# Mole (unit)

The mole (symbol: mol) is one of the seven SI base units and is commonly used in chemistry. It measures the amount of substance of a system and is defined as the amount of substance that contains as many elementary entities as there are atoms in exactly 0.012 kilogram of carbon-12. This quantity is known as Avogadro's number and is approximately 6.0221415 × 10²³ (2002 CODATA value).

Because of the relationship of the atomic mass unit to Avogadro's number, a practical way of stating this for atoms or molecules is: That amount of the substance containing exactly the same number of grams as the number of the atomic weight of the substance. Since iron, for example, has an atomic weight of 55.845, there are 55.845 grams (0.055845 kilograms) in a mole of iron.

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## Elementary entities

When the mole is used to specify the amount of a substance, it must be specified what kind of 'elementary entities' (particles) in the substance are being counted. The particles can be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. For example, 18 grams of water contain about 1 mole of molecules, but 3 moles of atoms.

When the substance of interest is a gas, the particles are usually molecules. However, the noble gases (He, Ar, Ne, Kr, Xe, Rn) are all monoatomic, that is each particle of gas is a single atom. Almost all gases have the same molar volume of 22.4 litres per mole at standard temperature and pressure.

A mole of atoms or molecules is also called a 'gram atom' or 'gram molecule'.

## Background

The name mole first appeared in 1902 when it was used to express the gram molecular weight of a substance. So, for example, 1 mole of hydrochloric acid (HCl) has a mass of 36.5 grams (atomic weights Cl: 35.5 u, H: 1.0 u).

Colloquially speaking, the mole is a convenient way of counting large numbers of particles. If you are dealing with this many molecules or atoms, then you have a mole of molecules or atoms. If you have half this number of these entities, then you have half a mole of them.

## History

Prior to 1959 both the IUPAP and IUPAC used oxygen to define the mole, the chemists defining the mole as the number of atoms of oxygen which had mass 16 g, the physicists using a similar definition but with the oxygen-16 isotope only. The two organisations agreed in 1959/1960 to define the mole as such:

"The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol.""

This was adopted by the CIPM (International Committee for Weights and Measures) in 1967, and in 1971 it was adopted by the 14th CGPM (General Conference on Weights and Measures)

In 1980 the CIPM clarified the above definition, defining that the carbon-12 atoms are unbound and in their ground state.

## Utility of "moles"

Moles are very useful in chemical calculations, because they enable the calculation of yields and other values when dealing with particles of different mass.

Number of particles is a more useful unit in chemistry than mass or weight, because reactions take place between atoms (for example, two hydrogen atoms and one oxygen atom make one molecule of water) that have very different weights (one oxygen atom weighs almost 16 times as much as a hydrogen atom). However, the raw numbers of atoms in a reaction are not convenient, because they are very large; for example, just one millilitre of water contains over 3 × 10²² (or 30,000,000,000,000,000,000,000) molecules.

## Example calculation

In this example, moles are used to calculate the mass of CO2 given off when 1 g of ethane is burnt. The equation for this chemical reaction is:

7 O2 + 2 C2H6 → 4 CO2 + 6 H2O

Here, 7 moles of oxygen react with 2 moles of ethane to give 4 moles of carbon dioxide and 6 moles of water. Notice that the number of moles does not need to balance on either side of the equation. This is because a mole does not count mass or the number of atoms involved, simply the number of individual particles. In our calculation it is first necessary to work out the number of moles of ethane that has been burnt. The mass in grams of one mole of a substance is by definition its atomic or molecular mass. The atomic mass of hydrogen is 1, and the atomic mass of carbon is 12, so the molecular mass of C2H6 is (2 × 12) + (6 × 1) = 30. One mole of ethane is 30 g. The amount burnt was 1 g, or 1/30th of a mole. The molecular mass of CO2 (the atomic mass of carbon is 12 and that of oxygen is 16) is 2 × 16 + 12 = 44, so one mole of carbon dioxide is 44 g. From the formula we know that

1 mole of ethane gives off 2 moles of carbon dioxide (because 2 give off 4).

We also know the masses of a mole of both ethane and carbon dioxide, so

30 g of ethane gives off 2 × 44 g of carbon dioxide.

It is necessary to multiply the mass of carbon dioxide by 2 because two moles are produced. However, we also know that just 1/30th of a mole of ethane was burnt. Again:

1/30th of a mole of ethane gives off 2 × 1/30th of a mole of carbon dioxide,

so finally:

30 × 1/30 g ethane gives off 44 × 2/30 g of carbon dioxide = 2.93 g.

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