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Lattice Energy using Born-Lande equation using Kapustinskii Approximation Calculator

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Ionic Bonding Covalent Bonding Electronegativity

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Lattice Energy

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Distance of Closest Approach Madelung Constant

✖The Number of Ions is the number of ions formed from one formula unit of the substance.ⓘ Number of Ions [N_ions]			+10% -10%
✖The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom.ⓘ Charge of Cation [z⁺]			+10% -10%
✖The Charge of Anion is the negative charge over an anion with more electron than the respective atom.ⓘ Charge of Anion [z^-]			+10% -10%
✖The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.ⓘ Born Exponent [n_born]			+10% -10%
✖Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.ⓘ Distance of Closest Approach [r₀]			+10% -10%

✖The Lattice Energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound.ⓘ Lattice Energy using Born-Lande equation using Kapustinskii Approximation [U]

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Formula

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Lattice Energy using Born-Lande equation using Kapustinskii Approximation

Formula

U = - \frac{[Avaga-no] \cdot N ions \cdot 0.88 \cdot z + \cdot z - \cdot ({[Charge-e]}^{2}) \cdot (1 - (\frac{1}{n born}))}{4 \cdot π \cdot [Permitivity-vacuum] \cdot r 0}

Example

3647.696 J/mol = - \frac{[Avaga-no] \cdot 2 \cdot 0.88 \cdot 4 C \cdot 3 C \cdot ({[Charge-e]}^{2}) \cdot (1 - (\frac{1}{0.9926}))}{4 \cdot π \cdot [Permitivity-vacuum] \cdot 60 A}

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Lattice Energy using Born-Lande equation using Kapustinskii Approximation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Lattice Energy = -([Avaga-no]*Number of Ions*0.88*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)
U = -([Avaga-no]*N_ions*0.88*z⁺*z^-*([Charge-e]^2)*(1-(1/n_born)))/(4*pi*[Permitivity-vacuum]*r₀)
This formula uses 4 Constants, 6 Variables

Constants Used

[Permitivity-vacuum] - Permittivity of vacuum Value Taken As 8.85E-12
[Avaga-no] - Avogadro’s number Value Taken As 6.02214076E+23
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Lattice Energy - (Measured in Joule per Mole) - The Lattice Energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound.
Number of Ions - The Number of Ions is the number of ions formed from one formula unit of the substance.
Charge of Cation - (Measured in Coulomb) - The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom.
Charge of Anion - (Measured in Coulomb) - The Charge of Anion is the negative charge over an anion with more electron than the respective atom.
Born Exponent - The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.
Distance of Closest Approach - (Measured in Meter) - Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.

STEP 1: Convert Input(s) to Base Unit

Number of Ions: 2 --> No Conversion Required
Charge of Cation: 4 Coulomb --> 4 Coulomb No Conversion Required
Charge of Anion: 3 Coulomb --> 3 Coulomb No Conversion Required
Born Exponent: 0.9926 --> No Conversion Required
Distance of Closest Approach: 60 Angstrom --> 6E-09 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U = -([Avaga-no]*N_ions*0.88*z⁺*z^-*([Charge-e]^2)*(1-(1/n_born)))/(4*pi*[Permitivity-vacuum]*r₀) --> -([Avaga-no]*2*0.88*4*3*([Charge-e]^2)*(1-(1/0.9926)))/(4*pi*[Permitivity-vacuum]*6E-09)

Evaluating ... ...

U = 3647.69619277376

STEP 3: Convert Result to Output's Unit

3647.69619277376 Joule per Mole --> No Conversion Required

FINAL ANSWER

3647.69619277376 ≈ 3647.696 Joule per Mole <-- Lattice Energy

(Calculation completed in 00.004 seconds)

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< Lattice Energy Calculators

Lattice Energy using Born Lande Equation

Go Lattice Energy = -([Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)

Born Exponent using Born Lande Equation

Go Born Exponent = 1/(1-(-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/([Avaga-no]*Madelung Constant*([Charge-e]^2)*Charge of Cation*Charge of Anion))

Electrostatic Potential Energy between pair of Ions

Go Electrostatic Potential Energy between Ion Pair = (-(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)

Repulsive Interaction

Go Repulsive Interaction = Repulsive Interaction Constant/(Distance of Closest Approach^Born Exponent)

Lattice Energy using Born-Lande equation using Kapustinskii Approximation Formula

What is Born–Landé equation?

