Lattice Energy Using Born Lande Equation Using Kapustinskii Approximation Calculator

Born-Lande Equation Using Kapustinskii Approximation:

\[ U = -\frac{[Avaga-no] \times Nions \times 0.88 \times z+ \times z- \times ([Charge-e]^2) \times (1 - \frac{1}{nborn})}{4 \times \pi \times [Permitivity-vacuum] \times r0} \]

Number of Ions:

ions

Charge of Cation:

Charge of Anion:

Born Exponent:

unitless

Distance of Closest Approach:

Lattice Energy:

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1. What is the Born-Lande Equation Using Kapustinskii Approximation?

The Born-Lande equation with Kapustinskii approximation calculates the lattice energy of ionic compounds. It represents the energy released when gaseous ions combine to form a crystalline solid, accounting for electrostatic interactions and repulsive forces.

2. How Does the Calculator Work?

The calculator uses the Born-Lande equation with Kapustinskii approximation:

\[ U = -\frac{[Avaga-no] \times Nions \times 0.88 \times z+ \times z- \times ([Charge-e]^2) \times (1 - \frac{1}{nborn})}{4 \times \pi \times [Permitivity-vacuum] \times r0} \]

Where:

\( [Avaga-no] \) — Avogadro's number (6.022 × 10²³ mol⁻¹)
\( Nions \) — Number of ions in the formula unit
\( z+ \) — Charge of cation (Coulomb)
\( z- \) — Charge of anion (Coulomb)
\( [Charge-e] \) — Elementary charge (1.602 × 10⁻¹⁹ C)
\( nborn \) — Born exponent (5-12)
\( \pi \) — Mathematical constant pi
\( [Permitivity-vacuum] \) — Permittivity of vacuum (8.85 × 10⁻¹² C²/J·m)
\( r0 \) — Distance of closest approach (meters)

Explanation: The equation calculates the electrostatic energy of an ionic crystal lattice, accounting for both attractive and repulsive forces between ions.

3. Importance of Lattice Energy Calculation

Details: Lattice energy is crucial for understanding the stability of ionic compounds, predicting solubility, and explaining melting points and hardness of crystalline materials.

4. Using the Calculator

Tips: Enter the number of ions, cation and anion charges, Born exponent (typically 5-12), and distance of closest approach in meters. All values must be positive and within reasonable ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the Born exponent?
A: The Born exponent accounts for the repulsive forces between electron clouds of adjacent ions and typically ranges from 5 to 12 depending on the ionic compound.

Q2: How is the distance of closest approach determined?
A: It's the sum of the ionic radii of the cation and anion, which can be obtained from crystallographic data or standard tables of ionic radii.

Q3: Why use the Kapustinskii approximation?
A: The Kapustinskii approximation simplifies the calculation by using a constant factor (0.88) that accounts for the crystal structure, making it applicable to various ionic compounds.

Q4: What are typical lattice energy values?
A: Lattice energies typically range from 600-4000 kJ/mol for common ionic compounds, with higher values indicating stronger ionic bonding.

Q5: What are the limitations of this equation?
A: The equation assumes perfect ionic character and may not accurately represent compounds with significant covalent character or complex crystal structures.