A shortened version of the periodic table is shown below. For each element there are two number in the box e.g. for magnesium the numbers 24 and 12 are alongside its symbol, Mg. The number 12 is the atomic number, the proton number. The other number is the relative atomic mass, A_r. It is the average mass of magnesium atoms taking into account the presence of any isotopes of magnesium. The mass of 1 mole of magnesium is simply the A_r expressed in grams, so 1 mole of magnesium is 12g, and of course 1 mole of any substance contains 6 x 10²³ particles.

Examples using other elements from the periodic table.

• the element boron, ¹¹B, its A_r=11, so 11g of boron will contain 6x10²³ or 1 mole of boron atoms.
• the element calcium,⁴⁰Ca, its A_r=40, so 40g of calcium will contain 6x10²³ or 1 mole of calcium atoms.
• the element aluminium,²⁷Al, its A_r=27, so 27g of aluminium will contain 6x10²³ or 1 mole of aluminium atoms.

The mass of 1 mole of an element is just the A_r expressed in grams

Relative formula mass, M_r

Carbon dioxide is a small molecule made up of three atoms, 1 atom of carbon and 2 atoms of oxygen.
To calculate the relative formula mass, M_r of this molecule is a simple task, simply add up the relative atomic masses, A_r, for each of the atoms present. The calculated mass of the molecule is called the relative formula mass, it is given the symbol M_r.

example 1- Calculate the realtive formula mass of carbon dioxide.
M_r of CO₂ = (A_r of carbon) + (2xA_r of oxygen)
= 12 + 32
M_r of CO₂ = 44

example 2 - Calculate the relative formula mass, M_r, of glucose sugar, C₆H₁₂O₆.
M_r of C₆H₁₂O₆ = (6xA_r of carbon) + (12xA_r of hydrogen) + (6xA_r of oxygen)
= (6x12) + (12 x1) + (6x16) =180
M_r of C₆H₁₂O₆ = 180
If we express the A_r or M_r in grams then this will give us the mass of 1 mole, that is the mass of 6x10²³ particles of that substance.
e.g.1- Carbon dioxide has a relative formula mass, M_r, of 44. This means that 44g of carbon dioxide will contain 6x10²³ molecules of carbon dioxide. Or 3 moles of atoms. 2 moles of oxygen atoms and 1 mole of carbon atoms.
e.g.2- Glucose has a relative formula mass, M_r, of 180. This means that 180g of glucose will contain 6x10²³ molecules of glucose. Or 24 moles of atoms. 6 moles of carbon atoms and 12 moles of hydrogen atoms and 6 moles of oxygen atoms.

To avoid confusion and mix-ups great care needs to be taken to ensure you are very clear about the type of particle you are discussing e.g. oxygen gas is a diatomic gas, this means that exists as a molecule, formula O₂.
If we had 10 molecules of oxygen gas we would have 20 atoms of oxygen, since each molecule contains 2 atoms of oxygen. If we had 6x10²³ molecules, that is 1 mole of molecules then we would have 2x6x10²³ atoms of oxygen present, that is 2 moles of oxygen atoms.
The relative atomic mass of an oxygen atom is 16, A_r =16. So the mass of 1 mole of oxygen molecules is 32g. The mass of 1 mole of oxygen atoms is 16g. To avoid confusion you must be clear about the type of particle, atom, molecule or ion you are discussing.

Key points

• The relative atomic mass, A_r is the average mass of an element atoms taking into account the presence of any isotopes. The relative atomic mass of any element is simply found in the periodic table.
• The relative formula mass, M_r, is simply found by adding up the relative atomic masses for each element in the compound.
• The mass of 1 mole of a substance is simply the A_r or M_r expressed in grams.

Check your understanding - complete the following practice questions