Avogadro Constant

The mole and Avogadro's constant

Imagine you are going to the supermarket. On your list: one dozen eggs, two pints of milk, and a baker's dozen bread rolls. These are all specific quantities. If you buy a dozen eggs, you'll know that you'll end up with precisely twelve. Two pints of milk is 1136.5 millilitres, whilst a baker's dozen is thirteen. There should be no confusion about how many eggs or bread rolls or how much milk you need to buy.

Well, another way of specifying quantities is the mole.

If we say we have one mole of hydrogen atoms, we know that we have precisely 6.02214076 × 10²³ hydrogen atoms. If we say that we have two moles of oxygen molecules, we know that we have 2 × 6.02214076 × 10²³ = 1.20442815 × 10²⁴ oxygen molecules. And if we say that we have 9.853 moles of methane molecules, we know that we have 9.853 × 6.02214076 × 10²³ = 5.93361529 × 10²⁴ methane molecules. Think of a mole as just another quantity. Just like a pair means two, or half a dozen means six, a mole means 6.02214076 x 10²³.

Avogadro's constant definition

Let's have a closer look at that number we mentioned before: 6.02214076 × 10²³. As we said, this is known as the Avogadro constant, or simply just Avogadro's constant.

Avogadro's constant equations

Now that we know about moles and Avogadro's constant, we can look at some of the equations linking them. First of all, we'll explore the relationship between moles, mass numbers, and Avogadro's constant.

Moles, molar mass, and Avogadro's constant

You might be looking at Avogadro's constant and thinking that it is a fairly odd number. Where did it come from? Scientists must have chosen it for some particular reason - they didn't just pick a random value out of the blue! In fact, Avogadro's constant, which we know is just the number of entities in a mole, is exactly equal to the number of carbon atoms in 12.0 g of carbon-12. This means that one mole of carbon-12 atoms has a mass of exactly 12.0 g.

You might notice something. Carbon-12 atoms have a relative atomic mass of 12.0; 12.0 is also the mass of one mole of these atoms. This leads us on to our next important point: the mass of one mole of any substance is equal to its relative atomic mass, or relative molecular mass in grams. We can also call the mass of one mole of a substance its molar mass.

So, to find molar mass, you take a substance's relative atomic mass or relative molecular mass, and add g·mol^-1 to the end.

Notice how in this example, we multiplied the relative molecular mass of methane, 16.0, by the number of moles, 1, to find its mass? This leads us to a useful bit of maths. There's a handy equation we can use to relate molar mass, number of moles, and mass:

$\mathrm{number}\mathrm{of}\mathrm{moles}=\frac{\mathrm{mass}}{\mathrm{molar}\mathrm{mass}}$

Have a go at the following question.

Here's another example.

Moles, number of particles, and Avogadro's constant

Let's now look at the relationship between the number of moles, number of particles, and Avogadro's constant. We briefly met this when we first introduced you to moles up above, but we'll explore it again.

We know that one mole of any substance contains 6.022 x 10²³ entities. This is just Avogadro's constant. Two moles of a substance would therefore contain twice as many entities: 2 x 6.022 x 10²³ = 1.2044 x 10²⁴. From this, we can deduce the following equation:

$\mathrm{number}\mathrm{of}\mathrm{entities}=\mathrm{number}\mathrm{of}\mathrm{moles}\times \mathrm{Avogadro}\text{'}\mathrm{s}\mathrm{constant}$

Sometimes, you might have to use a combination of this equation, and the equation linking moles, mass, and relative atomic or relative molecular mass, in order to answer a question. Let's have a go.

Relative atomic mass, the mass of one particle, and Avogadro's constant

Do you remember at the beginning, when we quoted the mass of a single hydrogen atom as 1.66 × 10^-24 grams? Now let's learn how we worked that value out.

Remember: one mole of a substance - or to be precise, 6.022 x 10²³ of its entities - has a mass equal to its relative atomic or relative molecular mass. As we learned, 6.022 x 10²³ atoms of carbon have a mass of 12.0 g. If we divide this mass by the number of carbon atoms, we can find the mass of one atom. Here's the equation:

$\mathrm{mass}\mathrm{of}\mathrm{one}\mathrm{entity}=\frac{\mathrm{molar}\mathrm{mass}}{\mathrm{Avogadro}\text{'}\mathrm{s}\mathrm{constant}}$

That's it! We hope you've now got a good understanding of moles, Avogadro's constant, and how to use these values in equations.