Hey it’s professor Dave, let’s learn how to calculate the formula of a hydrated salt.
We commonly refer to sodium chloride as salt, but this isn’t the only salt there is.
Salt is actually just another term for an ionic compound, so magnesium bromide, calcium
fluoride, any compound consisting of formally charged ions is called a salt, not just the
one that we know of as table salt.
And we also know that some salts exist as hydrates, where some number of water molecules
are actually incorporated into the lattice structure of each formula unit in the solid.
But let’s say we had some hydrate of a known salt, and we were unsure of how many water
molecules were involved in this hydrate.
How might we find out?
It’s actually quite simple, it just involves an experiment and some simple calculations.
For example, let’s say we have 15.67 grams of a magnesium carbonate hydrate.
We know that in this substance there is some magnesium carbonate, and there is some water.
It should be easy to know what mass there is of each component.
All we have to do is get rid of the water, which is easy to do with gentle heating.
The heat will cause the water molecules to gain kinetic energy until they leave the lattice
as water vapor.
Once the salt is completely dry, or anhydrous, meaning no more water is left, we measure
the mass again, and this time we get 7.58 grams.
That means that the dry magnesium carbonate itself must have this mass, and the difference
between this number and the original mass, or 8.09 grams, must be the mass of the water
that was vaporized.
Now that we have the mass of each component, let’s convert these values into moles.
7.58 grams of magnesium carbonate, divided by the molar mass will give us around 0.09
moles of the salt, which still remains.
And 8.09 grams of water, divided by its molar mass, will give us around 0.45 moles of water
molecules, which used to be inside the salt but are now up in the air.
Dividing both of these values by the smaller of the two will give us their ratio, which
we can clearly see is 1 to 5.
That means that for every formula unit of the magnesium carbonate in the lattice, there
must have been precisely five water molecules.
That will allow us to write the complete formula for this hydrated salt, because where we may
have had to include an X before, indicating that we did not know the number of water molecules
associated with one formula unit of this substance, we can now accurately place a five here as
the coefficient for water, because we have empirically determined that there must be
five water molecules for every formula unit of the ionic solid.
We can now use this information to infer certain things about the geometry of this compound,
or any number of other things.
This is yet another powerful example of how we can do simple, quantitative calculations
to indirectly ascertain specific facts about molecular structure that we could never see
with our own eyes, such as the formula of a hydrated salt. Let's check comprehension.