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Lattice Energy using Born-Mayer equation Calculator

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Lattice Energy

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Distance of Closest Approach Madelung Constant

✖The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges.ⓘ Madelung Constant [M]			+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 Constant Depending on Compressibility is a constant dependent on the compressibility of the crystal, 30 pm works well for all alkali metal halides.ⓘ Constant Depending on Compressibility [ρ]			+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-Mayer equation [U]

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Lattice Energy using Born-Mayer equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
U = (-[Avaga-no]*M*z⁺*z^-*([Charge-e]^2)*(1-(ρ/r₀)))/(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.
Madelung Constant - The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges.
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.
Constant Depending on Compressibility - (Measured in Meter) - The Constant Depending on Compressibility is a constant dependent on the compressibility of the crystal, 30 pm works well for all alkali metal halides.
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

Madelung Constant: 1.7 --> No Conversion Required
Charge of Cation: 4 Coulomb --> 4 Coulomb No Conversion Required
Charge of Anion: 3 Coulomb --> 3 Coulomb No Conversion Required
Constant Depending on Compressibility: 60.44 Angstrom --> 6.044E-09 Meter (Check conversion here)
Distance of Closest Approach: 60 Angstrom --> 6E-09 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U = (-[Avaga-no]*M*z⁺*z^-*([Charge-e]^2)*(1-(ρ/r₀)))/(4*pi*[Permitivity-vacuum]*r₀) --> (-[Avaga-no]*1.7*4*3*([Charge-e]^2)*(1-(6.044E-09/6E-09)))/(4*pi*[Permitivity-vacuum]*6E-09)

Evaluating ... ...

U = 3465.76323739326

STEP 3: Convert Result to Output's Unit

3465.76323739326 Joule per Mole --> No Conversion Required

FINAL ANSWER

3465.76323739326 ≈ 3465.763 Joule per Mole <-- Lattice Energy

(Calculation completed in 00.004 seconds)

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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< Lattice Energy Calculators

Lattice Energy using Born Lande Equation

LaTeX 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

LaTeX 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

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

Repulsive Interaction

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

Lattice Energy using Born-Mayer equation Formula

LaTeX Go

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-Mayer equation?

Lattice Energy using Born-Mayer equation calculator uses 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) to calculate the Lattice Energy, The Lattice Energy using Born-Mayer equation is an equation that is used to calculate the lattice energy of a crystalline ionic compound. It is a refinement of the Born–Landé equation by using an improved repulsion term. Lattice Energy is denoted by U symbol.

How to calculate Lattice Energy using Born-Mayer equation using this online calculator? To use this online calculator for Lattice Energy using Born-Mayer equation, enter Madelung Constant (M), Charge of Cation (z⁺), Charge of Anion (z^-), Constant Depending on Compressibility (ρ) & Distance of Closest Approach (r₀) and hit the calculate button. Here is how the Lattice Energy using Born-Mayer equation calculation can be explained with given input values -> 3465.763 = (-[Avaga-no]*1.7*4*3*([Charge-e]^2)*(1-(6.044E-09/6E-09)))/(4*pi*[Permitivity-vacuum]*6E-09).

FAQ

What is Lattice Energy using Born-Mayer equation?

The Lattice Energy using Born-Mayer equation is an equation that is used to calculate the lattice energy of a crystalline ionic compound. It is a refinement of the Born–Landé equation by using an improved repulsion term and is represented as U = (-[Avaga-no]*M*z⁺*z^-*([Charge-e]^2)*(1-(ρ/r₀)))/(4*pi*[Permitivity-vacuum]*r₀) or 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). The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges, 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 Constant Depending on Compressibility is a constant dependent on the compressibility of the crystal, 30 pm works well for all alkali metal halides & Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.

How to calculate Lattice Energy using Born-Mayer equation?

The Lattice Energy using Born-Mayer equation is an equation that is used to calculate the lattice energy of a crystalline ionic compound. It is a refinement of the Born–Landé equation by using an improved repulsion term is calculated using 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). To calculate Lattice Energy using Born-Mayer equation, you need Madelung Constant (M), Charge of Cation (z⁺), Charge of Anion (z^-), Constant Depending on Compressibility (ρ) & Distance of Closest Approach (r₀). With our tool, you need to enter the respective value for Madelung Constant, Charge of Cation, Charge of Anion, Constant Depending on Compressibility & 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 Madelung Constant, Charge of Cation, Charge of Anion, Constant Depending on Compressibility & 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 = Lattice Enthalpy-(Pressure Lattice Energy*Molar Volume Lattice Energy)
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)

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