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Standard form, unit conversions, significant figures, rearranging equations, percentages, ratios and reading rate graphs, with chemistry examples.
Specification references this topic covers: AQA 5.6.1; Edexcel C1.30, C1.43.
Maths is part of every chemistry calculation. Most marks are lost not because the chemistry is hard, but because of a slip with units, rounding or rearranging an equation.
This matters because maths skills carry a large share of the marks in a Combined Science exam, especially in Chemistry and Physics. The same few skills come up again and again, so practising them pays off in every topic.
By the end you will be able to use standard form, convert units, round properly, rearrange equations, work with percentages and ratios, and read rate graphs.
Standard form writes a number as A × 10ⁿ, where A is between 1 and 10 and n is a whole number. It is used for very large and very small numbers. 3 500 000 = 3.5 × 10⁶. 0.00072 = 7.2 × 10⁻⁴.
For a big number n is positive: count how many places the decimal point moves left. For a small number n is negative: count how many places it moves right.
Chemistry uses it for sizes. An atom has a radius of about 0.1 nm, which is 1 × 10⁻¹⁰ m. A nanometre (nm) is 1 × 10⁻⁹ m. Avogadro's constant is 6.02 × 10²³ per mole.
Always check the units before you calculate. 1 dm³ = 1000 cm³, so divide by 1000 to go from cm³ to dm³. 1 kg = 1000 g, so divide by 1000 to go from g to kg. 1 g = 1000 mg.
Concentration is often given in g/dm³ or mol/dm³, so a volume in cm³ must be changed to dm³ first. Times are in seconds unless you are told otherwise. Temperature changes in °C and kelvin are the same size.
A good habit is to write the unit beside every number and to write the unit of your answer. If a unit is missing from an answer you can lose a mark.
To round to a number of decimal places, look at the next digit. If it is 5 or more, round up. 3.4567 to 2 decimal places is 3.46.
Significant figures count from the first non-zero digit. 0.004568 to 2 significant figures is 0.0046. 24.07 to 3 significant figures is 24.1. Do not round in the middle of a calculation. Round only at the end, and give the answer to the same number of significant figures as the data, or to the number asked.
Estimate to check your answer makes sense. For 19.8 ÷ 4.1, think 20 ÷ 4 = 5. If your answer is 0.5 or 50, check again.
Most chemistry calculations use a short equation: moles = mass ÷ Mr, concentration = mass ÷ volume, mean rate = amount ÷ time, percentage by mass = Ar × number of atoms ÷ Mr × 100.
To rearrange, do the same thing to both sides. From concentration = mass ÷ volume you can get mass = concentration × volume and volume = mass ÷ concentration. A formula triangle can help: cover the quantity you want to find.
Set your working out in lines: write the equation, substitute with units, calculate, then give the answer with a unit. For example, 4.0 g in 250 cm³: 4.0 ÷ 0.250 = 16 g/dm³.
A percentage is a fraction out of 100. Percentage = part ÷ whole × 100. In chemistry you meet it as percentage by mass.
Percentage by mass of an element in a compound = (Ar × number of atoms of that element ÷ Mr of the compound) × 100. For MgO, Mr = 24 + 16 = 40 and Mg is 24 ÷ 40 × 100 = 60%.
Ratios come from balanced equations. In 2H₂ + O₂ → 2H₂O, the ratio of H₂ to O₂ is 2 : 1. So 6 mol of H₂ react with 3 mol of O₂. To use a ratio, scale each part by the same factor.
On a graph of volume of gas against time, a steep line means a fast reaction and a flat line means the reaction has stopped. Plot the independent variable on the x-axis, label both axes with units, choose a scale that fills the page, and draw a smooth line of best fit through the points.
The gradient of a straight line is the change in y divided by the change in x. For a curve, draw a tangent to the curve at the time you want and find its gradient. This gives the rate at that moment. For example, if a tangent goes from (10 s, 20 cm³) to (50 s, 60 cm³), the gradient is (60 − 20) ÷ (50 − 10) = 1.0 cm³/s.
Read values off carefully, use a ruler, and say what the pattern shows: for example, "the rate decreases because the reactants are being used up."
Standard form: A × 10ⁿ with A between 1 and 10. Convert cm³ to dm³ by dividing by 1000.
Round at the end. Estimate to check. Write the unit with every answer.
Percentage = part ÷ whole × 100. Ratios come from balanced equations. A rate is a gradient: change in y ÷ change in x.
Write 0.000 000 25 m in standard form.
Answer: 2.5 × 10⁻⁷ m
A student dissolves 4.0 g of salt to make 250 cm³ of solution. Calculate the concentration in g/dm³.
Answer: 16 g/dm³
Calculate the percentage by mass of iron in iron(III) oxide, Fe₂O₃. Relative atomic masses: Fe = 56, O = 16.
Answer: 70%
Maths skills for chemistry practice questions for GCSE Combined Science Chemistry. Try each one, then open the answer. Easy questions come first.
Write 3 500 000 in standard form.
Answer: 3.5 × 10⁶
How many dm³ are in 500 cm³?
Answer: 0.5
Convert 2.5 kg to g.
Answer: 2500
Round 3.4567 to 2 decimal places.
Answer: 3.46
Round 0.004568 to 2 significant figures.
Answer: 0.0046
Calculate the concentration in g/dm³ when 10 g of solid dissolves to make 500 cm³ of solution.
Answer: 20 g/dm³
Write 0.00072 in standard form.
Answer: 7.2 × 10⁻⁴
Calculate the percentage by mass of oxygen in magnesium oxide, MgO. Ar: Mg = 24, O = 16
Answer: 40%
Longer questions in the style of a written paper, with the marking points. These are Yumio practice questions.
(a) Write 0.000 042 m in standard form. [1 mark] (b) Convert 250 cm³ to dm³. [1 mark] (c) A student dissolves 5.0 g of a solid in 250 cm³ of water. Calculate the concentration in g/dm³. [2 marks]
Answer: (a) 4.2 × 10⁻⁵ m (b) 0.25 dm³ (c) 20 g/dm³
A student collects gas from a reaction. The volume is 0 cm³ at 0 s, 40 cm³ at 20 s, 60 cm³ at 40 s and 70 cm³ at 60 s. (a) Calculate the mean rate in the first 20 s. [2 marks] (b) Calculate the mean rate between 40 s and 60 s. [1 mark] (c) Explain why the rate decreases. [1 mark]
Answer: (a) 2.0 cm³/s (b) 0.50 cm³/s (c) the reactants are being used up so their concentration falls
Using cm³ in a concentration without converting to dm³
Divide cm³ by 1000 to get dm³ first.
Writing 45 × 10⁻⁴ as standard form
Standard form needs a first number between 1 and 10: 4.5 × 10⁻³.
Rounding part way through a calculation
Keep the full numbers on your calculator and round at the end.
Leaving out the unit in the answer
Write the unit of every answer, such as g/dm³, cm³/s or mol.
Dividing the wrong way in a gradient
Gradient = change in y ÷ change in x.
Maths skills for chemistry is on both Foundation and Higher papers for GCSE Combined Science Chemistry, aimed at around grade 4.
Using cm³ in a concentration without converting to dm³. Divide cm³ by 1000 to get dm³ first.
Open Show answer under each question on this page. The questions are Yumio practice questions, not past exam questions.
See how the papers are set: AQA Combined Science papers and Edexcel Combined Science papers.
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