Lattice Energy & Solubility Suite

Lattice Energy & Born–Haber Cycle

Lattice Energy ($U$) is the energy released when gaseous ions combine to form one mole of a solid ionic crystal. To find this value, we use the Born–Haber Cycle, which links various thermodynamic processes through Hess's Law.

$$\Delta H_f^\circ = \Delta H_{sub} + IE + \frac{1}{2}D + EA + U_{lattice}$$

$\Delta H_f^\circ$: Formation | $U$: Lattice Energy | $EA$: Electron Affinity

Lattice Energy Calculation

Arithmetic Support: Use *, ^, and - (e.g., 10*2 Meaning 10 Multiply By 2 And 10^2 Meaning 10² -411 for formation).

Heat of Formation ($\Delta H_f$)

Sublimation ($\Delta H_s$)

Bond Dissociation ($D$)

Ionization Energy ($IE$)

Electron Affinity ($EA$)

Solubility Prediction

Compares Lattice Stability vs Hydration Strength

Total Hydration Energy (kJ/mol)

Lattice Energy ($U$) (kJ/mol)

The Born–Landé Equation

While the Born–Haber cycle is based on experimental enthalpies, the **Born–Landé equation** allows for the theoretical calculation of lattice energy based on electrostatic forces and crystal geometry.

$$E = -\frac{N_A M Z^+ Z^- e^2}{4\pi\epsilon_0 r_0} \left( 1 - \frac{1}{n} \right)$$

Where $N_A$ is Avogadro's constant, $M$ is the Madelung constant, $Z$ are ion charges, $r_0$ is the equilibrium distance, and $n$ is the Born exponent (ranging from 5 to 12).

Madelung Constant Lookup ($M$)

The Madelung constant accounts for the 3D geometry of the crystal lattice in the Born-Landé equation.

Crystal Structure	Example	Madelung Constant ($M$)
Rock Salt	NaCl	1.74756
Cesium Chloride	CsCl	1.76267
Zinc Blende	ZnS	1.63806
Fluorite	CaF2	2.51939
Rutile	TiO2	2.40800

Lattice Energy Research & Trends

In solid-state physics, lattice energy predicts the stability of perovskites used in solar cells. Stronger lattice energy usually correlates to lower solubility and higher thermal resistance.

Compound	Lattice Energy (kJ/mol)	Radius Comparison	Melting Point (°C)
NaCl	-786	Standard	801
LiF	-1030	Very Small	845
MgO	-3795	Divalent (+2/-2)	2852
Al2O3	-15916	Trivalent	2072

Solved Practice Example

Problem: Calculate $U$ for $KCl$ given $\Delta H_f = -437$, $\Delta H_s = 89$, $IE = 419$, $1/2 D = 121$, $EA = -349$.
Solution: $U = \Delta H_f - (\Delta H_s + IE + 0.5D + EA)$
$U = -437 - (89 + 419 + 121 - 349) = -717 \text{ kJ/mol}$

Advanced Chemistry Calculators