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Lattice Energy using Born-Mayer equation Formula

GoLattice Energy using Born Lande Equation Formula

GoLattice Energy using Lattice Enthalpy Formula

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The Lattice Energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound. Check FAQs

U = \frac{- [Avaga-no] \cdot M \cdot z + \cdot z - \cdot ({[Charge-e]}^{2}) \cdot (1 - (\frac{ρ}{r 0}))}{4 \cdot π \cdot [Permitivity-vacuum] \cdot r 0}

U - Lattice Energy?M - Madelung Constant?z⁺ - Charge of Cation?z^- - Charge of Anion?ρ - Constant Depending on Compressibility?r₀ - Distance of Closest Approach?[Avaga-no] - Avogadro’s number?[Charge-e] - Charge of electron?[Permitivity-vacuum] - Permittivity of vacuum?π - Archimedes' constant?

Lattice Energy using Born-Mayer equation Example

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Here is how the Lattice Energy using Born-Mayer equation equation looks like with Values.

Here is how the Lattice Energy using Born-Mayer equation equation looks like with Units.

Here is how the Lattice Energy using Born-Mayer equation equation looks like.

3465.7632 = \frac{- 6E+23 \cdot 1.7 \cdot 4 \cdot 3 \cdot ({1.6E-19}^{2}) \cdot (1 - (\frac{60.44}{60}))}{4 \cdot 3.1416 \cdot 8.9E-12 \cdot 60}

3465.7632J/mol = \frac{- 6E+23 \cdot 1.7 \cdot 4C \cdot 3C \cdot ({1.6E-19C}^{2}) \cdot (1 - (\frac{60.44A}{60A}))}{4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 60A}

3465.7632 = \frac{- 6E+23 \cdot 1.7 \cdot 4 \cdot 3 \cdot ({1.6E-19}^{2}) \cdot (1 - (\frac{60.44}{60}))}{4 \cdot 3.1416 \cdot 8.9E-12 \cdot 60}

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Lattice Energy using Born-Mayer equation Solution

Follow our step by step solution on how to calculate Lattice Energy using Born-Mayer equation?

FIRST Step Consider the formula

U = \frac{- [Avaga-no] \cdot M \cdot z + \cdot z - \cdot ({[Charge-e]}^{2}) \cdot (1 - (\frac{ρ}{r 0}))}{4 \cdot π \cdot [Permitivity-vacuum] \cdot r 0}

Next Step Substitute values of Variables

∴

U = \frac{- [Avaga-no] \cdot 1.7 \cdot 4C \cdot 3C \cdot ({[Charge-e]}^{2}) \cdot (1 - (\frac{60.44A}{60A}))}{4 \cdot π \cdot [Permitivity-vacuum] \cdot 60A}

Next Step Substitute values of Constants

∴

U = \frac{- 6E+23 \cdot 1.7 \cdot 4C \cdot 3C \cdot ({1.6E-19C}^{2}) \cdot (1 - (\frac{60.44A}{60A}))}{4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 60A}

Next Step Convert Units

∴

U = \frac{- 6E+23 \cdot 1.7 \cdot 4C \cdot 3C \cdot ({1.6E-19C}^{2}) \cdot (1 - (\frac{6E-9m}{6E-9m}))}{4 \cdot 3.1416 \cdot 8.9E-12F/m \cdot 6E-9m}

Next Step Prepare to Evaluate

∴

U = \frac{- 6E+23 \cdot 1.7 \cdot 4 \cdot 3 \cdot ({1.6E-19}^{2}) \cdot (1 - (\frac{6E-9}{6E-9}))}{4 \cdot 3.1416 \cdot 8.9E-12 \cdot 6E-9}

Next Step Evaluate

∴

U = 3465.76323739326J/mol

LAST Step Rounding Answer

∴

U = 3465.7632J/mol

Lattice Energy using Born-Mayer equation Formula Elements

Variables

Constants

Lattice Energy

The Lattice Energy of a crystalline solid is a measure of the energy released when ions are combined to make a compound.

Symbol: U

Measurement: Molar EnthalpyUnit: J/mol

Note: Value can be positive or negative.

Formulas to find Lattice Energy

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.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Madelung Constant

Charge of Cation

The Charge of Cation is the positive charge over a cation with fewer electron than the respective atom.

Symbol: z⁺

Measurement: Electric ChargeUnit: C

Note: Value can be positive or negative.

