The Avogadro's Ideal Gas Law Calculator applies Avogadro's law (V₁/n₁ = V₂/n₂) to find unknown gas volume or moles at constant T and P. Demonstrates the direct proportionality between gas volume and amount of substance — the molar gas relationship essential for gas stoichiometry calculations.
44.828
22.414
L/mol
22.414
L/mol
22.414
L/mol
1.2044e+24
44.828
22.414
L/mol
22.414
L/mol
22.414
L/mol
1.2044e+24
Add gas to a balloon at constant temperature and pressure and it expands. Remove gas and it contracts. The volume and the amount of substance are directly proportional — double the moles, double the volume. This elegant simplicity is Avogadro's law, and the calculator for Avogadro's ideal gas law solves any of the four variables in the V₁/n₁ = V₂/n₂ relationship when the other three are known.
Avogadro's law states that at constant temperature T and pressure P, the volume V of an ideal gas is directly proportional to the number of moles n:
V ∝ n (at constant T, P)
V₁/n₁ = V₂/n₂ = k (constant)
The physical basis is the ideal gas model: gas molecules occupy negligible volume compared to the container, exert no intermolecular forces, and move randomly. Under these conditions, each additional mole of gas — regardless of molecular identity — requires the same additional volume to maintain the same pressure at the same temperature. Consequently, 1 mole of any ideal gas at STP (0°C, 1 atm) occupies 22.414 liters; at SATP (25°C, 100 kPa), the molar volume is 24.789 L/mol. The ideal gas law calculator handles the complete PV = nRT relationship.
With V₁/n₁ = V₂/n₂, any one variable can be found from the other three:
Example: a sealed balloon contains 0.500 mol air at 15.0 L. After pumping in more air to reach 1.20 mol total (T and P held constant): V₂ = 15.0 × (1.20/0.500) = 36.0 L. Use this online calculator for any Avogadro's law problem. The Charles's law calculator handles the temperature-volume relationship at constant n and P.
Avogadro's law provides the physical justification for Gay-Lussac's law of combining volumes — the observation that reacting gases combine in simple whole-number volume ratios. For the reaction H₂(g) + Cl₂(g) → 2HCl(g): 1 volume of hydrogen reacts with 1 volume of chlorine to produce 2 volumes of HCl. Because volume is proportional to moles at constant T and P, the volume ratios directly reflect the stoichiometric mole ratios (1:1:2). This connection between volumetric observations and atomic theory was a cornerstone of Dalton's and Avogadro's early 19th-century work establishing the mole concept. The combined gas law calculator and gas laws calculators cover the complete ideal gas toolkit.
Avogadro's law is exact only for ideal gases. Real gases deviate when intermolecular forces are significant (high pressure, low temperature) or when molecular volume is non-negligible (high pressure). The compressibility factor Z = PV/nRT quantifies deviation from ideality: Z = 1 for ideal gases; Z < 1 for attractive-dominated gases (most gases below their Boyle temperature); Z > 1 for repulsion-dominated gases (hydrogen and helium at moderate pressure). For most engineering calculations involving gases well above their boiling points and below 10 atm pressure, Avogadro's law and the ideal gas model are accurate to within 1–2%.
Avogadro's Law states:
$$\frac{V_1}{n_1} = \frac{V_2}{n_2}$$
Or equivalently:
$$V = kn \quad (\text{constant at fixed } P, T)$$
where k = RT/P from the ideal gas law. This means volume is directly proportional to the number of moles. Solving for each variable:
$$V_2 = V_1 \times \frac{n_2}{n_1}, \quad n_2 = n_1 \times \frac{V_2}{V_1}$$
The constant k at STP (standard temperature and pressure: 0 °C, 1 atm) gives the molar volume:
$$V_m = \frac{RT}{P} = \frac{8.314 \times 273.15}{101325} = 22.414 \text{ L/mol}$$
This means any ideal gas — hydrogen, oxygen, nitrogen, argon — occupies the same volume per mole at the same conditions. The identity of the gas does not matter, only the number of molecules.
The total number of molecules is found by multiplying moles by Avogadro's number:
$$N = n \times N_A = n \times 6.022 \times 10^{23}$$
This law was revolutionary because it implied that gas volume directly measures the number of particles, enabling chemists to determine molecular formulas and atomic weights.
If V/n ratios differ between initial and final states, then temperature or pressure changed. At STP, the molar volume should be 22.414 L/mol — deviation indicates non-ideal behavior. The total molecule count gives a sense of scale: even 1 mole contains an astronomically large 6.022 x 10²³ particles.
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Doubling the moles from 1 to 2 at constant T and P doubles the volume from 22.414 L to 44.828 L. Each mole adds exactly one molar volume.
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A 100-liter container at STP holds about 4.46 moles of gas — approximately 2.69 x 10²⁴ molecules. This works regardless of which gas it is.
Avogadro's Law states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles: V₁/n₁ = V₂/n₂. Equal volumes of different gases contain equal numbers of molecules.
At STP (0 °C = 273.15 K, 1 atm = 101325 Pa), one mole of any ideal gas occupies 22.414 liters. This value is derived directly from the ideal gas law: V = nRT/P.
No. That is precisely Avogadro's insight — the law is independent of gas identity. One mole of helium, one mole of oxygen, and one mole of carbon dioxide all occupy the same volume at the same T and P (assuming ideal behavior).
Avogadro's number is N_A = 6.02214076 × 10²³ mol⁻¹. It is the number of particles (atoms, molecules, ions) in exactly one mole of substance. It connects the macroscopic (moles, grams) and microscopic (individual molecules) worlds.
Since gas volumes are proportional to moles, you can use volume ratios as mole ratios in balanced chemical equations. For example, 2 L of H₂ reacts with 1 L of O₂ to produce 2 L of H₂O vapor (at constant T, P), matching the 2:1:2 mole ratio.
Real gas molecules have finite volume and intermolecular attractions. At high pressures or low temperatures, these effects become significant and the actual volume per mole deviates from the ideal 22.414 L. Heavier, more polar molecules deviate more.
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