Number of Ions using Kapustinskii Approximation Calculator

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Ionic Bonding

Covalent Bonding

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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]

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✖The Number of Ions is the number of ions formed from one formula unit of the substance.ⓘ Number of Ions using Kapustinskii Approximation [N_ions]

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Formula

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Number of Ions using Kapustinskii Approximation

Formula

`"N"_{"ions"} = "M"/0.88`

Example

`"1.931818"="1.7"/0.88`

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Number of Ions using Kapustinskii Approximation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Ions = Madelung Constant/0.88
N_ions = M/0.88
This formula uses 2 Variables

Variables Used

Number of Ions - The Number of Ions is the number of ions formed from one formula unit of the substance.
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.

STEP 1: Convert Input(s) to Base Unit

Madelung Constant: 1.7 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_ions = M/0.88 --> 1.7/0.88

Evaluating ... ...

N_ions = 1.93181818181818

STEP 3: Convert Result to Output's Unit

1.93181818181818 --> No Conversion Required

FINAL ANSWER

1.93181818181818 ≈ 1.931818 <-- Number of Ions

(Calculation completed in 00.004 seconds)

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Created by Prerana Bakli

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

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K J Somaiya College of science (K J Somaiya), Mumbai

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< 25 Lattice Energy Calculators

Lattice Energy using Born-Mayer equation

Go 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)

Constant depending on compressibility using Born-Mayer equation

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

Minimum Potential Energy of Ion

Go Minimum Potential Energy of Ion = ((-(Charge^2)*([Charge-e]^2)*Madelung Constant)/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach))+(Repulsive Interaction Constant/(Distance of Closest Approach^Born Exponent))

Repulsive Interaction Constant using Total Energy of Ion

Go Repulsive Interaction Constant = (Total Energy of Ion-(-(Madelung Constant*(Charge^2)*([Charge-e]^2))/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)))*(Distance of Closest Approach^Born Exponent)

Total Energy of Ion given Charges and Distances

Go Total Energy of Ion = ((-(Charge^2)*([Charge-e]^2)*Madelung Constant)/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach))+(Repulsive Interaction Constant/(Distance of Closest Approach^Born Exponent))

Lattice Energy using Born-Lande equation using Kapustinskii Approximation

Go 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)

Born Exponent using Born-Lande equation without Madelung Constant

Go Born Exponent = 1/(1-(-Lattice Energy*4*pi*[Permitivity-vacuum]*Distance of Closest Approach)/([Avaga-no]*Number of Ions*0.88*([Charge-e]^2)*Charge of Cation*Charge of Anion))

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))

Lattice Energy using Kapustinskii equation

Go Lattice Energy for Kapustinskii Equation = (1.20200*(10^(-4))*Number of Ions*Charge of Cation*Charge of Anion*(1-((3.45*(10^(-11)))/(Radius of Cation+Radius of Anion))))/(Radius of Cation+Radius of Anion)

Repulsive Interaction Constant given Madelung constant

Go Repulsive Interaction Constant given M = (Madelung Constant*(Charge^2)*([Charge-e]^2)*(Distance of Closest Approach^(Born Exponent-1)))/(4*pi*[Permitivity-vacuum]*Born Exponent)

Lattice Energy using Original Kapustinskii equation

Go Lattice Energy for Kapustinskii Equation = ((([Kapustinskii_C]/1.20200)*1.079) *Number of Ions*Charge of Cation*Charge of Anion)/(Radius of Cation+Radius of Anion)

Repulsive Interaction using Total Energy of ion given charges and distances

Go Repulsive Interaction = Total Energy of Ion-(-(Charge^2)*([Charge-e]^2)*Madelung Constant)/(4*pi*[Permitivity-vacuum]*Distance of Closest Approach)

Born Exponent using Repulsive Interaction

Go Born Exponent = (log10(Repulsive Interaction Constant/Repulsive Interaction))/log10(Distance of Closest Approach)

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 Constant given Total Energy of Ion and Madelung Energy

Go Repulsive Interaction Constant = (Total Energy of Ion-(Madelung Energy))*(Distance of Closest Approach^Born Exponent)

Repulsive Interaction Constant

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

Repulsive Interaction

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

Lattice Energy using Lattice Enthalpy

Go Lattice Energy = Lattice Enthalpy-(Pressure Lattice Energy*Molar Volume Lattice Energy)

Lattice Enthalpy using Lattice Energy

Go Lattice Enthalpy = Lattice Energy+(Pressure Lattice Energy*Molar Volume Lattice Energy)

Outer Pressure of Lattice

Go Pressure Lattice Energy = (Lattice Enthalpy-Lattice Energy)/Molar Volume Lattice Energy

Volume change of lattice

Go Molar Volume Lattice Energy = (Lattice Enthalpy-Lattice Energy)/Pressure Lattice Energy

Repulsive Interaction using Total Energy of Ion

Go Repulsive Interaction = Total Energy of Ion-(Madelung Energy)

Total Energy of Ion in Lattice

Go Total Energy of Ion = Madelung Energy+Repulsive Interaction

Number of Ions using Kapustinskii Approximation

Go Number of Ions = Madelung Constant/0.88

Number of Ions using Kapustinskii Approximation Formula

Number of Ions = Madelung Constant/0.88
N_ions = M/0.88

What is 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. It is named after Erwin Madelung, a German physicist.
Because the anions and cations in an ionic solid attract each other by virtue of their opposing charges, separating the ions requires a certain amount of energy. This energy must be given to the system in order to break the anion–cation bonds. The energy required to break these bonds for one mole of an ionic solid under standard conditions is the lattice energy.

How to Calculate Number of Ions using Kapustinskii Approximation?

Number of Ions using Kapustinskii Approximation calculator uses Number of Ions = Madelung Constant/0.88 to calculate the Number of Ions, The Number of ions using Kapustinskii approximation in the empirical formula was found out by using the approximation that Madelung Constant was approximately 0.88 times the number of ions in the empirical formula. Number of Ions is denoted by N_ions symbol.

How to calculate Number of Ions using Kapustinskii Approximation using this online calculator? To use this online calculator for Number of Ions using Kapustinskii Approximation, enter Madelung Constant (M) and hit the calculate button. Here is how the Number of Ions using Kapustinskii Approximation calculation can be explained with given input values -> 1.931818 = 1.7/0.88.

FAQ

What is Number of Ions using Kapustinskii Approximation?

The Number of ions using Kapustinskii approximation in the empirical formula was found out by using the approximation that Madelung Constant was approximately 0.88 times the number of ions in the empirical formula and is represented as N_ions = M/0.88 or Number of Ions = Madelung Constant/0.88. The Madelung constant is used in determining the electrostatic potential of a single ion in a crystal by approximating the ions by point charges.

How to calculate Number of Ions using Kapustinskii Approximation?

The Number of ions using Kapustinskii approximation in the empirical formula was found out by using the approximation that Madelung Constant was approximately 0.88 times the number of ions in the empirical formula is calculated using Number of Ions = Madelung Constant/0.88. To calculate Number of Ions using Kapustinskii Approximation, you need Madelung Constant (M). With our tool, you need to enter the respective value for Madelung Constant and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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