Relative formula mass — AQA GCSE Combined Science
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Relative formula mass explained
Relative formula mass compares the mass of one formula unit of a compound with one-twelfth of the mass of a carbon-12 atom, so it has no units.
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To calculate it, use the relative atomic masses of the elements, usually given in the periodic table or the question, and add them in the proportions shown by the formula. For water, H₂O, the calculation is (2 × 1) + 16 = 18. For calcium carbonate, CaCO₃, it is 40 + 12 + (3 × 16) = 100. Subscripts multiply the relative atomic mass of the atom or group they follow, and brackets are treated in the same way. Balancing numbers (coefficients) in front of a formula are ignored when calculating relative formula mass.
In a balanced chemical equation, the sum of the relative formula masses of the reactants in the quantities shown equals the sum of the relative formula masses of the products in the quantities shown.
This statement links conservation of mass to relative formula mass (Mr). In a balanced equation, the total Mr of all reactant species, each multiplied by its balancing number, equals the total Mr of all product species, each multiplied by its balancing number. For example, 2H₂ + O₂ → 2H₂O: reactants give 2 × 2 = 4 for H₂ plus 1 × 32 = 32 for O₂, totalling 36; products give 2 × 18 = 36. The balancing numbers are essential because they represent the quantities shown. This works because atoms are conserved in a chemical reaction, so the total mass of atoms on each side is unchanged. The skill is assessed by checking that you multiply each Mr by its balancing number before summing, and that you compare the two totals correctly.
Students should be able to calculate the percentage by mass in a compound given the relative formula mass and the relative atomic masses.
Percentage by mass shows the fraction of a compound's mass contributed by a particular element. First calculate the relative formula mass (Mr) of the compound by adding the relative atomic masses (Ar) of all atoms in its formula. Then find the total mass of the element of interest by multiplying its Ar by the number of its atoms in the formula. Divide that element's total mass by the compound's Mr and multiply by 100. For example, in H₂O, Mr = (2 × 1) + 16 = 18; the percentage by mass of hydrogen is (2 ÷ 18) × 100 = 11.1%. The method is assessed by checking correct Ar values, correct counting of atoms, correct Mr, and correct substitution into the percentage expression.
Your focus
- Define relative formula mass as the sum of the relative atomic masses of the atoms in a formula.
- Calculate the relative formula mass of a compound from its formula and given relative atomic masses.
- Apply subscripts and brackets correctly when summing atomic contributions, while ignoring balancing coefficients.
Show all 9 objectives
- Calculate the relative formula mass of a species from its formula.
- Apply balancing numbers to relative formula masses in an equation.
- Verify that the total relative formula mass of reactants equals that of products in a balanced equation.
- Calculate the relative formula mass of a compound from its formula.
- Determine the total mass of a named element within one formula unit.
- Calculate the percentage by mass of an element in a compound using Ar and Mr values.
Relative formula mass exam tips
Marking Points
- Relative formula mass is the sum of the relative atomic masses of all atoms shown in the formula of the compound.
- Each subscript in the formula multiplies the relative atomic mass of the atom or group immediately before it.
- Relative formula mass is calculated from the formula alone; balancing numbers (coefficients) in front of a formula are ignored.
- The value of M_r is a ratio and therefore has no units.
- Calculations should use the relative atomic masses supplied in the question or taken from the periodic table, showing each element's contribution.
- For formulae containing brackets, the subscript after the bracket multiplies every atom inside the bracket.
- State that relative formula mass is found by adding the relative atomic masses of all atoms in the formula.
- Multiply each species' Mr by its balancing number in the equation before adding.
- Sum the reactant values and sum the product values separately.
- Compare the two totals and conclude that they are equal for a correctly balanced equation.
- Use a worked example such as 2H₂ + O₂ → 2H₂O to show both totals equal 36.
- Calculate the relative formula mass of the compound by summing the relative atomic masses of all atoms in the formula.
- Identify the number of atoms of the required element in the formula.
- Calculate the total mass of that element as Ar × number of atoms.
- Divide the element's total mass by the compound's Mr and multiply by 100.
- Give the answer to an appropriate number of significant figures, typically three.
Examiner Tips
- 💡Write out each element's contribution separately before adding, so a marker can follow the method and any slip is easy to find.
- 💡Do not use balancing numbers (coefficients) in front of a formula when calculating its relative formula mass (M_r).
- 💡Write the Mr calculation for each species clearly before applying balancing numbers.
- 💡Show the multiplication step explicitly so the examiner can follow your reasoning.
- 💡Check that your equation is balanced before comparing the two totals.
- 💡Write out the Mr calculation line by line to avoid arithmetic slips.
- 💡State the formula percentage = (total mass of element ÷ Mr) × 100 before substituting values.
- 💡Check that your final percentage is less than 100 and is reasonable for the formula.
Common Mistakes
- Adding subscripts as if they were masses, for example treating H₂O as 1 + 2 + 16; correct this by multiplying each relative atomic mass by its subscript.
- Ignoring a subscript when several atoms of one element are present, for example calculating CO₂ as 12 + 16; correct this by including (2 × 16) for the two oxygen atoms.
- Including balancing coefficients in the calculation, for example calculating the M_r of 2H₂O as 36; correct this by ignoring the front multiplier and calculating the M_r of H₂O as 18.
- Adding Mr values without multiplying by balancing numbers: correct by multiplying each species' Mr by its coefficient first.
- Using relative atomic masses of individual atoms instead of the full relative formula mass of each species: correct by summing all atoms within each formula.
- Forgetting that balancing numbers apply to the whole species: correct by treating 2H₂O as two lots of Mr 18, giving 36.
- Using the relative atomic mass of the element instead of its total mass in the compound: correct by multiplying Ar by the number of atoms present.
- Dividing by the element's mass rather than the compound's Mr: correct by using Mr as the denominator.
- Forgetting to multiply by 100: correct by converting the fraction to a percentage.