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LATTICE ENERGI (Uo), Study notes of Physics

Born-Lande equation. –Crystal structure are known. • Kapustinskii equation ... Sketch the born-haber cycles and calculate the.

Typology: Study notes

2021/2022

Uploaded on 09/12/2022

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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-