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Avogadro Constant

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Chemistry

Atoms are small. Really, really small. In fact, one hydrogen atom has a mass of just -24 grams! This can make chemical calculations involving individual atoms quite tricky. To solve this problem, we measure quantities of atoms, particles, or molecules in units called moles. Moles are based on a number called the Avogadro constant.

  • This article is an introduction to the Avogadro constant and moles in physical chemistry.
  • We'll define mole and the Avogadro constant, before looking at the relationship between moles and mass number.
  • After that, we'll learn how you use the Avogadro constant in a variety of different equations, including how to find the number of atoms in a substance and the mass of one atom.

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 exactly 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.

The mole is a chemical unit used to represent 6.02214076 × 1023 entities. This number is known as the Avogadro constant, and has the symbol mol.

An entity is another word for a particle. It can refer to an atom, electron, ion, or molecule.

If we say we have one mole of hydrogen atoms, we know that we have exactly 6.02214076 × 1023 of hydrogen atoms. If we say that we have two moles of oxygen molecules, we know that we have 2 × 6.02214076 × 1023 = 24 of 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 = 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 look more closely 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 is the number of entities in a mole of any substance. It is equal to 6.02214076 × 1023.

We tend to shorten Avogadro's constant to 6.022 x 1023.

Amedeo Avogadro was an 18th and 19th-century scientist from the Kingdom of Sardinia, which is now a part of Italy. He is most famous for his theory about the volume of gases, known as Avogadro's law. This law states that two samples of the same volume of any ideal gases contain an equal number of molecules, provided they are kept at the same temperature and pressure. The Avogadro constant was first estimated in 1865 by Josef Loschmidt, but the term Avogadro's constant was only invented in 1909 by the physicist Jean Perrin, who named it in Avogadro's honour.

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, mass number, 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 12.0g of carbon-12. This means that one mole of carbon-12 atoms has a mass of exactly 12.0g.

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.

Relative atomic mass, Ar, and relative molecular mass, Mr, are also related to carbon-12. Relative atomic mass is the average mass of one atom of an element, compared to 1/12th of the mass of a carbon-12 atom. In other words, if you put all the atoms and their relative atomic masses on a scale, carbon-12 atoms would have a mass of exactly 12. Relative molecular mass is the same, but involves molecules instead of atoms. Check out Relative Atomic Mass for more.

Take methane, CH4. It has a relative molecular mass of 12.0 + 4(1.0) = 16.0. Therefore, one mole of methane has a mass of 16.0 grams. Or, in other words, 6.022 x 1023 molecules of methane has a mass of 16.0g.

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 relative atomic mass, number of moles, and mass:

This also applies to relative molecular mass:

Have a go at the following question.

Let's say that we have 34.5g of sodium, Na. How many moles of Na do we have?

To calculate the number of moles of our sample of sodium, we need to know its mass and its relative atomic mass. Well, sodium has a relative atomic mass of 23.0. To find the number of moles, we divide mass by relative atomic mass:

We therefore have 1.5 moles of sodium.

Here's another example.

A reaction yields 2.4 moles of water, H2O. What is the mass of this water in grams?

In this example, we know the number of moles of water produced. We can also work out its relative molecular mass: 2(1.0) + 1(16.0) = 18.0. We can use these values to find mass by rearranging the equation we used above:

Plugging our values into the equation, we get the following:

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 =

Find the number of oxygen molecules present in 88.0g of oxygen, O2.

What information do we know? Well, we know the mass of oxygen, and we can work out its relative molecular mass: 2 x 16.0 = 32.0. We can use these values to find the number of moles.

We can now use the number of moles and Avogadro's constant to find the number of molecules:

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 -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:

Take hydrogen. One mole of hydrogen atoms has a mass equal to its relative atomic mass, 1.0. If we sub that value into the equation, we get the following:

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.

Avogadro Constant - Key takeaways

  • A mole is a chemical quantity used to represent 6.02214076 × 1023 entities. This number is known as Avogadro's constant.
  • The mass of one mole of any substance is equal to its relative atomic or relative molecular mass in grams.
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  • .
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Avogadro Constant

Avogadro's constant is a quantity used in chemistry to represent the number of particles in a mole. It has a value of 6.02214076 × 1023, meaning that a mole of any substance contains exactly 6.02214076 × 1023 entities.

To calculate the number of atoms in a substance, multiply the number of moles by Avogadro's constant. For example, 1.5 moles of carbon atoms contain 1.5 x 6.022 x 1023 = 9.033 x 1023 atoms.

Avogadro's constant is equal to the number of entities in one mole of a substance. This means that if you know the number of entities, you can calculate the number of moles. This would equal the number of entities divided by Avogadro's constant, which is 6.022 x 1023. You can also work out the number of moles using a substance's relative atomic or relative molecular mass, and its mass in grams. Here, number of moles equals mass divided by relative atomic or molecular mass.

Avogadro's constant equals 6.02214076 × 1023, although we often shorten it to 6.022 × 1023.

Final Avogadro Constant Quiz

Question

What is a mole?

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Answer

A value used to express quantities in chemistry.

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Question

What is the value of Avogadro's constant, to three decimal places?

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Answer

6.022 x 1023

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Question

What is the relationship between moles and Avogadro's constant?

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Answer

One mole of a substance contains 6.022 x 1023 entities. This number is also known as Avogadro's constant.

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Question

How many moles of carbon atoms are there in a 20.4g sample of pure carbon?

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Answer

1.7 mol

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Question

What is the mass of 3.8 moles of ethane, C2H6?

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Answer

114.0g

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Question

How many atoms are in two moles of oxygen molecules, O2?

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Answer

2.4088 × 1024

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Question

A sample contains 3.76 x 1024 methanol molecules. How many moles of methanol are in the sample?

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Answer

6.101 mol

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Question

What's the mass of one sodium atom?

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Answer

3.819 x 10-23 g

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Question

What is the symbol for moles?

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Answer

mol

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Question

What is the relative mass of a carbon-12 atom on the carbon-12 scale?


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Answer

12.0

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Question

What is the mass of one mole of any substance?

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Answer

Its relative atomic mass or relative formula mass, in grams.

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Question

How many protons are in one mole of hydrogen ions?

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Answer

6.022 x 1023

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Question

How many electrons are there in one mole of hydrogen gas molecules, H2?

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Answer

1.2044 x 1024

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