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.
Key Takeaways: Avogadro’s Law
- Avogadro’s law states that volume is proportional to moles of gas at constant temperature and pressure.
- The formula is most often written as V/n = k.
- The law is independent of gas type.
- It is one of the four primary gas laws and part of the combined/ideal gas law.
- Deviations occur at high pressure or low temperature, but the law is a good approximation 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. The law is important because it distinguishes between atoms and molecules and allows calculation of molar masses. However, Avogadro’s paper went largely unnoticed until Cannizzaro revived it in 1858, which cemented its place in chemistry.
Avogadro’s law is also known as Avogadro’s hypothesis or Avogadro’s principle. It relates 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
V1/n1 = V2/n2
V1n2 = V2n1
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.
Other examples include:
- Inflating an air mattress or car tire.
- The role of lung capacity when breathing.
- Gas cylinders used in labs or hospitals (e.g., oxygen tanks).
- Carbonation in soda bottles when shaken and resealed (moles of CO₂ entering/leaving headspace gas).
Classroom Demonstration
A simple way to see Avogadro’s law in action is with everyday lab equipment. Take a plastic syringe and seal the tip with a cap. Drop effervescent tablets (such as Alka-Seltzer) into a small vial of water, then attach a balloon over the mouth of the vial. As the reaction produces carbon dioxide gas, the balloon inflates. The more tablets you add, the greater the number of moles of gas, and the larger the balloon volume. A similar demonstration involves adding measured amounts of baking soda and vinegar to a flask. These activities make the direct relationship between moles of gas and gas volume visible.
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:
V1 = 13.5 L
V2 = ?
n1 = 0.000524 mol
n2 = 0.00144 mol
Next, plug the values into the Avogadro’s law formula and rearrange the equation to calculate the answer:
V1/n1 = V2/n2
13.5 L / 0.000524 mol = V2 / 0.00144 mol
V2 / 0.00144 mol = 13.5 L / 0.000524 mol
V2 = (13.5 L / 0.000524 mol)(0.00144 mol)
V2 = 37.1 L
This problem shows the direct proportionality. Graphing and ratio reasoning also work for finding the solution.
See another Avogadro’s law example problem.
Limitations
Avogadro’s law describes the behavior of an ideal gas, but real gases do not always act ideally. At high pressures, gas particles have volume that cannot be ignored, so the measured volume is less than predicted. At very low temperatures, intermolecular forces between particles cause attraction or repulsion, which also results in deviations from the law. These effects become especially important near a gas’s condensation point. To correct for real gas behavior, chemists use equations such as the van der Waals equation, which includes terms for particle size and intermolecular forces.
FAQs and Misconceptions
Is Avogadro’s law the same as Avogadro’s number?
No. Avogadro’s law relates the volume of a gas to the number of moles, while Avogadro’s number is the number of particles in one mole of substance (6.022 × 10²³).
Does the type of gas matter?
Not under ideal conditions. One mole of hydrogen gas occupies the same volume as one mole of oxygen gas at the same temperature and pressure, even though the molecules have different masses.
Does Avogadro’s law apply to solids and liquids?
No. The law applies only to gases, because their particles are far apart and free to move, making volume proportional to moles.
Why did it take decades for Avogadro’s law to be accepted?
Confusion between atoms and molecules delayed acceptance. Chemists of the early 1800s disagreed on whether elements existed as single atoms or paired molecules. Only after Cannizzaro clarified this distinction in 1858 did Avogadro’s hypothesis gain wide recognition.
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