Lattice Energy using Born-Mayer equation Calculator

Lattice Energy Formula:

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

Madelung Constant:

Charge of Cation:

Charge of Anion:

Constant Depending on Compressibility (ρ):

Distance of Closest Approach (r₀):

Lattice Energy (J/mol):

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1. What is Lattice Energy using Born-Mayer equation?

Definition: The Born-Mayer equation calculates the lattice energy of ionic crystals, which is the energy released when gaseous ions combine to form a solid ionic compound.

Purpose: This calculation is essential in materials science and chemistry for understanding ionic compound stability and properties.

2. How Does the Calculator Work?

The calculator uses the Born-Mayer equation:

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

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 (unitless)
\( z^- \) — Charge of anion (unitless)
\( e \) — Elementary charge (1.602 × 10⁻¹⁹ C)
\( \rho \) — Constant depending on compressibility (typically 30 pm)
\( r_0 \) — Distance of closest approach between ions (pm)
\( \varepsilon_0 \) — Permittivity of free space (8.854 × 10⁻¹² F/m)

3. Importance of Lattice Energy Calculation

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

4. Using the Calculator

Tips: Enter the Madelung constant (1.748 for NaCl structure), ion charges, compressibility constant (default 30 pm), and interionic distance (in picometers).

5. Frequently Asked Questions (FAQ)

Q1: What is the Madelung constant?
A: It's a geometric factor that accounts for the arrangement of ions in the crystal lattice. Common values are 1.748 for NaCl, 1.638 for CsCl.

Q2: Why is the compressibility constant typically 30 pm?
A: This empirical value works well for alkali metal halides, accounting for electron cloud repulsion.

Q3: How do I find the distance of closest approach?
A: It's the sum of the ionic radii of the cation and anion, often available in chemistry reference tables.

Q4: Can I use this for covalent compounds?
A: No, the Born-Mayer equation is specifically for ionic compounds with significant charge separation.

Q5: How accurate is this calculation?
A: It provides a good estimate but doesn't account for all quantum mechanical effects. Experimental values may differ slightly.