Avogadro’s number calculations are pretty straight forward but many students are a little wary of them.

I think the problem is a mixture of them not being covered at school, and them not coming up on the exams often enough to give you chance to get your head around them.

This tutorial will cover the equations you need to know, along with worked examples, and there’s a multiple choice question quiz at the end to give you the opportunity to put your new knowledge into practice.

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Avogadro’s number equations

Avogadro’s number is the number of particles in 1 mole of a substance: 6.02 x 10²³ particles per mole (you may be given this number to a different level of precision).

In this context, particles can be molecules, atoms or ions.

You need to know 2 equations that involve Avogadro’s number:

1. the number of particles = moles x avogadro’s number
2. the mass of a particle = molar mass/avogadro’s number

You might need to use these equations as they are, or rearrange them.

You may also need to use them in combination with other equations e.g. mass = moles x molar mass.

Calculating the number of particles

Here’s an example question:

How many atoms are in 0.500 moles of Argon. Avogadro’s number is 6.02 x 10²³ particles per mole. 

This is a nice straightforward question. The equation we need is the number of particles = moles x avogadro’s number. 

We know the number of moles and avogadro’s number, so all we need to do is 0.5 x 6.02 x 10²³ = 3.01 x 10²³ 

And that’s all you need to do.

Let’s try a more difficult one

How many chloride ions are in 1.20 moles of MgCl2?

Again, we need to know the number of particles, so we’ll be using the number of particles = moles x avogadro’s number equation. But the problem is, the question asks about chloride ions, but the number of moles we have refers to the MgCl2, not the Cl_– ions. So before we can do anything else, we need to work out the number of moles of chloride ions. 

Here’s how we’ll do it: 1 mole of MgCl2 contains 2 moles of Cl_– ions, so as we have 1.20 moles of MgCl2 we have 2 x 1.20 = 2.50 moles of Cl_–.

We can now calculate the number of chloride ions: 2.40 x 6.02 x10²³ = 1.44 x10²⁴.

Here’s an example starting with mass

To work out the number of molecules (particles), we need to know the number of moles of SiCl4. We don’t have moles yet, but we do have mass so we can do moles = mass / molar mass

Moles = 18.2 / 170.1 = 0.107

Now we have the moles, we can work out the number of molecules:

Number of molecules = 0.107 x 6.02 x10²³ = 6.44 x10²²

Calculating the mass of a particle

Calculating the mass of a particle

if you need to calculate the mass of a particle, we need to use this equation: mass of a particle = molar mass / avogadro’s number.

When you use this equation, the units of the answer will be grams. If you need to give your answer in any other units you’ll need to do some converting.

Let’s try an example:

What is the mass of a molecule of ethane?

Ethane has the formula C2H6, so the molar mass is (12×2) + (1×6) = 30.
Therefore the mass of a molecule of ethane = 30/6.02 x10²³ = 4.98 x10^-23

Avogadro’s number calculations quiz

It’s time to put your new knowledge of Avogadro’s number calculations into practice.

This quiz has 10 multiple choice questions. Some are a straightforward test of your knowledge, others are exam-style problem solving questions.

You’ll need a period table, so grab the AQA one here. Don’t worry if you’re using another exam board, this will be fine.

Avogadro’s number calculations quiz