Mole calculations

If you are not sure what the mole or the relative atomic mass (A_r) are or perhaps you are not sure how to calculate the relative formula mass (M_r) of a substance then click here before you read this page.

Calculating the number of moles

To calculate the relative formula mass (M_r ) of a compound you simply add up the relative atomic masses (A_r) of the elements that make it up. For example the relative formula mass (M_r) of carbon dioxide (CO₂) is found by adding up the relative atomic masses (A_r) of carbon and oxygen e.g.

A_r of carbon =12     A_r of oxygen=16

So the relative formula mass (M_r) of CO₂ = (A_r of C) + (2x A_r of oxygen)
M_r= 12 + 32 =44.
Also we can say that the mass of 1 mole is just the M_r expressed in grams. So 1 mole of CO₂=44g.
This also means the mass of 6x10²³ molecules (that is Avogadro's number of molecules) of carbon dioxide has a mass of 44g.
If 44g of CO₂ = 1 mole of CO₂, then how many moles is say 11g of CO₂ ?
Well:

• 1 mole of CO₂ = 44g
so
• 0.5 moles of CO₂ = 22g
so
• 0.25 moles of CO₂ = 11g

These simple formulae allow you to calculate the number of moles of any element or compound present.

Example 2

The molecule shown opposite is the sugar glucose; its molecular formula is C₆H₁₂O₆.
The relative formula mass (M_r) of glucose (C₆H₁₂O₆) is found by adding up the relative atomic masses (A_r) of carbon, hydrogen and oxygen just as we did above for carbon dioxide e.g.

A_r of carbon=12,   A_r of hydrogen=1,     A_r of oxygen=16
so M_r of glucose, C₆H₁₂O₆ =(6x A_r of C) + (12x A_r of hydrogen) + (6x A_r of oxygen)
M_r= 72 + 12 + 96 =180.
Also the mass of 1 mole is just the M_r expressed in grams. So 1 mole of glucose, C₆H₁₂O₆ =180g.

So if we had; say 37g of glucose; how many moles of glucose would this be?
Well using the formula above we have:

In mole calculations:

• the number of moles is given the symbol: n
• the mass of the substance is simply: m
• relative atomic mass or relative formula mass is: A_r or M_r

You should be able to use the formula below to calculate either:

• the number of moles, n
• the mass of substance, m
• the M_r or A_r of a substance

All that is needed is a bit of simple arithmetic and the ability to rearrange any formula given. The highlighted box below shows all three formulae which you could be asked to use.

Example 3

What is the mass of 0.65 moles of glucose? To calculate the mass we use the formula :
mass = number of moles x M_r
m= n x M_r
m = 0.65 mol x 180 = 117g
so 0.65 moles of glucose has a mass of 117g.

Key points

• The mass of 1 mole of a substance is simply the relative formula mass (M_r) expressed in grams.
• You should learn and be able to apply the formulae given in the box above. The best way to do this is by completing questions - so click the link below and complete all the questions or have a go at working out the number of moles present for various elements and compounds in the activity opposite, you will likely need a calculator to complete this activity- don't forget to check your answers.

Check your understanding - Mole calculations

Check your understanding - Additional mole calculation questions