LATTICE ENERGI (Uo), Study notes of Physics

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pranjoto utomo

Definition and Symbol

• The energy given off when oppositely charged ions in the gas phase come together to form a solid.
• Symbol = Uo
• Signed by (-)
• The greater lattice energy:
  • Cation-anion distance <<<
  • Ions charge >>>

Born-Lande Equation



n

x 1 -

4 r

N.Z .Z .M.e

U

o o

• 2 o



n

x 1 -

r

M.Z .Z

x

N.e

U

o

o

2 o

• N = Avogadro number = 6.02x10^23
• Z+^ = positive charge
• Z-^ = negative charge
• M = Madelung constant
• e-^ = electron charge = 1.6021x10-19C

Madelung Constant

Lattice M

Rock salt 1.

CsCl 1.

Zinc blende 1.

Fluorite 2.

Compressibility factor

Cl [ Ar] n 9

Na [ Ne] n 7

18

17

11 10

Element n He 5 Ne 7 Ar, Cu 9 Kr, Ag 10 Xe, Au 12

 8

  2

7 9 n

Kapustinskii Equation



o o

o

r

x 1 -

r

120200. .Z .Z

U

 = number of ions per molecule  NaCl = 2 Z+^ = positive charge Z-^ = negative charge ro = cation-anion equilibrium distance = r+ + r-

Comparison

• Lattice energy of NaCl
  • Experiment = -755 kJ.mol-
  • Born-Lande = -770 kJ.mol-
  • Kapustinskii = -753 kJ.mol-

Example

Problem 1:

Sketch the born-haber cycles and calculate the enthalpy formation of sodium bromide: Na(s)

• ½ Br 2 (g) → NaBr(s)

• Hsublimation (Na) = 107 kJ.mol-
• Hdissociation (Br) = 194 kJ.mol-
• Ionization energy (Na) = 496 kJ.mol-
• Electron affinity (Br) = -325 kJ.mol-
• Lattice energy (NaBr) = -742 kJ.mol-

unbonded gaseous ions

Breaking bonds Forming gases

Forming (+) & (-) ions

Lattice energy

H

Na(s) + ½ Br 2 (g) NaBr(s)

Na+(g) + Br-(g)

metal + non-metal ionic compound

The enthalpy formation of NaBr:

Hof NaBr

=[(Hsub+ IE)Na+(Hdiss+(-EA) (^) Br]+(-Uo) (^) NaBr = (Hsub+ IE)Na + (Hdiss- EA)Br – (Uo)NaBr = 107 + 496 + 97 - 325 – 742 = -367 kJ.mol-

The more stable compound

• Why sodium chloride is NaCl not NaCl 2?

NaCl NaCl 2 IE 1 +496 kJ.mol-1^ +496 kJ.mol- IE 2 +4562 kJ.mol- Uo -787 kJ.mol-1^ -2155 kJ.mol- Hof -441 kJ.mol-1^ +2555 kJ.mol-

• NaCl 2
  • The lattice energy can not compensate the first and second ionization energy
  • The enthalpy formation is positive
  • Unstable

• Problem 2:
• Predict the stability of the ArCl molecule, from the reaction: Ar(g) + ½ Cl 2 (g) →ArCl (s)
• if:
  • ∆H dissociation of Cl 2 = 243 kJ.mol-
  • Electron Affinity of Cl-^ = -349 kJ.mol-
  • 1-st IE of Ar = 1526.3 kJ.mol-
  • Uo of ArCl(s) = -703 kJ.mol-