The Avogadro's Law Calculator solves V₁/n₁ = V₂/n₂ for any unknown gas quantity when temperature and pressure remain constant. Calculates new volume when moles change, or new mole count when volume changes — the direct proportionality between gas volume and amount of substance at constant T and P.
44.828
22.414
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44.828
22.414
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Avogadro's law captures one of the most elegant relationships in physical chemistry: at fixed temperature and pressure, equal volumes of any ideal gas contain equal numbers of molecules, regardless of molecular identity. This insight — counterintuitive when first proposed in 1811 — resolved decades of confusion in stoichiometry and established the theoretical foundation for the mole concept. The calculator for Avogadro's law solves V₁/n₁ = V₂/n₂ for any configuration of known and unknown variables.
Avogadro's law, stated mathematically:
V/n = k (constant at fixed T and P)
V₁/n₁ = V₂/n₂
This relationship implies that doubling the amount of gas doubles the volume; halving the amount halves the volume. The proportionality constant k = RT/P (from the ideal gas law PV = nRT) depends on temperature and pressure but not on the chemical identity of the gas. At standard temperature and pressure (0°C, 1 atm), k = 22.414 L/mol — the famous molar volume of an ideal gas at STP. A practical consequence: 1 mol of nitrogen gas, 1 mol of carbon dioxide, and 1 mol of xenon all occupy approximately 22.4 L at STP, despite their vastly different molecular masses (28, 44, and 131 g/mol respectively). Use this online calculator to solve any Avogadro's law problem.
Two classic problem types illustrate Avogadro's law applications:
The Avogadro ideal gas law calculator offers an extended version with STP/SATP reference calculations.
Amedeo Avogadro proposed his hypothesis in 1811 — that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules — but it was largely ignored for nearly 50 years. The controversy stemmed partly from confusion between atoms and molecules (Avogadro distinguished diatomic molecules like H₂ from atoms, while most contemporaries did not), and partly from Dalton's authority rejecting the idea. It was Stanislao Cannizzaro at the 1860 Karlsruhe Congress who systematically demonstrated the correctness of Avogadro's hypothesis and used it to establish a consistent table of atomic weights — a watershed moment that unified chemistry and enabled the development of the periodic table just nine years later. The ideal gas law calculator and gas laws calculators cover the complete ideal gas analysis toolkit.
Avogadro's law directly underlies the measurement of lung function. Spirometry measures lung volumes in liters; converting to moles of air (using n = PV/RT) reveals the actual number of gas molecules exchanged per breath. At rest, a tidal volume of 0.5 L at body temperature (37°C) and atmospheric pressure contains approximately 0.0194 mol of air = 1.17 × 10²² molecules per breath. At 12–20 breaths per minute, the lungs exchange approximately 1.4–2.3 × 10²³ air molecules per minute — on the order of Avogadro's number itself per minute of quiet breathing. This perspective makes the abstract scale of Avogadro's constant tangibly biological.
Avogadro's law states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles:
$$\frac{V_1}{n_1} = \frac{V_2}{n_2} = k \text{ (constant)}$$
Solving for the unknown:
$$V_2 = V_1 \times \frac{n_2}{n_1} \qquad n_2 = n_1 \times \frac{V_2}{V_1}$$
The constant \(k = V/n = RT/P\) depends on temperature and pressure. At STP (273.15 K, 1 atm), k = 22.414 L/mol — the standard molar volume. This means any ideal gas (regardless of its identity) occupies 22.414 liters per mole at STP.
$$V_{molar} = \frac{RT}{P} = \frac{0.08206 \times 273.15}{1} = 22.414 \text{ L/mol}$$
This law is the basis for gas stoichiometry: volume ratios of reacting gases equal their mole ratios in balanced chemical equations.
The result shows the final volume or number of moles after the change. The V/n constant equals the molar volume at the given temperature and pressure — at STP, it should be approximately 22.414 L/mol. The change factor indicates how many times the solved variable increased or decreased. Since volume is directly proportional to moles, adding more gas (at constant T and P) proportionally increases the volume.
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Doubling the moles from 1 to 2 at STP doubles the volume from 22.414 L to 44.828 L. This confirms that volume and moles are directly proportional.
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A volume of 11.207 L at STP corresponds to 0.5 moles of gas. This is a direct application of the molar volume concept — dividing any gas volume at STP by 22.414 gives the number of moles.
Avogadro's law states that equal volumes of ideal gases at the same temperature and pressure contain equal numbers of molecules. Equivalently, at constant T and P, V₁/n₁ = V₂/n₂. It was hypothesized by Amedeo Avogadro in 1811 and later confirmed experimentally.
The molar volume is the volume occupied by one mole of any ideal gas at specified conditions. At STP (0°C, 1 atm), it is 22.414 L/mol. At SATP (25°C, 1 bar), it is 24.790 L/mol. The molar volume is the same for all ideal gases regardless of their molecular identity.
In an ideal gas, molecules have negligible volume and no intermolecular forces. Therefore, the space occupied depends only on the number of molecules, temperature, and pressure — not on what the molecules are. One mole of helium, nitrogen, or CO₂ all occupy 22.414 L at STP.
For gas-phase reactions at constant T and P, volume ratios equal mole ratios. In the reaction 2H₂ + O₂ → 2H₂O, two volumes of hydrogen react with one volume of oxygen. This allows using volume measurements directly in stoichiometric calculations without converting to moles first.
Avogadro's number (Nₐ = 6.022 × 10²³) is the number of particles in one mole. It connects Avogadro's law to the molecular scale: at STP, 22.414 L of any ideal gas contains exactly 6.022 × 10²³ molecules. This number was named in Avogadro's honor but was determined long after his death.
Avogadro's law is a special case of PV = nRT. When P and T are constant, V = (RT/P) × n, showing V ∝ n with proportionality constant RT/P. This constant equals the molar volume at the given conditions.
Approximately, yes, at low to moderate pressures and above their boiling points. Real gas molecules have finite volume and intermolecular forces, causing deviations. The molar volume of real gases at STP varies slightly: He ≈ 22.434 L, H₂ ≈ 22.432 L, CO₂ ≈ 22.260 L (CO₂ deviates most due to stronger intermolecular forces).
Avogadro's hypothesis resolved a major confusion in early chemistry: it explained why hydrogen and chlorine gases combine in equal volumes to form HCl, and why molecules could be diatomic (H₂, O₂). This was crucial for distinguishing atoms from molecules and for determining correct molecular formulas.
When you blow air into a balloon, you increase the number of moles of gas inside. At roughly constant temperature and pressure (the balloon stretches to maintain near-atmospheric pressure), the volume increases proportionally to the added gas — a direct demonstration of V ∝ n.
The traditional STP uses 1 atm (101.325 kPa), giving 22.414 L/mol. IUPAC redefined standard pressure as 1 bar (100 kPa) in 1982, giving 22.711 L/mol. The difference arises because 1 bar is slightly less than 1 atm, so the gas occupies a slightly larger volume. Both values are used in different contexts.
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