubility
      
      
• Determining Lattice Energy
  • Lattice energy cannot be measured directly.
    • Can be calculated by Born-Haber cycle
      
      
• Born-Haber Cycle
  • A series of chosen steps from elements to ionic compound for which all the enthalpies are known , except lattice energy.
    ΔH_f = sum of ΔH^o for multistep path
  • Calculation Step
  
  
  Example : LiF
  
  
  Overall : Formation of LiF compound
      Li(s) + ½ F₂(g)     LiF(s)        ΔH^o
  _overall = 617 kJ
          ΔH^o_overall = ΔH^o_f

    Step 1 :- atomization of lithium

        Li(s)     Li(g)                ΔH_f = 161 kJ

            ΔH₁^o = ∆H^o_atom or ∆H^o _sublim

    Step 2 :- atomization of fluorine

        ½ F₂(g)     F(g)             ∆H₂^o = 79.5 kJ

            ∆H₂^o = ∆H^o _atom

    Step 3 :- ionization of lithium atom

        Li(g)         Li⁺(g) + e^-         ∆H₃^o = 520 kJ

            ∆H₃^o = IE₁

    Step 4 :- Electron affinity of F atom

        F(g) + e^-     F^- (g)            ∆H₄^o = -328 kJ

            ∆H₄^o = EA

    Step 5 :- Formation of LiF(s) from its gaseous ions

        Li⁺(g) + F^-(g)         LiF(s)        ∆H₅^o = ?

            ∆H₅^o = ∆H^o_lattice of LiF

• Factors Affecting Lattice Energy
  • From Coulomb's Law

                             ΔE  α  (n⁺Q⁺)(n^-Q^-)

                                                    ---------------------------                                                          

                                                d

∆H : electrostatic energy

n⁺ : number
of positive charge

n^- : number of negative charge 

Q⁺ : electrostatic charge (+)

Q^- : electrostatic charge (-)

d : distance between the ions = r⁺ + r^- (radius of ions)

• Ionic bond strength increase when
  • Q, charge (Q) increase
  • Size of atoms (d) decrease

• Hydration Process of Ionic Crystal in Water
  • 2 main process 
    • Breaking lattice energy of ionic crystal
    • Solvation (hydration)