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### Course: Chemistry library>Unit 7

Lesson 2: Bond energy

# Lattice energy

The energy required to separate the ions in a crystal lattice into individual gaseous ions is known as lattice energy. Lattice energy depends on the strength of interactions between cations and anions in the lattice, which we can estimate using Coulomb's law: Fₑ = (qq₂)/r². According to this equation, stronger interactions occur between ions with larger charges and smaller radii. Created by Sal Khan.

## Want to join the conversation?

• Is all ionic bond a solid since it forms the lattice crystal?
• Not every ionic compound is solid at room temperature.
Ionic liquids contain an organic anion and/or cation with an irregular shape, which do not form lattice crystals.
• Does Khan Academy provide a video on calculating Lattice Energy?
• Actually calculating a number, no. But Sal pretty much gave how to calculate here using Coulomb's Law. The only difference is that to turn from a proportionality statement to an equation you need to include Coulomb's constant, K. You need to know information about the charge of your ions, and their atomic radii to calculate the lattice energy then. Hope that helps.
• why cl(-1) has a bigger radius than cl neutral.
In some videos before the explanation was opposite - by saying that the radius decreased when electron is added because of the effective charge increase.
And also I saw an explanation for radius increases because the added electron is being repelled by the other electrons in the last shell and thus incresing the repelling force and increasing the radius(also some videos befor).
can someone help me with some clarity here ?
• The chloride ion has an atomic radius of 167 pm compared to a neutral chlorine atom at 99 pm. The only difference between the two species is that the chloride ion has an additional electron so the difference in size must be due to that.

Having an additional electron in the valence shell of the chloride ion increases the repulsive force of the other valence electrons and thus decreases their effective nuclear charge. Having a lessened effective nuclear charge means that the protons in the nucleus have less of an attractive force on the electrons and so the valence electrons are pushed out more so compared to the neutral chlorine atom whose valence electrons have a higher effective nuclear charge.

Hope that helps.
• Why does MgF2 have a greater Lattice Energy than NaCl? Can someone please simplify it? Sal talked about the force being larger on top, but I'm confused about the atomic radius... is the atomic radius of MgF2 smaller or larger than that of NaCl?
(1 vote)
• Lattice energies of ionic compounds broadly correspond with Coulomb's Law which Sal provided in the video. Coulomb's Law describes the force of attraction (or repulsion) between two point charges. Whether the force is attractive or repulsive depends on whether the charges have the same sign or not. In ionic compounds the force is always attractive since the ions have different charges. So lattice energy is measuring how attracted both the ions are to each other in an ionic compound.

If we observe the equation of Coulomb's Law the numerator consists of the product of the absolute value of the charges of the ions. And the denominator consists of of the distance between the two ions, squared. So both the magnitude of the ion's charges and their atomic radii effect the lattice energy. If the goal is to maximize the lattice energy then you'd want ions with larger magnitude charges and/or small in size ions. Generally the charges of the ions have more bearing than the distance between them when determining lattice energies. This means we can usually assume that ions with greater magnitude charges will result in greater lattice energies, and without having to take into consideration the atomic radii.

If we consider magnesium fluoride (MgF2) and sodium chloride (NaCl), then we would assume that magnesium fluoride would have a greater lattice energy. This is because the magnesium ion has a +2 charge (and the fluoride has a -1 charge), while the sodium and chloride ions have +1 and -1 charges respectively. So the product the magnesium fluoride's charges is 2 while the sodium chloride's charge product is only 1.

We can be thorough and also consider the atomic radii of all the ions concerned too. The distance between a magnesium and fluoride ion is 205 pm, while the distance between a sodium and chloride ion is 283 pm. So magnesium fluoride also has a smaller distance between the ions which also results in greater attraction between the ions and generates a greater lattice energy compared to sodium chloride. Sodium and magnesium have about the same atomic radii (102 pm and 72 pm respectively), with the main difference being because of the fluoride and chloride ions (133 pm and 181 pm respectively).

With both of these factors in mind, we should assume that magnesium fluoride has a greater lattice energy compared to sodium chloride. And this is true is look up their values: magnesium fluoride is 2922 kJ/mol while sodium chloride is only 786 kJ/mol.

