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Schätzen Sie ionic lattice energy unter Verwendung von the Born-Landé equation. Kostenloser Online chemistry Rechner.
Lattice Energy (U)
-756 kJ/mol
Lattice Energy (U) vs Cation Charge (z⁺)
Formel
Born-Landé Equation for Lattice Energy
Formula
U = −(A × N_A × e² × z⁺ × z⁻) / (4πε₀ × r₀) × (1 − 1/n)
Simplified with constants combined: U = −(A × 1389.4 × z⁺ × z⁻ / r₀) × (1 − 1/n)
Where r₀ is in angstroms (pm/100), and 1389.4 kJ·Å/mol combines N_A, e², and 4πε₀.
Where:
Lösungsbeispiel
NaCl: z⁺ = 1, z⁻ = 1, r₀ = 281 pm, A = 1.748, n = 8.
- 01U = -(A × 1389.4 × z⁺ × z⁻ / r₀) × (1 - 1/n)
- 02r₀ = 281 pm = 2.81 Å
- 03U = -(1.748 × 1389.4 × 1 × 1 / 2.81) × (1 - 1/8)
- 04U = -(864.2) × (0.875)
- 05U = -756 kJ/mol
Häufig Gestellte Fragen
What is lattice energy?
Lattice energy is the energy released when gaseous ions combine to form one mole of an ionic solid. Higher lattice energy means a more stable crystal.
What is the Madelung constant?
The Madelung constant accounts for the geometry of the crystal. For NaCl structure it is 1.748, for CsCl it is 1.763, for ZnS (zinc blende) it is 1.638.
What factors increase lattice energy?
Higher ion charges and shorter interionic distances increase lattice energy. MgO (2+, 2-) has much higher lattice energy than NaCl (1+, 1-).
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