**Avogadro’s law** states the volume of an ideal gas is directly proportional to the number of moles of gas, under conditions of constant temperature and pressure. As the number of moles of a gas increase, the volume increases proportionally. This is independent of the size of the gas particles or their molar mass, so gases of different elements and compounds are comparable to one another.

Of course, as with any ideal gas law, the behavior of real gases deviates slightly from predicted behavior. The law assumes each gas particle has no volume and that particles bounce off each other and their container in perfectly elastic conditions. Real gas molecules have volume and may be attracted or repelled by one another. Even so, Avogadro’s law is a useful approximation that is reasonably accurate for real gases under normal conditions.

### History

The law is named for Amedeo Avogadro. In 1812, Avogadro hypothesized that two ideal gas samples contained the same number of molecules if they were at the same temperature and pressure. For example, a vial of hydrogen gas and a vial of nitrogen gas contain the same number of molecules at the same volume, temperature, and pressure, even though the gases have different identities.

Avogadro’s law is also known as Avogadro’s hypothesis or Avogadro’s principle. It is related to the other ideal gas laws: Boyle’s law (1662), Charles’s law (1787) and Gay-Lussac’s law (1808). French physicist and mathematician André-Marie Ampère published the same law as Avogadro, but in 1814. In France, the relation was called **Ampère’s hypothesis**, **Avogadro–Ampère hypothesis**, or **Ampère–Avogadro hypothesis**.

### Avogadro’s Law Formula

There are four common formulas representing Avogadro’s law, where V is volume, n is number of moles of gas, and k is a constant:

V ∝ n

V/n = k

V_{1}/n_{1} = V_{2}/n_{2}

V_{1}n_{2} = V_{2}n_{1}

Because volume and number of moles are directly proportional to one another, a graph of volume versus number of moles is a straight line, extending upward from the origin.

### Example of Avogadro’s Law in Everyday Life

The best example of Avogadro’s law is blowing up a balloon. The balloon’s volume increases as you add moles of gas. Similarly, when you deflate a balloon, gas leaves the balloon and its volume shrinks.

### Avogadro’s Law Example Problem

A 13.5 L volume of gas contains 0.000524 moles of nitrogen gas. Assuming the temperature and pressure of the gas remain unchanged, what volume does 0.00144 moles of the gas fill?

First, write down what you know and identify the unknown value:

V_{1} = 13.5 L

V_{2} = ?

n_{1} = 0.000524 mol

n_{2} = 0.00144 mol

Next, plug the values into the Avogadro’s law formula and rearrange the equation to calculate the answer:

V_{1}/n_{1} = V_{2}/n_{2}

13.5 L / 0.000524 mol = V_{2} / 0.00144 mol

V_{2} / 0.00144 mol = 13.5 L / 0.000524 mol

V_{2} = (13.5 L / 0.000524 mol)(0.00144 mol)

V_{2} = 37.1 L

See another Avogadro’s law example problem.

### References

- Avogadro, Amedeo (1810). “Essai d’une manière de déterminer les masses relatives des molécules élémentaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons”.
*Journal de Physique*. 73: 58–76. English translation - Castka, Joseph F.; Metcalfe, H. Clark; Davis, Raymond E.; Williams, John E. (2002).
*Modern Chemistry*. Holt, Rinehart and Winston. ISBN 978-0-03-056537-3. - Scheidecker-Chevallier, Myriam (1997). “L’hypothèse d’Avogadro (1811) et d’Ampère (1814): la distinction atome/molécule et la théorie de la combinaison chimique”.
*Revue d’Histoire des Sciences*(in French). 50 (1/2): 159–194. doi:10.3406/rhs.1997.1277