Calculation techniques for the higher tier to determine the empirical and molecular formulae of a substance, masses of a required substance in a reaction, and calculations involving moles.

If you know the mass of a reactant and a product, you can use simple ratios to calculate reacting masses and product masses.

- Question
When 12 g of carbon is burned in air, 44 g of carbon dioxide is produced. What mass of carbon is needed to produce 11 g of carbon dioxide?

12 g of carbon makes 44 g of carbon dioxide.

12 ÷ 44 g of carbon will make 1 g of carbon dioxide.

Therefore, to make 11 g of carbon dioxide, you will need 11 × (12 ÷ 44 g) =

**3 g of carbon**.)**Alternative answer**An alternative method is as follows: Mass unknown = (Mass of known ÷

*M*_{r}known) ×*M*_{r}unknown.This works because (Mass of known ÷

*M*_{r}known) gives you the number of moles of the substance with the known mass. In this case:(11 g ÷ 44) × 12 =

**3 g of carbon**to make 11 g of carbon dioxide.

- Question
When 5.0 g of calcium carbonate is decomposed by heating, it produces 2.2 g of carbon dioxide. What mass of calcium carbonate is needed to produce 8.8 g of carbon dioxide?

5 g of calcium carbonate makes 2.2 g of carbon dioxide.

5 ÷ 2.2 g of calcium carbonate will make 1 g of carbon dioxide.

Therefore, to make 8.8 g of carbon dioxide, you will need 8.8 × (5 ÷ 2.2 g) =

**20 g of carbon**.**Alternative answer**An alternative method is as follows: Mass unknown = (Mass of known ÷

*M*_{r}known) ×*M*_{r}unknown.This works because (Mass of known ÷

*M*_{r}known) gives you the number of moles of the substance with the known mass. In this case:(8.8 g ÷ 44) × 100 =

**20 g of calcium carbonate**to make 8.8 g of carbon dioxide.

The mass of a product or reactant can be calculated using the balanced equation. Follow these steps.

- Write out the balanced symbol equation. Underline the two substances you are interested in.
- Write the given mass of a substance under its formula.
- Work out the total relative formula mass (
*M*_{r}) for each substance (the one you know**and**the one you are trying to find out). Write these under their formulae. - Calculate: unknown mass = (known mass ÷ total
*M*_{r}of known substance) × total*M*_{r}of unknown substance.

- Question
Calculate the mass of iron (Fe) that can be extracted from 8 g of Fe

_{2}O_{3}in the reaction with carbon.Step one 2Fe _{2}O_{3}+ 3C →4Fe + 3CO _{2}Step two 8 g ? g Step three 2 × 160 = 320 4 × 56 = 224 Step four mass of iron formed = (8 ÷ 320) × 224 = **5.6 g**