Using moles to balance equations (HT only) — AQA GCSE Combined Science
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Using moles to balance equations (HT only) explained
This Higher Tier skill finds the balancing numbers in a symbol equation from experimental masses.
Read the full explanation
Convert each mass in grams to moles by dividing by its relative formula mass (Mr). Then divide each number of moles by the smallest value to get a simple ratio. If the ratio is not whole numbers, multiply all values by the same factor to obtain the simplest whole number ratio. For example, if 2.4 g of Mg reacts with 1.6 g of O₂, moles Mg = 2.4 ÷ 24 = 0.10 mol and moles O₂ = 1.6 ÷ 32 = 0.050 mol. Dividing by 0.050 gives Mg:O₂ = 2:1, so the equation is 2Mg + O₂ → 2MgO. The ratio gives the balancing numbers.
Students should be able to balance an equation given the masses of reactants and products.
Balancing an equation from masses is a Higher Tier skill that involves converting each substance's mass into moles, then finding the simplest whole-number ratio. For example, if 4.8 g of magnesium reacts with 3.2 g of oxygen to form 8.0 g of magnesium oxide, divide each mass by its relative formula mass: Mg: 4.8 ÷ 24 = 0.20 mol; O₂: 3.2 ÷ 32 = 0.10 mol; MgO: 8.0 ÷ 40 = 0.20 mol. The mole ratio Mg:O₂:MgO is 0.20:0.10:0.20, which simplifies to 2:1:2. The balanced equation is 2Mg + O₂ → 2MgO. This method works because the law of conservation of mass means the number of atoms of each element is the same before and after reaction, so the mole ratio must be a simple whole-number ratio.
Students should be able to change the subject of a mathematical equation.
Changing the subject of an equation means rearranging it so a different variable stands alone on one side. In chemistry, this is essential when using the mole equation n = m ÷ Mᵣ. To make mass the subject, multiply both sides by Mᵣ: m = n × Mᵣ. To make relative formula mass the subject, divide both sides by n: Mᵣ = m ÷ n. The same inverse-operation method applies to any equation, such as concentration = amount ÷ volume, which rearranges to amount = concentration × volume. Always perform the same operation on both sides, keep the equation balanced, and check by substituting simple numbers. This skill supports quantitative chemistry calculations.
Your focus
- Convert masses of reactants and products into amounts in moles using relative formula masses.
- Find the simplest whole number ratio of moles from experimental mass data.
- Use the whole number ratio to write a balanced symbol equation.
Show all 9 objectives
- Convert the mass of each reactant and product into moles using n = m ÷ Mᵣ.
- Deduce the simplest whole-number mole ratio from the calculated amounts.
- Construct and check a balanced symbol equation that is consistent with the given masses.
- Rearrange a given equation to make a specified variable the subject.
- Apply inverse operations correctly to both sides of an equation.
- Substitute values into a rearranged equation and evaluate the result with correct units.
Using moles to balance equations (HT only) exam tips
Marking Points
- Calculate the relative formula mass (Mr) for each reactant and product from its formula.
- Convert each given mass to moles using moles = mass ÷ Mr.
- Divide each number of moles by the smallest number of moles to obtain a simple ratio.
- If necessary, multiply all values by the same whole number to convert the ratio to the simplest whole numbers.
- Write the balanced symbol equation using the whole number ratio as the balancing numbers.
- Calculate the amount in moles of each substance by dividing its mass by its relative formula mass or relative atomic mass.
- Use the mole ratios obtained to deduce the simplest whole-number ratio of reactants and products.
- Write the balanced symbol equation with the correct state symbols if they are given or can be deduced.
- Check that the final equation has the same number of atoms of each element on both sides and that any charges balance.
- Show working clearly, including units and the relative formula masses used, so that the method can be followed.
- Identify the variable that must become the subject and the operations connecting it to the other variables.
- Apply inverse operations to both sides of the equation so that the required variable is isolated.
- Keep the equation balanced by performing the same operation on every term.
- Substitute known values into the rearranged equation and evaluate the result with correct units.
- Check the rearrangement by substituting simple numbers or by reversing the operation.
Examiner Tips
- 💡Show the moles of each substance clearly, for example 'moles of Mg = 2.4 ÷ 24 = 0.10 mol'.
- 💡State the ratio before writing the equation, for example 'Mg:O₂ = 2:1', so your reasoning is visible.
- 💡Check that the final equation is balanced by counting atoms of each element on both sides.
- 💡Write down the relative formula mass for every substance before doing any division, as this reduces arithmetic errors and makes your method clear.
- 💡If the mole ratio is not immediately whole numbers, divide by the smallest value and then multiply all values by the same factor to obtain the simplest whole-number ratio.
- 💡After balancing, do a quick atom count for each element on both sides; this catches most errors and takes only a few seconds.
- 💡Write the original equation clearly, then show each rearrangement step so that your method can be followed even if the final answer has an arithmetic slip.
- 💡Substitute simple numbers into your rearranged equation to check it gives the same result as the original equation.
- 💡Include units in your final answer and make sure the unit matches the variable you have made the subject.
Common Mistakes
- Dividing mass by mass instead of converting each mass to moles first. Correction: always convert grams to moles using Mr before finding the ratio.
- Rounding mole values too early, which changes the final ratio. Correction: keep values unrounded until the ratio is found, then round only the final whole numbers.
- Forgetting to multiply all parts of the ratio by the same factor when a fractional ratio appears. Correction: multiply every value by the same number to reach whole numbers.
- Dividing mass by relative atomic mass for a molecular substance such as O₂ instead of by its relative formula mass of 32; correction: use the relative formula mass for the substance as written in the equation.
- Forgetting to simplify the mole ratio to the simplest whole numbers, for example leaving 0.20 : 0.10 : 0.20 instead of 2 : 1 : 2; correction: divide all values by the smallest value and multiply to remove fractions.
- Assuming the masses given are always in grams and using them directly as moles; correction: always convert mass to moles using n = m ÷ Mᵣ before finding the ratio.
- Applying an operation to only one side of the equation; correction: always perform the same operation on both sides to preserve equality.
- Confusing multiplication and division when rearranging, for example writing m = n ÷ Mᵣ instead of m = n × Mᵣ; correction: use inverse operations and check with simple numbers.
- Ignoring brackets when the subject appears in a term with more than one factor; correction: expand or factorise carefully before isolating the variable.