Higher tier only

Make sure you know what is meant by the terms Ar, Mr and you know how to calculate the mass of 1 mole of a substance before reading this page!

One of the main uses of moles in GCSE chemistry is in calculating the masses of reactants and products used up or produced in chemical reactions. The best way to learn how to do these calculations is by completing lots of examples!

Example 1. Calculate the mass of water produced by burning 25g of hydrogen in air.

Ar of H=1   Ar of O=16
Step 1- write a balanced symbolic equation for the reaction:
##### 2H2(g) + O2(g) → 2H2O(l)

Have you have ever wondered what the numbers shown in green are in the symbolic equation. Some people might read them as meaning 2 molecules of hydrogen react with 1 molecule of oxygen to make 2 molecules of hydrogen oxide or water.

However we are looking to calculate masses and weighing out 2 molecules of hydrogen and 1 molecule of oxygen is going to be a little tricky! So scale the whole equation up, scale up by a factor of 6 x1023, that is the number of particles present in 1 mole of any substance. That means we now have 2 moles of hydrogen reacting with 1 mole of oxygen to give 2 moles of water and not 2 molecules reacting with 1 molecule to form 2 molecules of water! The numbers in front of the substances in symbolic equations tell you the number of moles that are reacting or the number of moles of product that are produced.

Remember that moles are a measure of the amount of a substance. So:

• The Mr of hydrogen, H2 will be 2, so 1 mole of hydrogen will have a mass of 2 grams.
• The Mr of oxygen, O2, will be 32, so 1 mole of oxygen will have a mass 32 grams.
From the balanced symbolic equation above we can see that we need 2 moles of hydrogen, well 1 mole is 2g, so 2 moles will be 4g. This means that 4g of hydrogen reacts with 1 mole, 32g of oxygen to produce 2 moles of water. The Mr of water is (2x Ar H + Ar of Oxygen) 18, so 1 mole of water is 18g, in our equation we produce 2 moles of water, 36g. This is outlined below:
##### 4g + 32g → 36g
The original question was how much water is produced by burning 25g of hydrogen in air. Well we can use or equation to work this out:
##### 2H2(g) + O2(g) → 2H2O(l)
however the questions askes nothing about oxygen so we can simply ignore it or simply remove it from the equation, it only askes about hydrogen and water. So we have:
##### 4g → 36g
So from our equation we know that 4g of hydrogen produce 36g of water. Now for the moment until you get to grips with mole calculations, calculate how much water 1g of hydrogen would produce. Well if 4g of hydrogen produce 36g of water, then divide by 4 to get what 1g of hydrogen would produce:

dividing by 4:
##### 1g ofhydrogengives → 9g ofwater
so if 1 gram of hydrogen produces 9g of water. So to find out how much water is produced from burning 25g of hydroegn then simply multiply by 25 to find out how much water is produced.
##### 25g → 9g x 25 = 225g of water
this method might seem long winded but once you get into the swing of it, you will be carrying out mole calculations quickly.

Example 2: Calculate the mass of carbon dioxide produce by burning 750g of methane in air.

Methane (CH4) is the gas that is burned in a Bunsen burner and it is also the gas that is used at home for cooking and heating. It burns to release lots of heat energy according to the equations below:

A balanced symbolic equation is shown below for this reaction. We can see that 1 mole of methane produces 1 mole of carbon dioxide gas.

##### CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)
the questions does not ask about oxygen or water, so remove them from the equation. So we have 1 mole of methane produces 1 mole of carbon dioxide:

Recall that the Ar of carbon=12   Ar of hydrogen=1   Ar of oxygen=16

##### 1 mole of methane = 16g → 1 mole of CO2 = 44g

So we can summarise this as:

##### 16g of methane produces → 44g of carbon dioxide
divide both sides of the above equation by 16 to find out what 1g of methane (CH4), would produce:
##### 1g of methane produces → 44g /16 = 2.75g of carbon dioxide
so if 1 gram of methane produces 2.75g of carbon dioxide, then simply multiply by 750 to calculate how much carbon dioxide would be produced by 750g of methane:
##### 2.75 x 750 = 2062.5g of carbon dioxide gas, or 2.062 kg of carbon dioxide gas.

Example 3: Calculate the mass of copper metal obtained by the reduction of 100g of copper oxide

Black copper oxide powder was placed in a glass tube and heated gently using a Bunsen burner, as shown below. If hydrogen gas is then fed into the glass tube it will reduce the black copper oxide to brown metallic copper. Word and symbolic equations are shown below for this reduction reaction :

As before we need to start with the balanced symbolic equation for the reaction:

##### CuO(s) + H2(g) → Cu(s) + H2O(g)
From the balanced symbolic equation we can see that 1 mole of copper oxide produces 1 mole of copper metal. The question does not ask about the hydrogen or hydrogen oxide (water) so simply remove them from the equation to simplify things a bit! We now have:

##### 1 mole CuO(s)→ 1 mole Cu(s)

Calculate the relative fomula mass (Mr) of copper oxide using the relative atomic masses (Ar) from the periodic table and we have:
Ar of Cu=63.5   Ar of O=16

or

##### 79.5g CuO(s)→ 63.5g Cu(s)

As above calculate the amount of copper obtained from 1g of copper oxide, which is easily done by simply dividing each side of the equation above by 79.5. This gives:

or

##### 1g CuO(s)→ 0.8g Cu(s)
So if 1g of copper oxide produces 0.8g of copper, then 100g of copper oxide will simply produce 80g of copper.

Example 4: How much iron can be produced from 150 tonnes of iron oxide?

In a blast furnace iron oxide is reduced to iron, the reaction is given by the equation below.

Ar of Fe = 56   Ar C =12   Ar O =16
##### Fe2O3(s) + 3CO(g) → 2Fe(s) + 3CO2(g)
As before calculate the mass of 1 mole of each of the reactants and products and scale up by the number of moles of each substance present:
##### 160g + 84g → 112g + 132g
The question askes nothing about carbon monoxide or carbon dioxide so remove these from our original equation:
##### 160g of iron oxide will produce → 112g of iron
From the symbolic equation we can see that 1 mole of iron oxide will produce 2 moles of iron. So now it is simply a matter of scaling up from grams to tonnes.
Now 1000Kg is 1 tonne. So we have:
##### 160tonnes → 112tonnes
as before work out how much iron you will get from 1 tonne of iron oxide:
##### 1 tonne of iron oxide → 0.75 tonnes of iron.
so simply multiply the answer by 750 to calculate the mass of iron obtained from 750 tonnes of iron oxid, 0.7 x 750 = 525 tonnes of iron.

I have drawn out these calculations to show you step by step how to carry out mole calculations. With practice you will be able to complete mole calculations in a few steps, but until you are confident with what you are doing go slow and make sure you are clear about what you are doing in each step.