Hope that helps.
• Why does Sal say "infinitely far apart" at around ? How can atoms be "infinitely far apart"? I'm assuming this has to do with calculus but I don't get how that applies to atoms/molecules.
• Technically ions cannot be infinitely far apart. Even at very large distances they still feel an electric force according to Coulomb's law. So mathematically they would only feel no force only if they were at some unattainably infinite distance apart. Here when we talk about pulling ions in a lattice apart, realistically we do so to such a distance that the force they feel is negligible.

Hope that helps.
• What is the difference between lattice energy and Coulomb's Law? In the video, Sal uses the same equation, but my lecturer uses the equation for lattice energy with only a r in the denominator (not squared). I hope I'm not misunderstanding anything. Thank you!
(1 vote)
• Lattice energy and Coulomb's Law are related concepts in the field of chemistry, particularly when discussing the forces that hold ionic compounds together. However, they are not the same thing, and the equations involving them can sometimes look similar but have different meanings and applications.

Coulomb's Law: Coulomb's Law is a fundamental principle in physics that describes the electrostatic interaction between two charged particles. It states that the force of attraction or repulsion between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The mathematical expression for Coulomb's Law is typically written as:

F = k * (q1 * q2) / r^2

Where:

F is the electrostatic force between the two charges.
k is Coulomb's constant, a fundamental constant of nature.
q1 and q2 are the magnitudes of the charges.
r is the distance between the charges.
Coulomb's Law is used to describe how charged particles interact with each other, such as electrons and protons in atoms or ions in ionic compounds.

Lattice Energy: Lattice energy is a concept in chemistry that represents the energy required to completely separate one mole of an ionic compound into its constituent ions in the gas phase. In other words, it quantifies the strength of the ionic bonds that hold the ions together in a crystal lattice. Lattice energy depends on the charges of the ions and the distance between them, among other factors.

The mathematical expression for lattice energy is often given as:

U = k * (q1 * q2) / r

Where:

U is the lattice energy.
k is a proportionality constant.
q1 and q2 are the charges of the ions.
r is the distance between the ions.
Notice that in the expression for lattice energy, the distance "r" is not squared, unlike in Coulomb's Law. This difference arises because lattice energy represents the energy required to separate ions to an infinite distance, while Coulomb's Law deals with the force between two individual charged particles at a specific distance.

In summary, the key difference between Coulomb's Law and the equation for lattice energy lies in their applications and the interpretation of the distance term. Coulomb's Law describes the force between two charged particles at a specific distance and is a fundamental principle of electrostatics, while lattice energy represents the energy required to completely separate ions in an ionic compound and is used to understand the stability of ionic solids. Your lecturer's use of a non-squared "r" in the lattice energy equation is correct for this specific context.
• why would salt disassociate in water if its already pulled from the Cl-? is the \delta- of oxygen more attracive than coulombs force?
(1 vote)
• In a chemistry context salt is just a synonym for an ionic compound. So an entire lattice of sodium chloride or magnesium fluoride would be considered salts. When salts dissolve, or dissociate, in water the water molecules orientate themselves properly and surround the individual ions and separate them from the larger lattice.

It should be noted that not all ionic compounds dissolve in water. Salts ultimately only dissolve if their energy, specifically Gibbs free energy, is lowered by this process. Ultimately this means, if they do dissolve, that the ions feel more attraction for the water molecules than they do for the other ions.

Hope that helps.
• Is there a vidoe on how to draw the lattice structure? 😭
(1 vote)
• Which has shorter bond lengths, ionic or covalent? Whe n I google this question, I get the general rule "ionic bonds tend to be much shorter and much stronger". However, if I look up actual bond lengths, Lithium Fluoride and Beryllium Oxide have bond lengths twice as long as Cyanide, CO2, Carbon Tetrafluoride, or even a Carbon-Carbon bond. What's up with that?
(1 vote)
• Does 2+ charge in magnesium play a role? If magnesium has 2 negatively charged fluorine ions around then do they cancel out 2+ charge?
(1 vote)
• Magnesium having a charge of +2 just means that it needs a negative charge of -2 from some anion(s) to make the unit neutral. Ionic compound's formula unit must be electrically neutral.

Hope that helps.
(1 vote)