About the Avogadro's Law Calculator
This Avogadro's law calculator finds the missing volume or amount of gas when gas is added to or removed from a container at constant temperature and pressure. Choose which of V₁, n₁, V₂ or n₂ you want, enter the other three, and it solves V₁/n₁ = V₂/n₂ and plots the straight-line relationship between volume and moles.
It is aimed at chemistry students working gas-law problems, and anyone reasoning about balloons being inflated, gas reactions where the number of moles changes (2H₂ + O₂ → 2H₂O vapour), or why equal volumes of different gases contain the same number of molecules. Any volume unit works as long as both states use the same one.
Avogadro's law assumes ideal-gas behaviour and that temperature and pressure do not change. For reference the calculator also shows the molar volume implied by your first state and how it compares with 22.71 L/mol, the ideal molar volume at IUPAC STP (0 °C and 100 kPa).
With the default inputs, the answer is 8.75. Change any value above to recalculate instantly.
How to use the avogadro's law calculator
- 1Choose the quantity you want to find.
- 2Select the volume unit used for both states.
- 3Enter the three known values.
- 4Read the answer and check the straight-line V–n chart.
Formula and method
Avogadro's law states that at constant temperature and pressure the volume of an ideal gas is directly proportional to the number of moles: V/n stays constant. Doubling the amount of gas doubles the volume. It follows from the ideal gas law PV = nRT with P and T fixed, since V/n = RT/P.
To solve, the calculator takes the complete state (V and n known), forms the constant V/n and applies it to the other state. Only ratios matter, so any volume unit works if both volumes use it. The law also implies that equal volumes of any ideal gases at the same T and P contain equal numbers of molecules.
- V₁, n₁
- Initial volume and amount of gas (mol)
- V₂, n₂
- Final volume and amount of gas (mol)
Worked examples
Adding gas to a balloon
A 5.0 L balloon holds 0.20 mol of gas. Pumping in more gas to make 0.35 mol at the same temperature and pressure gives V₂ = 5.0 × 0.35 ÷ 0.20 = 8.75 L.
Moles left after a leak
A flexible container shrinks from 12 L to 9 L as gas escapes. n₂ = 0.5 × 9 ÷ 12 = 0.375 mol, so a quarter of the gas has leaked out.
Hydrogen burning: 3 mol gas → 2 mol water vapour
2H₂ + O₂ → 2H₂O(g) turns 3 mol of gas into 2 mol. At the same T and P, 600 mL of the mixture becomes 600 × 2 ÷ 3 = 400 mL of steam.
Frequently asked questions
What is Avogadro's law?+
Avogadro's law says that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles: V₁/n₁ = V₂/n₂. Amedeo Avogadro proposed it in 1811.
What is the molar volume of a gas?+
For an ideal gas it is RT/P: about 22.71 L/mol at IUPAC STP (0 °C, 100 kPa), 22.41 L/mol at 0 °C and 1 atm, and about 24.79 L/mol at 25 °C and 100 kPa.
Does Avogadro's law work for any gas?+
It holds closely for most gases at ordinary temperatures and pressures. Strongly interacting gases (like ammonia or steam near condensation) and gases at high pressure deviate because real molecules attract each other and take up space.
How is Avogadro's law related to the ideal gas law?+
Rearranging PV = nRT gives V/n = RT/P. If temperature and pressure are held fixed, RT/P is a constant, which is exactly Avogadro’s law. Boyle’s and Charles’s laws come from the same equation.