Reacting Mass Calculations

The number of moles of a substance can be found by using the following equation:

$number of moles = \frac{mass of substance in grams}{molar mass (g {mol}^{- 1})}$

It is important to be clear about the type of particle you are referring to when dealing with moles
- E.g. 1 mole of CaF₂ contains one mole of CaF₂ formula units, but one mole of Ca²⁺and two moles of F^-ions

Reacting masses

The masses of reactants are useful to determine how much of the reactants exactly react with each other to prevent waste
To calculate the reacting masses, the chemical equation is required
This equation shows the ratio of moles of all the reactants and products, also called the stoichiometry, of the reaction
To find the mass of products formed in a reaction the following pieces of information are needed:
- The mass of the reactants
- The molar mass of the reactants
- The balanced equation

Worked example

Calculate the mass of magnesium oxide that can be made by completely burning 6.0 g of magnesium in oxygen.

magnesium (s) + oxygen (g) → magnesium oxide (s)

Answer:

Step 1: The symbol equation is:

2Mg(s) + O₂(g) → 2MgO(s)

Step 2: The relative atomic masses are:

magnesium : 24.31 oxygen : 16.00

Step 3: Calculate the moles of magnesium used in reaction

$number of moles = \frac{6.0 g}{24.31 g {mol}^{- 1}} = 0.25 mol$

Step 4: Find the ratio of magnesium to magnesium oxide using the balanced chemical equation

	Magnesium	Magnesium oxide
Mol	2	2
Ratio	1	1
Change in mol	-0.25	+0.25

Therefore, 0.25 mol of MgO is formed

Step 5: Find the mass of magnesium oxide

mass = mol x M

mass = 0.25 mol x 40.31 g mol^-1

mass = 10.08 g

Therefore, mass of magnesium oxide produced is 10 g (2 sig figs)

Worked example

Calculate the mass of aluminium, in tonnes, that can be produced from 51 tonnes of aluminium oxide. The equation for the reaction is:

2Al₂O₃ ⟶ 4Al + 3O₂

Answer:

Step 1: Calculate the moles if aluminium oxide used

mass of Al₂O₃ in g = 51 x 10⁶= 51,000,000 g

moles = $\frac{51, 000, 000 g}{101.96 g {mol}^{- 1}}$ = 500,196.16 mol

Step 2: Find the ratio of Al₂O₃ to Al using the molar ratio from the balanced equation

2Al₂O₃ : 4Al

Ratio is thus 1 : 2

So 500,196.16 mol moles of Al₂O₃ produces 100,0392.31 moles of Al

Step 3: Calculate mass of Al

mass = Moles x M_r

mass = 1,000,392.31 mol x 26.98 g mol^-1 = 26,990,584.54 g

Step 4: Convert mass from grams to tonnes

$\frac{26, 990, 584.54 g}{10^{6}}$ = 26.99 tonnes

Exam Tip

As long as you are consistent it doesn't matter whether you work in grams or tonnes or any other mass unit as the reacting masses will always be in proportion to the balanced equation.

Reacting Mass Calculations (HL IB Chemistry)

Revision Note