The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound. In 1918 Max Born and Alfred Landé proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice and a repulsive potential energy term. The ionic lattice is modeled as an assembly of hard elastic spheres which are compressed together by the mutual attraction of the electrostatic charges on the ions. They achieve the observed equilibrium distance apart due to a balancing short range repulsion.

How to Calculate Lattice Energy using Born-Lande equation using Kapustinskii Approximation?

Lattice Energy using Born-Lande equation using Kapustinskii Approximation calculator uses Lattice Energy = -([Avaga-no]*Number of Ions*0.88*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach) to calculate the Lattice Energy, The lattice energy using Born-Lande equation using Kapustinskii approximation of a crystalline solid is a measure of the energy released when ions are combined to make a compound. Lattice Energy is denoted by U symbol.

How to calculate Lattice Energy using Born-Lande equation using Kapustinskii Approximation using this online calculator? To use this online calculator for Lattice Energy using Born-Lande equation using Kapustinskii Approximation, enter Number of Ions (N_ions), Charge of Cation (z⁺), Charge of Anion (z^-), Born Exponent (n_born) & Distance of Closest Approach (r₀) and hit the calculate button. Here is how the Lattice Energy using Born-Lande equation using Kapustinskii Approximation calculation can be explained with given input values -> 3647.696 = -([Avaga-no]*2*0.88*4*3*([Charge-e]^2)*(1-(1/0.9926)))/(4*pi*[Permitivity-vacuum]*6E-09).

FAQ

What is Lattice Energy using Born-Lande equation using Kapustinskii Approximation?

The lattice energy using Born-Lande equation using Kapustinskii approximation of a crystalline solid is a measure of the energy released when ions are combined to make a compound and is represented as U = -([Avaga-no]*N_ions*0.88*z⁺*z^-*([Charge-e]^2)*(1-(1/n_born)))/(4*pi*[Permitivity-vacuum]*r₀) or Lattice Energy = -([Avaga-no]*Number of Ions*0.88*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach). The Number of Ions is the number of ions formed from one formula unit of the substance, The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom, The Charge of Anion is the negative charge over an anion with more electron than the respective atom, The Born Exponent is a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically & Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.

How to calculate Lattice Energy using Born-Lande equation using Kapustinskii Approximation?

The lattice energy using Born-Lande equation using Kapustinskii approximation of a crystalline solid is a measure of the energy released when ions are combined to make a compound is calculated using Lattice Energy = -([Avaga-no]*Number of Ions*0.88*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach). To calculate Lattice Energy using Born-Lande equation using Kapustinskii Approximation, you need Number of Ions (N_ions), Charge of Cation (z⁺), Charge of Anion (z^-), Born Exponent (n_born) & Distance of Closest Approach (r₀). With our tool, you need to enter the respective value for Number of Ions, Charge of Cation, Charge of Anion, Born Exponent & Distance of Closest Approach and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Lattice Energy?

In this formula, Lattice Energy uses Number of Ions, Charge of Cation, Charge of Anion, Born Exponent & Distance of Closest Approach. We can use 3 other way(s) to calculate the same, which is/are as follows -

Lattice Energy = -([Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(1/Born Exponent)))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)
Lattice Energy = (-[Avaga-no]*Madelung Constant*Charge of Cation*Charge of Anion*([Charge-e]^2)*(1-(Constant Depending on Compressibility/Distance of Closest Approach)))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)
Lattice Energy = Lattice Enthalpy-(Pressure Lattice Energy*Molar Volume Lattice Energy)

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