# Mole concept & Avogadro’s constant

1.1.1: Describe the mole concept and apply it to substances. The mole concept applies to all kinds of particles: atoms, molecules, ions, formula units etc. The amount of substance is measured in units of moles. The approximate value of Avogadro’s constant (L), 6.02 x 1023 mol-1, should be known.

Atoms and molecules are pretty small (understatement!) and, as scientists are interested in being able to describe quantities of matter in terms of the mass and number of particles contained per unit mass, this poses a problem.

Measuring the mass of individual atoms, we find that one hydrogen atom has a mass of about 1.66 x 10-27g

This number is far too small to be useful and so it makes sense to deal with quantities of atoms which can be measured in the laboratory.

### The hydrogen standard

Hydrogen is the smallest atom and it was originally used as the standard by which all the other atoms were compared. It was assigned a value of 1 unit and other atoms masses calculated compared to hydrogen atoms.

The 1H isotope has a mass assigned a value of exactly 1 atomic mass unit. This was the original reference.

### The carbon 12 standard

Nowadays the 12C isotope is used as a reference for comparison of relative atomic masses. This isotope has the assigned mass of 12.00000, all other atoms are measured relative to 12C.

Measured on this scale hydrogen atoms (on average) have a relative mass of 1.00797

Carbon atoms have a relative mass of 12.01111 on average. Although this seems strange at first sight, it is because carbon has several isotopes 12C, 13C, and 14C and the relative mass of carbon is given as the weighted average of all of the isotopes in a naturally occurring sample. Clearly, the average must be greater than 12.0000.

Most tables use the relative atomic masses rounded up to one or two decimal places.

Carbon atoms have a mass approximately 12 times that of a hydrogen atom, therefore they have a RELATIVE mass of 12 (there are no units as it is a comparison – see relative measures)

Provided the number of carbon atoms is equal to the number of hydrogen atoms the mass of carbon is always 12 times the mass of hydrogen.

Clearly there will be a specific number of hydrogen atoms that when weighed have a mass of 1g and that the same number of carbon atoms MUST have a mass of 12g. This number, named after its discoverer is called:

Avogadro’s number or constant is the number to which the mass of an atom must be multiplied to give a mass in grams numerically equal to its relative atomic mass.

This gives rise to two important definitions

• The amount of any substance containing an Avogadro number of particles of that substance is called a mole.
• 1 mole of any substance has a mass equal to its relative mass expressed in grams

The relationship between moles, mass and number of particles can be expressed by simple formulae:

#### The structure of matter

It is now accepted that matter in all its forms is made up of indivisible particles that themselves have mass. These particles are called atoms, molecules and ions. The nature of the substance is dictated by the atoms elements that have bonded together to make the bulk substance. This may be an ionic structure, a covalent structre or a metallic structure.

Molecules are made up of two or more atoms chemically bonded together.

Ions are specialised atoms or groups of atoms chemically combined together that have lost or gained electrons and posess an overall electrical charge.

The fundamental particle that is the building block of matter is therefore the atom. There are about 90 naturally occuring types of atoms each with a different arrangement of sub-atomic particles (protons, neutrons and electrons) and consequently different masses.

The structure of matter is one of the following:

• atoms —> molecules —> bulk compound or element
• atoms —> bulk element
• atoms —> ions —> bulk ionic compound

The masses that are measured in the laboratory are masses corresponding to vast numbers of tiny atoms or molecules. Logically atoms that are heavier will register larger masses for equal numbers of atoms.

## Relative atomic mass

If one carbon atom has a mass of 12 atomic mass units and one magnesium atom has a mass of 24 atomic mass units, then as a magnesium atom is twice as heavy as a carbon atom it follows that this ratio will be maintained for any number of atoms.

On the atomic mass scale the carbon 12 isotope is designated a value of 12 atomic mass units and all other masses are measured relative to this (relative atomic mass)

## The mole concept

It is convenient to consider the number of atoms needed to make 12g of carbon and for this number to be given a name – one mole of carbon atoms. This allows us to talk about relative quantities of substances in the macroscopic world and to know the relative number of atoms (or smallest particles) in each bulk substance.

The actual number of atoms that is needed to give the relative atomic mass expressed in grams is called Avogadro’s number (symbol L)

Avogadro’s number = 6,02 x 1023

## Definition of a mole

There are two useful definitions.

1. The relative atomic (molecular) mass of a substance expressed in grams
2. An Avogadro number of particles of any substance

1.1.2: Calculate the number of particles and the amount of substance (in moles). Convert between the amount of substance (in moles) and the number of atoms, molecules or formula units

1 mole = 6.02 x 1023 formula units of that substance.

We can also talk about the atoms within molecules.

For example, 1 mole of water contains 2 moles of hydrogen atoms and 1 mole of oxygen atoms. It is a simple matter of multiplying the moles of the compound by the atoms or ions that make it up. 