Any body is characterized by its **mass**. Because the mass of different particles (molecules, atoms, electrons, ions) is not the same, the number of particles in the same amount of mass is different for each substance.

For example, because the mass of an oxygen molecule *m _{O2}* is 16 times bigger than the mass of a hydrogen molecule

*m*, the number of oxygen molecules

_{H2}*N*contained in 1 kg of oxygen gas is 16 times less than the number of hydrogen molecules

_{O2}*N*contained in 1 kg of hydrogen gas. We can write the relationship between the number and mass of oxygen and hydrogen molecules, for the same mass of gas, as:

_{H2}From (1), we can write the **number of molecules** ratio between oxygen and hydrogen, for the same amount of gas:

*Observation*: The mass of the oxygen and hydrogen molecules are taken from The Periodic Table of Elements.

### Mole definition

Because atoms and molecules are very small (microscopic), weighing or counting them directly is not possible. Therefore, mostly in chemistry, there is a need to define a **new unit of measurement** for the amount of substance, which contains the **same number of particles** (molecules, atoms, electrons, ions), **regardless of the type of substance**. This unit of measurement is called **the mole**.

The mole is defined as the amount of substance of a system which contains as many fundamental units as the number of atoms contained in 12 g of Carbon 12 (symbol ^{12}C). The **fundamental units** can be: molecules, atoms, ions, nuclei, electrons or formula units.

The mole is a measurement unit in the SI base, with the symbol **mol**.

Every time we use the mole as a unit of measurement, we also have to specify the fundamental unit (e.g 2.5 mol of H_{2}O molecules).

### Molar volume definition

The volume occupied by 1 mol of substance is called **molar volume**. It’s usually symbolized as *V _{m}*.

From experimental data, at standard temperature and pressure (**stp**) conditions (t_{0} = 0 °C, p_{0} = 1.013·10^{5} N/m^{2}), it’s proven that **all gases have the same molar volume** V_{m0} = 22.41 L = **22.41·10 ^{-3} m^{3}**.

### Molar mass definition

The mass of a mole of substance is called **molar mass**. In other words, the molar mass is defined as the mass of a mole of that substance, measured in grams per mole [g/mol or g·mol^{-1}]. To calculate the molar mass of a substance we need to know the atomic mass of the elements within the substance.

For example, the atomic mass of Iron is 55.845 **amu** (atomic mass units) which means that **the molar mass of 1 mol of Fe is 55.845 g**.

The same applies for other elements, **the molar mass of 1 mol of carbon is 12.0107 g**.

*Observation*: The atomic mass of the chemical elements is taken from The Periodic Table of Elements.

### Avogadro’s number

The number of atoms contained in 1 mol of carbon-12 (which has the molar mass of 12 g) is called the **Avogadro’s number**. The symbol for Avogadro’s number is *N _{A}* and it is equal with

**6.0221367·10**.

^{23}mol^{-1}Any 1 mol of any substance contains 6.022·10^{23} fundamental units. A **fundamental unit** can be **atoms** (e.g. iron, Fe), **molecules** (e.g. oxygen, O_{2}) or **formula units** (e.g. water, H_{2}O)

Since the number of Avogadro is the same for all substances, it is a **universal constant**.

The **total number of fundamental units** *N* (atoms or molecules) contained in *ν* **moles of substance** is given by:

The **molar mass of a substance** *μ* is equal with the product between the **mass of the fundamental unit** *m* (atom or molecule) and **Avogadro’s number** *N _{A}*.

From (3) and (4) we can observe that Avogadro’s number is the link between the macroscopic and microscopic units of substance.

