Why Are Chemists Talking About Moles?

How many eggs is a dozen eggs? 12, obviously.

How many books is a dozen books? Again, obviously 12.

How many pens is a dozen pens? Why are we doing this? Obviously it`s 12. It doesn`t matter what we`re measuring, a dozen things is always 12 things.

This seemingly pointless exercise above is to explain to you why the idea of the mole isn`t really all that difficult.

In the same way that a dozen "things" is always 12 "things",

a mole of "things" is always 6.022 x 10²³ "things".

Why did we choose 6.022 x 10²³ (also known as Avogadro`s number, and sometimes given the symbol L) to be a mole, and why do we even bother with moles? Well, it has to do with how we measure atomic mass. Atomic mass, if you remember, is defined so that ¹²C has an atomic mass of precisely 12, and everything else is then measured in relation to ¹²C. Well, it so happens that (6.022 x 10²³) ¹²C atoms weighs precisely 12g.

So, 6.022 x 10²³ atoms/molecules of any substance weighs that atom`s/molecule`s atomic mass/molecular mass in grams:

A mole of He weighs 4g a mole of He is 6.022 x 10²³ atoms of He

A mole of H₂O weighs 18g a mole of H₂O is 6.022 x 10²³ molecules of H₂O

A mole of F₂ weighs 38g a mole of F₂ is 6.022 x 10²³ molecules of F₂

And because a mole is just a number of atoms/molecules, it obeys the formula:

(number of moles in a sample) = (mass of sample) / (relative formula mass of sample)

e.g.

"Find the number of moles in 1.9g of F₂"

(number of moles in the sample) = (1.9) / (38)

(number of moles in the sample) = 0.05 mol (we often use mol as the unit for the number of moles)

But it gets even better than that! Because a mole of molecules is just 6.022 x 10²³ molecules, we can work out the number of molecules in a sample if we know the number of moles:

(number of molecules in the sample) = (number of moles in the sample) x (Avogadro`s number)

e.g.

"Find the number of molecules in 1.9g of F₂"

(number of moles in the sample) = 0.05 mol from above, then:

(number of molecules in the sample) = (0.05) x (6.022 x 10²³)

(number of molecules in the sample) = 3.011 x 10²²

A slightly trickier example

"How many atoms are there in a mole of H₂O?"

Now we need to be careful: a mole of H₂O is (6.022 x 10²³) molecules of H₂O, but each H₂O molecule contains 3 atoms (2 hydrogen atoms, and one oxygen atom). So the answer is:

(6.022 x 10²³) x 3

= 1.8066 x 10²⁴ atoms

If this doesn`t quite make sense, it`s like asking "how many legs are there in a dozen chickens?" each chicken has 2 legs, so 12 chickens together have 24 legs.

Putting it all together

Let`s combine everything we`ve learned into one last example (it doesn`t get much harder than this):

"How many chlorine atoms are in 19g of TiCl₄?"

First, we need to find the relative formula mass of TiCl₄

M_{r, TiCl4} = A_r,Ti + (4 x A_r,Cl)

M_{r, TiCl4} = 47.9 + (4 x 35.5)

M_{r, TiCl4} = 189.9

Then, we need to find the number of moles of TiCl₄ in the sample:

(number of moles in the sample) = (mass of sample) / (relative formula mass of sample)

(number of moles in the sample) = (19) / (189.9)

(number of moles in the sample) = 0.1 mol

But, each mole of TiCl₄ molecules contains 4 moles of Cl atoms, so there are 0.4 moles of Cl atoms in the sample.

Then, we simply multiply by Avogadro`s number:

(number of atoms of Cl in the sample) = (number of moles of Cl in the sample) x (Avogadro`s number)

(number of atoms of Cl in the sample) = 0.4 x 6.022 x 10²³

(number of atoms of Cl in the sample) = 2.41 x 10²³ atoms

Why do we even bother with moles?

It seems a lot of effort to convert between moles and atoms, so why do we bother with moles in the first place? It is simply a case of convenience. In any chemical sample, there will be trillions upon trillions of atoms and molecules, so referring to things in terms of moles makes the numbers considerably easier to work with. I`ll let you decide which of the following rolls off the tongue easier:

"Add half a mole of sodium metal to the container."

"Add three hundred and one sextillion one hundred quintillion atoms of sodium metal to the container."

Understanding what a mole actually is, and how to use them, is the first step to mastering all calculations in GCSE and A-level chemistry.