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Chemistry: Avogadro's Law Calculator

Solve V₁/n₁ = V₂/n₂ for any variable. Relates gas volume to moles at constant temperature and pressure.

V₁/n₁ = V₂/n₂

L
mol
L
← Solved
mol

Final Volume (V₂)

20
L

State Comparison

Initial

10 L

1 mol

Final

20 L

2 mol

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Avogadro's Law

Avogadro's Law states that equal volumes of gases at the same temperature and pressure contain the same number of molecules: V₁/n₁ = V₂/n₂.

Key Principles

  • Direct proportionality: Volume ∝ Moles (at constant T and P)
  • Avogadro's Number: 6.022 × 10²³ (particles per mole)
  • Standard Molar Volume: 22.4 L/mol at STP (0°C, 1 atm)

Applications

  • Gas stoichiometry: Relating volumes of reactants and products
  • Balloon inflation: Adding more air (moles) increases volume
  • Breathing: Lungs expand as air molecules enter

Gas Laws Family 💡

Avogadro's Law (V ∝ n) complements Boyle's (V ∝ 1/P), Charles's (V ∝ T), and Gay-Lussac's (P ∝ T). Combined, they form the Ideal Gas Law: PV = nRT.

Quick Answer: What is Avogadro's Law and what does V₁/n₁ = V₂/n₂ mean?

Avogadro's Law states that equal volumes of any ideal gas at the same temperature and pressure contain the same number of molecules. Mathematically: V/n = constant, or in the comparative form V1/n1 = V2/n2 — where V is volume (in any consistent unit: L, mL, m³) and n is the amount of gas in moles. This holds at constant temperature (T) and constant pressure (P). The practical consequence: if you double the number of moles of gas in a flexible container at constant T and P, the volume exactly doubles. This is why a balloon inflated with twice as many moles of helium is exactly twice the volume. The universal proportionality constant is the molar volume: at STP (0°C, 1 atm), 1 mole of any ideal gas occupies 22.414 L; at SATP (25°C, 100 kPa), it's 24.789 L. Use this calculator to solve for any one unknown (V1, V2, n1, or n2) given the other three — results update instantly.

Where Avogadro's Law Fits in the Ideal Gas Law Hierarchy

Law (Year) Relationship Constant Held Fixed Contribution
Boyle's Law (1662) P × V = const T, n Pressure–volume inverse relationship
Charles's Law (1787) V / T = const P, n Volume–temperature proportionality
Gay-Lussac's Law (1808) P / T = const V, n Pressure–temperature proportionality
Avogadro's Law (1811) V / n = const T, P Volume–amount (moles) proportionality
Combined Gas Law P1V1/T1 = P2V2/T2 n Boyle + Charles + Gay-Lussac combined
Ideal Gas Law (synthesis) PV = nRT — All four laws unified; R = 8.314 J/(mol·K)
Avogadro's Law is the 'n' in PV = nRT. Setting P and T constant in the ideal gas law gives V = (nRT/P) → V ∝ n → V/n = RT/P = constant. The molar volume at STP (0°C, 101.325 kPa) = RT/P = (8.314 × 273.15) / 101,325 = 22.414 L/mol.

Pro Tips & Common Avogadro's Law Mistakes

Do This

  • ✓Use Avogadro's Law for stoichiometric gas volume calculations in chemical reactions — this is its most powerful application. At constant T and P, the ratio of gas volumes in a reaction equals the ratio of their stoichiometric coefficients. For example, combustion of methane: CH4 + 2O2 → CO2 + 2H2O. At constant T and P: 1 L CH4 reacts with exactly 2 L O2 and produces exactly 1 L CO2 (plus water vapor). This means: if you burn 10 L of natural gas (as CH4), you need 20 L of O2 from air — since air is ~21% O2, that requires 20 ÷ 0.21 = 95.2 L of air. This is the basis of air–fuel ratio calculations for burner and combustion engine design.
  • ✓Remember the two standard molar volumes and which standard conditions they correspond to. STP (Standard Temperature and Pressure, IUPAC pre-1982): 0°C (273.15 K) and 1 atm (101.325 kPa) → molar volume = 22.414 L/mol. This is what most older textbooks and NIST tables quote. SATP (Standard Ambient Temperature and Pressure, IUPAC post-1982): 25°C (298.15 K) and 100 kPa exactly → molar volume = 24.789 L/mol. Modern calculations and thermodynamics tables (especially for ΔG° and K values) use SATP. Using 22.4 L/mol for a problem stated at 25°C introduces a 10.6% volume error — significant for precision work.