Formulas to find Charge of Cation

Charge of Anion

The Charge of Anion is the negative charge over an anion with more electron than the respective atom.

Symbol: z^-

Measurement: Electric ChargeUnit: C

Note: Value can be positive or negative.

Formulas to find Charge of Anion

Constant Depending on Compressibility

The Constant Depending on Compressibility is a constant dependent on the compressibility of the crystal, 30 pm works well for all alkali metal halides.

Symbol: ρ

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Constant Depending on Compressibility

Distance of Closest Approach

Distance of Closest Approach is the distance to which an alpha particle comes closer to the nucleus.

Symbol: r₀

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Distance of Closest Approach

Avogadro’s number

Avogadro’s number represents the number of entities (atoms, molecules, ions, etc.) in one mole of a substance.

Symbol: [Avaga-no]

Value: 6.02214076E+23

Charge of electron

Charge of electron is a fundamental physical constant, representing the electric charge carried by an electron, which is the elementary particle with a negative electric charge.

Symbol: [Charge-e]

Value: 1.60217662E-19 C

Permittivity of vacuum

Permittivity of vacuum is a fundamental physical constant that describes the ability of a vacuum to permit the transmission of electric field lines.

Symbol: [Permitivity-vacuum]

Value: 8.85E-12 F/m

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Lattice Energy

Go Lattice Energy using Born Lande Equation

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

Go Lattice Energy using Lattice Enthalpy

U = ΔH - (p LE \cdot V m_LE)

Go Lattice Energy using Born-Lande equation using Kapustinskii Approximation

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}

Other formulas in Lattice Energy category

Go Born Exponent using Born Lande Equation

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

Go Electrostatic Potential Energy between pair of Ions

E Pair = \frac{- (q^{2}) \cdot ({[Charge-e]}^{2})}{4 \cdot π \cdot [Permitivity-vacuum] \cdot r 0}

Go Repulsive Interaction

E R = \frac{B}{{r 0}^{n born}}

Go Repulsive Interaction Constant

B = E R \cdot ({r 0}^{n born})

How to Evaluate Lattice Energy using Born-Mayer equation?

Lattice Energy using Born-Mayer equation evaluator 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 evaluate 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 evaluate Lattice Energy using Born-Mayer equation using this online evaluator? To use this online evaluator 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.

FAQs on Lattice Energy using Born-Mayer equation

What is the formula to find Lattice Energy using Born-Mayer equation?

The formula of Lattice Energy using Born-Mayer equation is expressed as 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). Here is an example- 3465.763 = (-[Avaga-no]*1.7*4*3*([Charge-e]^2)*(1-(6.044E-09/6E-09)))/(4*pi*[Permitivity-vacuum]*6E-09).

How to calculate Lattice Energy using Born-Mayer equation?

With Madelung Constant (M), Charge of Cation (z⁺), Charge of Anion (z^-), Constant Depending on Compressibility (ρ) & Distance of Closest Approach (r₀) we can find Lattice Energy using Born-Mayer equation using the formula - 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). This formula also uses Avogadro’s number, Charge of electron, Permittivity of vacuum, Archimedes' constant .

What are the other ways to Calculate Lattice Energy?

Here are the different ways to Calculate Lattice Energy-

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)

Can the Lattice Energy using Born-Mayer equation be negative?

Yes, the Lattice Energy using Born-Mayer equation, measured in Molar Enthalpy can be negative.

Which unit is used to measure Lattice Energy using Born-Mayer equation?

Lattice Energy using Born-Mayer equation is usually measured using the Joule per Mole[J/mol] for Molar Enthalpy. Kilojoule per Mole[J/mol] are the few other units in which Lattice Energy using Born-Mayer equation can be measured.

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Lattice Energy using Born-Mayer equation Formula

​GoLattice Energy using Born Lande Equation Formula

​GoLattice Energy using Lattice Enthalpy Formula

Lattice Energy using Born-Mayer equation Example

Lattice Energy using Born-Mayer equation Solution

Lattice Energy using Born-Mayer equation Formula Elements

Other Formulas to find Lattice Energy

Other formulas in Lattice Energy category

How to Evaluate Lattice Energy using Born-Mayer equation?

FAQs on Lattice Energy using Born-Mayer equation

Variable Name

GoLattice Energy using Born Lande Equation Formula

GoLattice Energy using Lattice Enthalpy Formula