Lattice Energy using Born Lande Equation Calculator

Lattice Energy Formula:

\[ U = -\frac{N_A \cdot M \cdot z^+ \cdot z^- \cdot e^2 \cdot (1 - \frac{1}{n})}{4 \pi \varepsilon_0 r_0} \]

Madelung Constant:

Charge of Cation:

Charge of Anion:

Born Exponent:

Distance of Closest Approach (m):

meters

Lattice Energy (J/mol):

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1. What is Lattice Energy using Born-Lande Equation?

Definition: The Born-Lande equation calculates the lattice energy of an ionic crystal based on electrostatic interactions between ions.

Purpose: It helps chemists and material scientists understand and predict the stability of ionic compounds.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ U = -\frac{N_A \cdot M \cdot z^+ \cdot z^- \cdot e^2 \cdot (1 - \frac{1}{n})}{4 \pi \varepsilon_0 r_0} \]

Where:

\( U \) — Lattice energy (J/mol)
\( N_A \) — Avogadro's number (6.022×10²³ mol⁻¹)
\( M \) — Madelung constant (depends on crystal structure)
\( z^+ \) — Charge of cation
\( z^- \) — Charge of anion
\( e \) — Electron charge (1.602×10⁻¹⁹ C)
\( n \) — Born exponent (typically 5-12)
\( \varepsilon_0 \) — Vacuum permittivity (8.85×10⁻¹² C²/J·m)
\( r_0 \) — Distance between ion centers (meters)

3. Importance of Lattice Energy Calculation

Details: Lattice energy helps predict solubility, melting points, and stability of ionic compounds. Higher lattice energy means more stable crystals.

4. Using the Calculator

Tips: Enter the Madelung constant (1.748 for NaCl), ion charges, Born exponent (typically 5-12), and interionic distance in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is the Madelung constant?
A: A dimensionless constant that depends on the crystal geometry, accounting for ion arrangement.

Q2: How do I determine the Born exponent?
A: It's typically 5-12, with 7-10 being common. It can be estimated from compressibility data.

Q3: What units should I use for distance?
A: Enter the distance in meters (1 Ångström = 1×10⁻¹⁰ m).

Q4: Why is lattice energy negative?
A: The negative sign indicates energy is released when the crystal forms from gaseous ions.

Q5: How accurate is the Born-Lande equation?
A: It provides good estimates but neglects van der Waals forces and zero-point energy.