To put it simply, **a mole is a number**, as:

- a dozen is 12
- a pair is 2
- a
**mole**is 6.022·10^{23}

### Mole summary

The mole is:

- a unit of measurement used in chemistry
- a bridge between the atom or molecule (microscopic) and the amount of substance used in laboratories (macroscopic)
- the mass of substance containing the same number of fundamental units as there are atoms in exactly 12 g of carbon-12
- Avogadro’s number 6.022·10
^{23}of anything - a way of counting the atoms of a substance by weighing it

A mole of substance:

- has a specific
**mass** - occupies a given
**volume**

**Example of moles for mono-atomic substances**

Substance | Number of atoms | Molar mass [g] | Molar volume [L] |

1 mol of Xenon, Xe | 6.022·10^{23} | 131.293 | 22.41 (gas) |

1 mol of Helium, He | 6.022·10^{23} | 4.002602 | 22.41 (gas) |

1 mol of Neon, Ne | 6.022·10^{23} | 20.1707 | 22.41 (gas) |

As you can see, 1 mol of any substance has the same number of atoms and the same molar volume (for gases). The molar mass varies from substance to substance and depend on the atomic mass of the element (see The Periodic Table of Elements).

**Example of moles for bi-atomic substances**

The molar mass of a bi-atomic substance is the twice the atomic mass of the element. For example, an oxygen molecule O_{2} is made up from two oxygen atoms. The atomic mass of an oxygen atom is approx. 16 g which makes the molar mass of 1 mol of oxygen 32 g.

Substance | Number of molecules | Molar mass [g] | Molar volume [L] |

1 mol of Hydrogen, H_{2} | 6.022·10^{23} | 1.00794 · 2 ≅ 2 | 22.41 (gas) |

1 mol of Oxygen, O_{2} | 6.022·10^{23} | 15.9994 · 2 ≅ 32 | 22.41 (gas) |

1 mol of Nitrogen, N_{2} | 6.022·10^{23} | 14.0067 · 2 ≅ 28 | 22.41 (gas) |

### Examples of moles for poly-atomic substances (compounds)

The molar mass of a poly-atomic substance (also called formula unit) is the sum of the atomic mass of each atom and molecule. For example, the molar mass of 1 mol of water (H_{2}O) is the sum between the atomic masses of all the constituent atoms: 1.00794 · 2 + 15.9994 ≅ 18 g.

Substance | Number of formula units | Molar mass [g] | Molar volume [L] |

1 mol of Water, H_{2}O | 6.022·10^{23} | 1.00794 · 2 + 15.9994 ≅ 18 | 22.41 (vapor) |

1 mol of Salt, NaCl | 6.022·10^{23} | 22.98976 + 35.453 ≅ 58 | 22.41 (gas) |

1 mol of Methane, CH_{4} | 6.022·10^{23} | 12.0107 + 1.00794 · 4 ≅ 16 | 22.41 (gas) |

### Chemistry examples involving moles

**Example 1**. How many atoms we have in 2.7 moles of Krypton (Kr) ?

We know that 1 mol of any substance has 6.022·10^{23} atoms. Therefore in 2.7 moles of Krypton we are going to have: 2.7 · 6.022·10^{23} = **16.2594·10 ^{23} atoms of Krypton**.

**Example 2**. How many moles there are in 1000 g (1 kg) of Iron (Fe) ?

From The Periodic Table of Elements we know that 1 mol of Iron has 55.93319 g. To find out the how many moles of Iron we have in 1 kg, we calculate the ratio: 1000 / 55.93319 = **17.8785 moles of Iron**.

**Example 3**. How many atoms there are in 2 g of Lead (Pb) ?

From The Periodic Table of Elements we know that 1 mol of Lead has 207.2 g. Also we know that 1 mol of any substance has 6.022·10^{23} atoms. Writing the numbers down, gives:

**Example 4**. What is the mass of 1 atom of Titanium (Ti) ?

From The Periodic Table of Elements we know that 1 mol of Titanium has 47.867 g. Also we know that 1 mol of any substance has 6.022·10^{23} atoms. Writing the numbers down, gives:

Don’t forget to Like, Share and Subscribe!