# The mole

In the previous article, The structure of matter, you have learned how matter is constitued. This article will teach you what is the mole, and why and how to use it.

## The definition of the mole

The **mole** is the unit of measurement of amounts of substance. One mole is the amount of substance containing 6.02 x 10^{23} atoms, molecules or ions. Its abbreviation is *mol*.

The number 6.02 x 10^{23} is called the **Avogadro constant**, written *N _{A}*. This constant corresponds to the number of atoms contained in 12 grams of Carbon 12.

## Why the mole ?

The samples of matter that chemist manipulate contain huge numbers of atoms, molecules or ions. It is thus much more convenient to express these quantities in numbers of moles, who are often small, than in numbers of molecules, who are typically much bigger and also harder to represent mentally.

Thus, an **amount of substance** in expressed in mole. It is written *n*. It is calculated by dividing the number of atoms, molecules or ions of the sample, written *N*, by the Avogadro constant. Thus, we can write *n* = *N*/*N _{A}*.

100 g of glucose is equivalent to 0.56 mole of glucose molecules and to 3.37 × 10^{23} glucose molecules. Which number is easier to use: 0.56 or 3.37 × 10^{23} ? Chemists always prefer the mole to express such quantities.

The mole is particularly useful to chemists when they design a chemical reaction, because it allows them to determine the right quantities of chemical substances they have to mix. This is called *stoichiometry*.

## The molar mass

The **molar mass** of an atom, molecule or ion is the mass of one mole of this atom, molecule or ion. It is written *M*, and its unit is the g/mol.

The molar mass of the atoms of each element is written in the periodic table.

The molar mass of Phosphorus is 30.97 g/mol. The molar mass of Gold is 107.87 g/mol.

The molar mass of a molecule is calculated by adding the molar mass of each of its atoms.

The glucose molecule contains 6 atoms of carbon (M = 12.01 g/mol), 12 atoms of hydrogen (M = 1.01 g/mol) and 6 atoms of oxygen (M = 16.00 g/mol). Thus, the molar mass of glucose is (6x12.01)+(12x1.01)+(6x16.00) = 180,18 g/mol.

The molar mass of an ion is considered equal to the molar mass of the molecule or atom it corresponds to.

The molar mass of the chloride ion (Cl^{-}) is equal to the molar mass of the chlorine atom (Cl) : 35.45 g/mol. The molar mass of the ferric ion (Fe^{3+}) is equal to the molar mass of the iron atom (Fe) : 55.85 g/mol.

The molar mass allows you to convert any mass of a pure sample (called *m*) of matter into its amount of substance, using the formula n = m/M.

The molar mass of ethanol is 46.07 g/mol. Thus, 5 grams of ethanol contain 5/46.07 = 0.11 mol of ethanol.