Higher tier only

### 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 of carbon dioxide, CO_{2} is found by adding up the A_{r} of carbon and
oxygen e.g.

A_{r} of carbon =12 A_{r} of oxygen=16

so M_{r} of CO_{2} = ( A_{r} of C) + (2x A_{r} of oxygen)

M_{r}= 12 + 32 =44.

Also 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 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 substance.

#### Example 2

The molecule shown opposite is glucose sugar, its molecular formula is C_{6}H_{12}O_{6}.

The relative formula mass of glucose, C_{6}H_{12}O_{6} is found by adding up the 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}

This leads up to 3 formula for calculating the:

- number of moles, n
- the mass of substance, m
- the M
_{r} or A_{r}

Example

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.

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