Higher tier only

If you are not sure what the mole or the relative atomic mass (A_{r}) are or 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.
The relative formula mass (M_{r}) of carbon dioxide, CO_{2} 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 CO_{2} = (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 CO_{2}=44g.

This also means the mass of 6x10^{23} molecules (that is Avogadros number of molecules) of carbon dioxide is 44g.

If 44g of C0_{2} = 1 mole of C0_{2}, then how many
moles is say 11g of C0_{2} ?

well:

- 1 mole of C0
_{2} = 44g
so
- 0.5 moles of C0
_{2} = 22g
so
- 0.25 moles of C0
_{2} = 11g

You may have worked this out in your head quickly in one step by dividing 11 by 44. If you did then
you used the formula below:

These simple formula 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 C_{6}H_{12}O_{6}.

The relative formula mass (M_{r}) of glucose (C_{6}H_{12}O_{6}) 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,
C_{6}H_{12}O_{6} =(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, C_{6}H_{12}O_{6} =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 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 = mumber 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 susbstance 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 - don't forget to check your answers.
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