Structure 1.4.1—The mole (mol) is the SI unit of amount of substance. One mole contains exactly

the number of elementary entities given by the Avogadro constant.

**What You’ll Learn:**

- Convert the amount of substance, n, to the number of specified elementary entities.
- An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or a specified group of particles.
- The Avogadro constant N
_{A}is given in the data booklet. It has the units mol^{–1}.

**Keywords**

IBDP chemistry, mole, mol, amount of substance, elementary entities, atoms, molecules, ions, electrons, carbon-12, Avogadro’s constant, N_{A}, 6.022 x 10^{23} mol^{-1}, amount of substance, n, number of entities, formula, oxygen atoms, water molecules, data booklet, units

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**Syllabus Links**

The mole (mol) is a unit used to express the amount of a substance. One mole of any substance contains the same number of elementary entities (such as atoms, molecules, ions, electrons, etc.) as there are in 12 grams of pure carbon-12. This number is known as Avogadro’s constant (N_{A}) and is approximately 6.022 x 10^{23} mol^{-1}.

To convert the amount of substance, n, to the number of specified elementary entities, you can use the following formula:

Number of entities = n (amount of substance in moles) × N_{A} (Avogadro’s constant)

Example 1: How many atoms are in 2 moles of oxygen atoms?

To calculate this, we can use the formula mentioned above:

Number of entities = n × N_{A} Number of entities = 2 moles × (6.022 × 10^{23} mol^{-1}) Number of entities = 1.204 × 10^{24} oxygen atoms

Example 2: How many molecules are in 0.5 moles of water (H_{2}O) molecules?

Again, we can use the formula:

Number of entities = n × N_{A} Number of entities = 0.5 moles × (6.022 × 10^{23} mol^{-1}) Number of entities = 3.011 × 10^{23} water molecules

Remember that Avogadro’s constant (N_{A}) is given in the data booklet, so you don’t have to memorize it. Just make sure to use the correct units when performing calculations with moles and the Avogadro constant.

Questions

- What is the formula to convert the amount of substance (n) to the number of specified elementary entities using the Avogadro constant (NA)?
- If the amount of substance (n) of a sample of carbon atoms is 2 moles, how many carbon atoms are present in the sample?
- Calculate the number of water molecules in a 5-mole sample of water, using the Avogadro constant.
- If you have a 3.5-mole sample of sodium chloride (NaCl), how many sodium ions and chloride ions are present in the sample?
- How many electrons are there in a 1-mole sample of electrons?
- Given that the amount of substance (n) of a sample of nitrogen gas (N
_{2}) is 4 moles, determine the number of nitrogen molecules present in the sample. - A sample contains 1.5 moles of a diatomic molecule (X
_{2}). Calculate the total number of atoms of element X in the sample. - If a sample consists of 0.5 moles of calcium ions (Ca
^{2+}), how many calcium ions are there in the sample? - Calculate the number of specified groups of particles in a 2.5-mole sample, where each specified group consists of three atoms.
- Given a 3-mole sample of a compound with a formula of XY
_{2}, how many individual atoms of X and Y are present in the sample?