Avogadro's Law Calculator
Calculate the missing volume or amount of gas using Avogadro's law. Enter the initial volume and amount, plus the new amount or new volume, and get the result with full steps.
Find the Missing Volume or Amount of Gas
Avogadro's Law Formula
Where:
- \(V_1\), \(V_2\) — initial and final volume of the gas
- \(n_1\), \(n_2\) — initial and final amount of gas (moles)
The formula states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles. Rearranged, it gives the missing value directly: \(V_2 = V_1 \cdot \frac{n_2}{n_1}\) or \(n_2 = n_1 \cdot \frac{V_2}{V_1}\).
Avogadro's Law – Calculation Example
Example: a gas occupies 2 L in a flexible container at fixed temperature and pressure, containing 0.5 mol of gas. More gas is added until the sample holds 1.5 mol. What is the new volume?
\[ V_2 = V_1 \cdot \frac{n_2}{n_1} = 2\ \text{L} \cdot \frac{1.5\ \text{mol}}{0.5\ \text{mol}} = 6\ \text{L} \]
Result: the final volume is 6 L. Tripling the amount of gas (from 0.5 mol to 1.5 mol) triples the volume, exactly as Avogadro's law predicts.
How to Use the Calculator
- Open the Solve for dropdown and choose whether you want the Final volume (V₂) or the Final amount (n₂). The field for the value you already know appears; the other one is hidden.
- Enter the Initial Volume (V₁) and pick its unit (L, mL, cm³, m³, ft³ or US gallons).
- Enter the Initial Amount (n₁) in mol, mmol or kmol.
- Enter the known final value: Final Amount (n₂) if you are solving for volume, or Final Volume (V₂) with its unit if you are solving for the amount.
- Read the result, the step-by-step calculation, and the verification that \(V_1/n_1 = V_2/n_2\).
All unit conversions are handled automatically — you can enter V₁ in litres and V₂ in cubic feet, and the answer for n₂ comes back in the unit you chose for n₁.
What Is Avogadro's Law?
Avogadro's law, proposed by Amedeo Avogadro in 1811, states that equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules. An equivalent statement is that the volume of a gas sample is directly proportional to the amount of gas (in moles) when temperature and pressure are held constant. Doubling the moles of gas doubles the volume; removing half the gas halves the volume.
The law is one of the cornerstone relationships of the ideal gas law, \(PV = nRT\). If pressure \(P\) and temperature \(T\) are constant, solving for \(V\) gives \(V = \frac{nRT}{P}\), so \(V/n = \text{constant}\). Avogadro's law is simply the comparison of this ratio between two states of the same gas under the same conditions.
A useful consequence is the molar volume: one mole of any ideal gas occupies the same volume at a given temperature and pressure. At STP (0 °C, 1 atm) that volume is 22.414 L; at 25 °C and 1 bar it is 24.789 L. This makes it possible to convert between gas volumes and moles without weighing the gas — a routine step in stoichiometry, gas collection over water, and industrial gas measurements.
When interpreting your result, remember that the proportionality works in both directions: if the calculator reports a factor of 3 between \(n_2\) and \(n_1\), the volume also changed by a factor of 3. If your calculated molar volume \(V/n\) is far from 22–25 L/mol at near-ambient conditions, double-check the inputs — it may signal a unit or decimal error.
Reference Values
| Conditions | Molar volume of an ideal gas |
|---|---|
| 0 °C, 1 atm (STP) | 22.414 L/mol |
| 25 °C, 1 atm | 24.465 L/mol |
| 25 °C, 1 bar (SATP) | 24.789 L/mol |
Assumptions, Limitations and Tips
- Ideal-gas behaviour. Avogadro's law assumes gas particles have negligible volume and exert no intermolecular forces. Real gases follow it closely at low pressure and temperatures well above their boiling point, but deviate at high pressure or near condensation. For dense gases, the Van der Waals Equation Calculator gives a more accurate description.
- Constant temperature and pressure. The law applies only when both \(T\) and \(P\) are the same before and after the change. A flexible container (piston or balloon) open to constant external pressure is the typical setup. If temperature also changes, use the combined or ideal gas law instead.