Avoid This

  • ✗Don't apply Avogadro's Law to real gases at high pressure or low temperature — it assumes ideal behavior. Avogadro's Law is derived from the ideal gas model, which assumes zero intermolecular forces and zero molecular volume. Real gases deviate significantly at: (1) high pressure (>10 atm for common gases) where molecular volume and repulsive forces dominate; (2) low temperature (approaching boiling point) where attractive forces (van der Waals) cause real molar volumes to be smaller than 22.4 L. For example, at 100 atm and 25°C, the molar volume of N2 = 0.236 L/mol vs the ideal 0.248 L/mol (−5% deviation). For CO2 at the same conditions: 0.194 L/mol vs 0.248 L/mol (−22% deviation due to CO2's strong van der Waals interactions). Use van der Waals or Peng-Robinson equations of state for high-pressure gas engineering.
  • ✗Don't confuse Avogadro's Hypothesis (volumes) with Avogadro's Number (particles per mole) — they are related but distinct concepts. Avogadro's Hypothesis (1811): equal volumes of gas at same T and P contain equal numbers of molecules — this is the qualitative principle. Avogadro's Number / Constant (NA = 6.02214076 × 1023 mol−1): the exact number of entities per mole — defined exactly since 2019 SI redefinition. They complement each other: Avogadro's Hypothesis tells you that gases with the same volume (same T, P) have the same n; NA tells you exactly how many molecules that n represents. For 22.414 L of O2 at STP: n = 1 mol → 6.022 × 1023 molecules, each pair of which weighs 32 g (molar mass of O2).

Frequently Asked Questions

Why does Avogadro's Law only apply at constant temperature and pressure?

From kinetic molecular theory, the pressure of an ideal gas is: P = nRT/V. For V/n to be constant, we need T and P fixed: V/n = RT/P. If T changes, the ratio RT/P changes even at the same n → V changes for reasons other than the amount of gas. If P changes, the gas compresses or expands independently of n. The ideal gas law (PV = nRT) contains all four variables simultaneously — Avogadro's Law is the special case where only V and n vary (P, T held constant). In practice, this corresponds to flexible containers at atmospheric pressure (like balloons, tire inflation, gas collection over water) where the pressure of the container adjusts to atmospheric. A rigid container like a steel tank does not follow Avogadro's Law — adding more gas increases pressure, not volume.

How is Avogadro's Law used in automotive airbag design?

Automotive airbags inflate via rapid decomposition of sodium azide: 2 NaN3 → 2 Na + 3 N2. Avogadro's Law is used to calculate how much NaN3 is needed to produce the required volume of N2. Example: a standard driver-side airbag requires ~67 L of N2 at deployment (~35°C, ~1 atm). At SATP conditions: n(N2) = 67 L ÷ 24.789 L/mol ≈ 2.70 mol N2. From stoichiometry: mol NaN3 = 2.70 × (2/3) = 1.80 mol. Mass NaN3 = 1.80 × 65.01 g/mol = 117 g. This must all decompose and inflate within ~30 milliseconds of crash detection — the speed of the gas volume expansion (following Avogadro's principle: moles produced → proportional volume) is engineered to match the deceleration time of the crash.

Is 1 mole of any gas always 22.4 liters?

Only approximately, and only for ideal gases at STP (0°C, 1 atm). The statement “22.4 L/mol” is Avogadro's molar volume at STP — it's an approximation that holds well for non-polar gases at low pressure and room temperature. Deviations for real gases at STP: H2 = 22.433 L/mol (+0.08%); He = 22.434 L/mol (+0.09%); CH4 = 22.360 L/mol (−0.24%); CO2 = 22.260 L/mol (−0.69%). The deviations are small at STP but grow rapidly at lower temperatures or higher pressures. At room temperature (25°C, 1 atm), the correct molar volume is 24.465 L/mol (not 22.4). The IUPAC SATP molar volume (25°C, 100 kPa) is 24.789 L/mol. In precision calculations, always compute V = nRT/P directly rather than using the molar volume shortcut.

How do I use this calculator for a gas collection experiment (eudiometer / gas over water)?

In a gas-over-water collection, the collected gas is a mixture with water vapor. Apply Dalton's Law first: Pgas = Ptotal − PH&sub2;O (vapor pressure of water at that temperature; at 25°C: 23.8 mmHg = 3.17 kPa; at 20°C: 17.5 mmHg = 2.34 kPa). Then use Avogadro's Law with Pgas for the dry gas. Example: 250 mL of H2 collected at 25°C and total pressure 1 atm (101.325 kPa). Dry H2 pressure = 101.325 − 3.17 = 98.16 kPa. Convert to STP: VSTP = V × (Pgas/PSTP) × (TSTP/T) = 250 × (98.16/101.325) × (273.15/298.15) = 222.6 mL. Then n(H2) = 0.2226 L ÷ 22.414 L/mol = 9.93 × 10−3 mol. Skipping the vapor pressure correction introduces a 3.1% error in the moles calculated.

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