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V₁ / n₁ = V₂ / n₂ (constant temperature and pressure)
Select which variable to calculate.
Enter the initial volume (L or mL).
Enter the initial amount of gas in moles.
Enter the final volume (L or mL).
Enter the final amount of gas in moles.
Unit for volume values.
Number of decimal places in results.
📋 Avogadro's Law Reference Formula, rearrangements & examples
Formula & Rearrangements
V₁ / n₁ = V₂ / n₂
V₁ = V₂ × n₁ / n₂
V₂ = V₁ × n₂ / n₁
n₁ = n₂ × V₁ / V₂
n₂ = n₁ × V₂ / V₁
Conditions Constant T and P
Proportionality V ∝ n
Constant V / n = k
Worked Example
Given: V₁ = 6 L, n₁ = 3 mol, n₂ = 5 mol
Find: V₂ = ?
V₂ = V₁ × n₂ / n₁
V₂ = 6 × 5 / 3
V₂ = 10 L
Source LibreTexts, Omni Calculator
Real-World Applications
Inflating a balloonVolume ∝ moles added
Bicycle tire pumpMore air → higher pressure
Helium vs. air balloonSame volume, same molecules
Rocket propulsionGas volume expansion
Scuba tanksMoles of gas in fixed volume
Source: Vedantu, Let's Talk Science
Note: Avogadro's Law states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. The law is named after Amedeo Avogadro (1776–1856), who proposed this hypothesis in 1811. It is a special case of the Ideal Gas Law (PV = nRT) when T and P are constant.
📌 Key Formula: V₁/n₁ = V₂/n₂  |  Constant Temperature and Pressure  |  V ∝ n

What Is Avogadro's Law?

Avogadro's Law states that the volume of a gas is directly proportional to the number of moles (or number of particles) of gas when the temperature and pressure are held constant. The mathematical expression is:

V₁ / n₁ = V₂ / n₂

where V₁ and n₁ are the initial volume and amount of gas, and V₂ and n₂ are the final volume and amount of gas.

This law was proposed by the Italian scientist Amedeo Avogadro in 1811. It is one of the three classical gas laws, alongside Boyle's Law (pressure-volume) and Charles's Law (volume-temperature), and is the constant-temperature, constant-pressure special case of the Ideal Gas Law (PV = nRT).

Key characteristics of Avogadro's Law:

  • Direct proportionality: As the amount of gas increases, volume increases proportionally.
  • Constant conditions: Temperature and pressure must remain unchanged.
  • Equal volumes: Equal volumes of different gases at the same T and P contain the same number of molecules.
  • Molar volume: At STP (0 °C, 1 atm), one mole of any ideal gas occupies 22.4 L.

How to Use This Calculator

This calculator solves for any one of the four variables in Avogadro's Law:

  • V₁ — Initial volume
  • n₁ — Initial amount of gas (moles)
  • V₂ — Final volume
  • n₂ — Final amount of gas (moles)

To use the calculator:

  • Select which variable you want to solve for using the dropdown.
  • Enter the three known values in the corresponding input fields.
  • Press "Calculate" to find the missing value.
  • The calculator will show the step-by-step solution and the final result.

For example, to find the final volume when 6 L of gas containing 3 moles is increased to 5 moles at constant temperature and pressure:

V₂ = V₁ × n₂ / n₁

V₂ = 6 × 5 / 3

V₂ = 10 L

Real-World Applications

  • Inflating a balloon: When you blow air into a balloon, you are adding gas molecules, which causes the volume to increase.
  • Bicycle tire pump: Adding air to a tire increases both the amount of gas and the pressure (in a rigid container).
  • Helium vs. air balloons: Equal volumes of helium and air contain the same number of molecules, but helium is lighter.
  • Rocket propulsion: The expansion of gas volume as propellant burns is a direct application of Avogadro's Law.
  • Scuba tanks: The amount of gas in a fixed-volume tank determines the pressure and dive time.

❓ Avogadro's Law FAQ

What is Avogadro's Law formula?

The formula is V₁/n₁ = V₂/n₂. It relates the initial and final volumes and amounts of gas at constant temperature and pressure.

What are the conditions for Avogadro's Law?

The law applies when temperature and pressure are constant. Only the amount of gas and the volume change.

What is the difference between Avogadro's Law and the Ideal Gas Law?

Avogadro's Law is a special case of the Ideal Gas Law (PV = nRT) where temperature and pressure are held constant. It focuses specifically on the volume-amount relationship.

What is Avogadro's number?

Avogadro's number (6.022 × 10²³) is the number of particles (atoms, molecules, ions) in one mole of a substance. It is a fundamental constant in chemistry.

What is molar volume at STP?

At STP (0 °C and 1 atm), one mole of any ideal gas occupies 22.4 liters. This is a direct consequence of Avogadro's Law.

Why is Avogadro's Law important?

Avogadro's Law explains why equal volumes of different gases contain the same number of molecules, which is fundamental to understanding chemical reactions involving gases and stoichiometry.

Can I use this calculator for real gases?

Avogadro's Law is accurate for ideal gases at moderate pressures and temperatures. At high pressures or near liquefaction, real-gas corrections (like the van der Waals equation) are needed.

How accurate is this calculator?

This calculator uses the exact formula V₁/n₁ = V₂/n₂. Accuracy depends on the precision of the input values. You can adjust the decimal precision in the output.

Is this calculator free?

Yes, this calculator is completely free to use. No registration or personal data storage is required.

Who discovered Avogadro's Law?

Avogadro's Law was proposed by Amedeo Avogadro (1776–1856), an Italian scientist, in 1811. It was later confirmed experimentally by other scientists.