- Amount means moles of gas only. Adding a liquid or solid to the container does not change \(n\); only gaseous species count. Dissolved gas evolving from solution does count.
- Consistent units. Because the law is a ratio, \(V_1\) and \(V_2\) just need the same unit, and \(n_1\) and \(n_2\) the same unit — the calculator handles this for you, including mixed units.
- Number of molecules. Multiplying the final amount by the Avogadro constant, \(N_A = 6.02214076 \times 10^{23}\ \text{mol}^{-1}\), tells you how many molecules the final sample contains — the calculator reports this automatically.
If your problem involves comparing how fast two gases diffuse rather than how much space they occupy, see the Graham's Law Calculator. For reactions where the amount of gas changes over time, the Reaction Half-Life Calculator can help you track \(n\) before applying Avogadro's law.
Frequently Asked Questions
How do I calculate Avogadro's law by hand?
Write the ratio \(V_1/n_1 = V_2/n_2\), then cross-multiply to isolate the unknown. For example, if \(V_1 = 5\ \text{L}\), \(n_1 = 2\ \text{mol}\), and \(n_2 = 6\ \text{mol}\), then \(V_2 = V_1 \cdot n_2/n_1 = 5 \times 6/2 = 15\ \text{L}\). Always keep volumes in one unit and amounts in one unit; the ratio then makes intermediate conversions unnecessary.
Does Avogadro's law depend on which gas it is?
No — that is the key insight. At the same temperature and pressure, equal volumes contain equal numbers of molecules regardless of the gas's identity. One mole of hydrogen, nitrogen, or carbon dioxide all occupy about 22.414 L at STP. Only the number of moles matters, not the molar mass, which is why you can relate gas volume to moles without ever weighing the sample.
What are the differences between Avogadro's law, Boyle's law, Charles's law, and Gay-Lussac's law?
Each law fixes two variables and relates the other two. Boyle's law: \(P_1V_1 = P_2V_2\) at constant temperature and moles. Charles's law: \(V_1/T_1 = V_2/T_2\) at constant pressure and moles. Gay-Lussac's law: \(P_1/T_1 = P_2/T_2\) at constant volume and moles. Avogadro's law: \(V_1/n_1 = V_2/n_2\) at constant temperature and pressure. All four are special cases of the ideal gas law \(PV = nRT\).
When should I use Avogadro's law instead of the combined gas law?
Use Avogadro's law when temperature and pressure stay the same and only the amount of gas (or the volume) changes, such as adding gas to a balloon or piston open to the atmosphere. If the temperature or pressure also differs between the two states, the combined gas law \(P_1V_1/(n_1T_1) = P_2V_2/(n_2T_2)\) is needed instead, because Avogadro's ratio \(V/n\) only stays constant when \(P\) and \(T\) are fixed.
Why must volumes and moles be positive — can't a gas have zero volume or amount?
A ratio like \(V_1/n_1\) is undefined when either value is zero, so the law cannot describe a sample with no gas or no volume. Physically, the limit \(n \to 0\) does mean \(V \to 0\), but the calculation degenerates. If your problem gives a zero initial amount, you need a different approach, such as using the molar volume (22.414 L/mol at STP) to define the initial state from scratch.
How do I convert a gas volume to moles without knowing the mass?
Divide the volume by the molar volume at the same conditions. At STP (0 °C, 1 atm), \(n = V/22.414\ \text{L/mol}\); at 25 °C and 1 bar, use 24.789 L/mol. For example, 5.6 L of any ideal gas at STP contains \(5.6/22.414 \approx 0.25\ \text{mol}\). Note that the molar volume depends on temperature and pressure, so always match it to the actual conditions of your sample.
What are common mistakes when solving Avogadro's law problems?
The most frequent errors are mixing units (e.g. litres with millilitres), using Celsius instead of kelvin when temperature matters, and forgetting that temperature and pressure must be constant. Others include counting dissolved solids or liquids as gas moles, and assuming a rigid container — in a rigid vessel, adding gas changes pressure, not volume. Finally, sanity-check your molar volume: a value far from 22–25 L/mol near ambient conditions usually signals a decimal or unit mistake.