Simple Calculations Involving Moles

Today we're going to talk about the mole. It's a very useful concept in chemistry.

A mole is equal to 6.02 x 10^23 of something. Normally we use it in relation to atoms or molecules. You could use it in relation to other things, too, but generally the number's too big to be practical for daily use.

The mass numbers on your periodic table tell you how much one mole (i.e. 6.02 x 10^23) of atoms of that element weigh. You can add the mass numbers of the elements in a compound together to get the molar mass of that compound. Remember?

The first kind of calculation listed on my course outline is mole to mole. Remember our good old formula from my last post?

Do you also remember me saying the the coefficient indicates that you need twice as many HCl molecules as calcium carbonate molecules? Because if you understand this, you understand mole to mole calculations.

Basically, in the above equation, if you have 2 moles of HCl, you have 1 mole of calcium carbonate, 1 mole of calcium chloride, 1 mole of carbon dioxide and 1 mole of water. If you have 4 moles of HCl, you have 2 moles of calcium carbonate, 2 moles of calcium chloride, 2 moles of carbon dioxide and 2 moles of water. And if you have 1 mole of HCl, you have half a mole of calcium carbonate, half a mole of calcium chloride, half a mole of carbon dioxide and half a mole of water. And so on. Inversely, if you have 5 moles of calcium carbonate, you have 10 of HCl, 5 of calcium chloride, 5 of carbon dioxide and 5 of water. You see, the coefficients just indicate the ratio between the substances in the equation.

But how do you know how many moles you have of a substance? Well, you don't really, unless you're told something that would give you a starting point to work out the number of moles. If you're lucky, you'll be told the number of moles, but more often than not, you'll be given the mass of one or more of the elements, which leads us to mass to mole calculations.

In mass to mole calculations, you essentially take the mass that you're given and divide it by the molar mass of that compound. For example, let's just say that you have 72.916g of HCl. The molar mass of HCl is 1.008 + 35.45 = 36.458g. 72.916/36.458 = 2, so you have 2 moles of HCl.

There's even a fancy equation for this. n = (m/M) where n = number of moles, m = the mass of the substance (i.e. what you have) and M = molar mass (i.e. mass of 1 mole of the substance).

I'm going to try an explain this formula a bit so you're not blindly committing it to memory.

As I've hopefully explained before, M, the molar mass of the substance, gives the mass of 1 mole of the substance. So it's logical that if you multiply this by n, the number of moles of the substance, it should give you the mass of n moles of the substance, i.e. the mass that you have:

nM = m

And then you can just rearrange this formula to get the good ol' n = (m/M)!

Now let's go to the next step: mass to mass calculations- working out the mass of a substance in the equation given the mass of another substance. Mass to mass calculations basically combine mole-to-mole and mass-to-mole calculations. The steps to something like this:

1. Mass to mole
2. Mole to mole
3. Mole to mass

As an example, let's just say that in our beloved formula above we have the mass of HCl (I'm just going to leave it as 72.916, for simplicity) and we want to find the mass of water. First, we convert mass to mole as we did in the previous step. We got 2 moles of HCl. Then we have to convert moles to moles. Since we have twice as much HCl as water, we have to halve the number of moles. We have one mole of water.

Which leaves us with the last step, mole to mass. This is easy. Just take the number of moles and multiply by the molar mass. 1 x (1.008 x 2 + 16) = 18.016g. Yayyyyyyyy. That's basic stoichiometry for you.

But what happens if you are looking for the volume of a gas at STP (standard temperature and pressure) instead? What if you want to perform a mass to volume calculation instead?

In this case, the first two steps are the same. Do mass to mole, then mole to mole. Remember, EVERYTHING GOES THROUGH THE MOLE. So if you ever get stuck on a chemical equation problem, just convert everything to moles and work from there.

Mole to volume isn't too hard when you know the magic number. The magic number in this case is 22.71. One mole of a gas at STP has a volume of 22.71L. Therefore, you just need to multiply this magic number by the number of moles you have to get the volume of gas that you have! Simple, isn't it? And it even comes with its own nifty formula which can be rearranged as needed:

n = (V/22.71)

And then there's volume to volume calculations. The premise here is simple too. Convert volumes to moles by rearranging the above formula, do a mole to mole calculation and then convert to volume.

My goodness those moles are useful.

There's a 5-step method to stoichiometry, but you see, I prefer to condense it into 4 steps.

1. Write a balanced equation.
2. Convert everything to moles.
3. ???
4. PROFIT!!!

Okay, that was a bit silly, but you get the idea. The Mole is Stoichiometry King. Worship it. Or else.