Lattice energy | Molecular and ionic compound structure and properties | AP Chemistry | Khan Academy

- [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.