Combined gas law calculator (Boyle, Charles and Gay-Lussac)
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Result
Gas laws need absolute temperatures. Pressures and volumes may be in any unit, as long as both states use the same one. The amount of gas stays the same.
Solve gas law problems for a fixed amount of gas that changes from one state to another. Choose the combined gas law, Boyle’s law (constant temperature), Charles’s law (constant pressure) or Gay-Lussac’s law (constant volume), pick the unknown, and enter the other values. Temperatures can be in °C, K or °F; the calculator converts them to kelvin, rearranges the law and checks the answer.
Step-by-step solution
Convert the temperatures to kelvin
Gas law
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Key formulas
- Ideal gas law
- pV = nRT
- Gas constant
- R = 8.314 J/(mol·K)
- Combined gas law
- p1V1/T1 = p2V2/T2
- Moles
- n = m/M
- Temperature
- T[K] = T[°C] + 273.15
How to use the combined gas law
- List the known values for both states: P₁, V₁, T₁ and P₂, V₂, T₂.
- Convert every temperature to kelvin: T(K) = T(°C) + 273.15. The gas laws only work with absolute temperature.
- Use the same unit for both pressures and the same unit for both volumes; any unit works because only their ratios matter.
- Rearrange P₁V₁/T₁ = P₂V₂/T₂ for the unknown, for example V₂ = P₁V₁T₂/(T₁P₂), and substitute the values.
- If a quantity stays constant, it cancels: Boyle’s law P₁V₁ = P₂V₂, Charles’s law V₁/T₁ = V₂/T₂, Gay-Lussac’s law P₁/T₁ = P₂/T₂.
Questions and answers
Why must the temperature be in kelvin?
The laws say that volume or pressure is proportional to temperature, which is only true from absolute zero. With °C, doubling 10 °C to 20 °C would wrongly suggest double the volume; in kelvin the change is from 283 K to 293 K, about 3.5%.
When is the combined gas law valid?
For an ideal gas with a fixed amount of gas (no leaks and no reactions). Real gases follow it well at moderate pressures and at temperatures well above their boiling points.
How is the combined gas law related to PV = nRT?
From PV = nRT, PV/T = nR, which is constant when n does not change. So P₁V₁/T₁ = P₂V₂/T₂. Use the ideal gas law when you need the amount of gas itself.
Should I use gauge or absolute pressure?
Absolute pressure. A tyre gauge reads the pressure above atmospheric, so add about 101 kPa (14.7 psi) before using the gas laws.
Practise it yourself
Practise Ideal gas law
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.