Main content

# 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*= (*q*₁*q*₂)/*r*². 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?(6 votes)
- 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.(9 votes)

- Does Khan Academy provide a video on calculating Lattice Energy?(3 votes)
- 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.(6 votes)

- 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 ?(2 votes)- 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.(7 votes)

- 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.(5 votes)

- Why does Sal say "infinitely far apart" at around3:45? 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.(0 votes)
- 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.(5 votes)

- 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.(2 votes)

- 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.(2 votes)

- 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)

## Video transcript

- [Instructor] You may already be familiar with Coulomb's law, which is really the most important or underlying law behind
all of what we know about electrostatics and how things with charge
attract or repulse each other, but a simplified version of Coulomb's law is just that the force
between charged particles, the magnitude of the force is going to be proportional
to the product of the charges, so q one would be the charge of one of the charged particles. Maybe this is an ion. Q two would the charge
of the other particle. Maybe that's an ion, divided by r squared. And if we're talking about ions, r is going to be the distance
between their nuclei, and if the charges are different, it's going to be force of attraction. If the charges are the same, it's going to be a force of repulsion. And we can use Coulomb's law
to think about ionic compounds. So let's go with maybe the
most common ionic compound in our daily life, and that is table salt. Table salt is sodium chloride, so sodium chloride. We have talked about this in other videos. It is made up of
positively-charged sodium cations, so you have an Na plus, so sodium is a group one element. It's very easy to nab
an electron off of it and then it has a positive charge, and it's made up of a chloride anion, so Cl minus. Chloride is a group seven element. It really wants to get that extra electron to have eight valence electrons
in its outermost shell, and so it's very likely
to grab an electron maybe from a sodium, and so these two characters
are going to be attracted to each other. Notice, they have opposite charges. And when you have a bunch of
sodium and chloride together, you'll have a structure that
looks something like this. And in chemistry, we call this a lattice. Now in everyday language, you might associate things like lattices with kind of a crossing pattern like that, and in chemistry, when we're
talking about a lattice, we're talking about a
three-dimensional structure of atoms or three-dimensional
structure of ions that have a repeating pattern to them, and you can see that here, and in future videos,
we'll go into more detail onto lattice structures, but you can see in this picture, the purples are the sodium cations and the greens are the chloride anions. And the reason why the
sodium cations are so small, you can see that if you
look at the periodic table of elements here. We have said that as you go to the right, your radius decreases, but what's happening is when sodium loses that outermost electron, then its electrons have a noble
gas configuration of neon. So it really loses that
third shell, it gets smaller, and not only does it
lose that third shell, but it has 11 protons, so it's going to have a very strong pull on those electrons in that second shell. And similarly, chloride is
going to gain an electron so it's going to have a noble
gas configuration of argon. So it is going to be bigger. Now when we talked about covalent bonds, we talked about the bond energy, the energy needed to pull apart the atoms that were forming the covalent bonds. There's a similar notion
for ionic bonds like this and that is lattice energy, and that is energy necessary to pull the ions apart so that they are infinitely
far apart from each other, and lattice energy is usually measured in kilojoules per mole, which is also what we
measure bond energy in because they're really the same notion, except lattice energy, you're breaking up a lattice of ions, while in bond energy, you're normally talking
about covalent bonds. Now I want you to think about something. What's going to have a
higher lattice energy? Would it be sodium chloride, or let's pick something else. Let's say we had rubidium. Rubidium chloride, which is going to have
a higher lattice energy? What's going to take more energy to pull the ions apart? And I'll give you a hint with this periodic table of elements. All right, well, rubidium chloride, that's made up, instead
of a sodium cation, that's made up of a rubidium cation, so you have Rb plus, and of course, you have the chloride anion, Cl minus, and so what's the difference here? The anion is both, is
chloride in both cases, but when you look at
rubidium versus sodium, rubidium, when it loses an electron, it's going to have a noble gas structure, electron structure of krypton, while sodium, once it loses an electron, it's, its electron, its electron configuration
is going to look like neon. So the sodium cation is smaller, and what does that tell us? Well, if this one right over here, let me circle it like this. If this is smaller, and we have similar charges on top, you have a plus one and
a negative one on top, that's the charges between the two ions, but now you have a smaller
radius between the nuclei because sodium is smaller than rubidium. While the radius goes down, the force goes up, so you're going to have
stronger Coulomb forces in a lattice of sodium chloride than in a lattice of rubidium chloride. Because the force of
attraction is stronger, it's going to take more
energy to pull it apart. So because of that, you're going to have a higher, higher lattice energy. Lattice energy for sodium
chloride than rubidium chloride. Let's think about another ionic compound. Let's say we were to think
about magnesium fluoride, F two, and this is made up of a magnesium cation that has a positive two charge, so two plus, in a lattice with
a bunch of fluoride anions, so with a bunch of fluoride anions. So how would the lattice energy of magnesium fluoride compare to what we just saw up here? So magnesium has a larger charge than these cations up here, so if you viewed the charge
of magnesium as q one, you're going to have
something larger up there and that fluoride is a
smaller anion than chloride. We can see that if we
look at the periodic table of elements again. Florine is smaller than chlorine, and so even if you added an
electron to both of them, fluoride is still going to be smaller, and magnesium, when you take
two electrons off of it, it's going to have the
noble gas configure, electron configuration of neon, but it's going to pull even more on those, that, those second shell electrons because it has 12 protons
versus sodium only has 11. So what we see here is not only
does magnesium have a larger positive charge than
the sodium cation does, but it's going to be smaller. And the fluoride has a comparable
charge to the chloride, but it too is going to be smaller. So we have a larger charge on top, at least for the magnesium, and you have smaller radii for the bottom, so in magnesium fluoride, the Coulomb forces between
the ions and the lattice are even stronger, and so the lattice energy, the energy necessary to pull it apart, is going to be higher, so out of the three we just looked at, the highest lattice energy is
going to be magnesium fluoride followed by sodium chloride followed by rubidium chloride.