Use gas volumes and solution concentrations in equations
Convert gas volumes or solution concentrations to moles, apply the balanced equation, and keep volume conditions and units explicit.
AS Level; Cambridge International Chemistry 9701, 2025–2027 syllabus. Use the data and constants supplied for the question, show mole-ratio working, and report a justified number of significant figures. Written practice is self-checked
Before you begin
- Use common chemical symbols and formulae, and rearrange a simple equation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
When can gas volumes be compared directly using equation coefficients?
What you will learn
- Use mole ratios with reacting gas volumes
- Use concentration and volume to calculate reacting amounts in solution
Gas volume is linked to amount only at stated conditions
At the same temperature and pressure, equal gas volumes contain equal numbers of molecules, so gas volumes follow the equation coefficient ratio. If a molar gas volume is supplied, use n=V/Vm with compatible units. The syllabus data section gives 24.0 dm³ mol⁻¹ at room conditions and 22.4 dm³ mol⁻¹ at STP.
If conditions are not the same or the problem supplies a different molar gas volume, do not assume the same volume ratio. Balance the equation first, then keep cm³ or dm³ units consistent with the chosen constant.
Solution concentration links amount and volume
For concentration c in mol dm⁻³ and volume V in dm³, n=cV. Convert a volume in cm³ to dm³ by dividing by 1000 before multiplying by c. The amount ratio then comes from the balanced equation.
A titration or solution reaction can be solved by calculating moles of the known solution, applying the coefficient ratio, and converting to the requested concentration or mass. Write the volume conversion explicitly to avoid a factor-of-1000 error.
Pause and explain
What is 25.0 cm³ in dm³?
Worked example
At room conditions, what volume of oxygen is needed to burn 0.50 mol of methane? CH₄ + 2O₂ → CO₂ + 2H₂O. Use Vm = 24.0 dm³ mol⁻¹.
Show the worked solution
- The equation requires 2 mol O₂ per 1 mol CH₄.
- n(O₂)=2×0.50=1.00 mol.
- V=nVm=1.00×24.0.
Answer 24.0 dm³ O₂.
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Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
At room conditions, calculate the volume of CO₂ formed from 0.30 mol CaCO₃. CaCO₃ + 2HCl → CaCl₂ + CO₂ + H₂O. Use Vm=24.0 dm³ mol⁻¹.
Give me a hint
The equation gives a 1:1 ratio between CaCO₃ and CO₂.
Compare my reasoning
- n(CO₂)=0.30 mol.
- Multiply by 24.0 dm³ mol⁻¹.
- Include the gas identity and condition.
7.2 dm³ CO₂.
Look for these in your work
- Coefficient ratio used
- Molar gas volume applied
- Unit and species stated
What volume of 0.200 mol dm⁻³ NaOH contains 0.00500 mol NaOH? Give the answer in cm³.
Give me a hint
Use V=n/c in dm³, then convert to cm³.
Compare my reasoning
- V=0.00500/0.200=0.0250 dm³.
- Multiply by 1000 to convert dm³ to cm³.
- Keep three significant figures.
25.0 cm³.
Look for these in your work
- Concentration rearranged correctly
- Volume converted to cm³
- Significant figures retained
25.0 cm³ of 0.100 mol dm⁻³ H₂SO₄ neutralises 40.0 cm³ NaOH. H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O. Find the NaOH concentration.
Give me a hint
Find acid moles, use the 1:2 ratio, then divide by alkali volume in dm³.
Compare my reasoning
- n(H₂SO₄)=0.100×0.0250=0.00250 mol.
- n(NaOH)=2×0.00250=0.00500 mol.
- c(NaOH)=0.00500/0.0400.
0.125 mol dm⁻³ NaOH.
Look for these in your work
- cm³ converted to dm³
- Equation ratio applied
- Concentration unit correct
Common mistakes
- Using 24.0 dm³ mol⁻¹ without the stated room conditions
- Multiplying mol dm⁻³ by a volume in cm³
- Using the wrong species coefficient ratio
- Treating liquid-water volume as a gas volume
What can you explain now?
When can gas volumes be compared directly using equation coefficients?
Compare with the explanation
When gases are at the same temperature and pressure
Equal gas volumes then contain equal amounts.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How do you turn gas volume or solution concentration into moles before applying a coefficient ratio?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.