Structure 1.4.6—Avogadro’s law states that equal volumes of all gases measured under the same conditions of temperature and pressure contain equal numbers of molecules.

**What You’ll Learn:**

- Solve problems involving the mole ratio of reactants and/or products and the volume of gases.

**Keywords**

IBDP chemistry, mole, mol, amount of substance, elementary entities, atoms, molecules, ions, electrons, carbon-12, Avogadro’s constant, N_{A}, 6.022 x 10^23 mol^{-1}, amount of substance, n, number of entities, formula, oxygen atoms, water molecules, data booklet, units

.

**Syllabus Links**

Structure 1.5—Avogadro’s law applies to ideal gases. Under what conditions might the behaviour of a real gas deviate most from an ideal gas?

## Avogadro’s law of gases

Avogadro’s law states that equal volumes of all gases measured under the same conditions of temperature and pressure contain equal numbers of molecules. This law is a fundamental principle in chemistry that relates the volume of a gas to the number of molecules it contains. It is named after the Italian scientist Amedeo Avogadro, who first proposed it in 1811.

This law works for gases because the behavior of gases can be modeled using the kinetic molecular theory. According to this theory, gases are composed of a large number of small particles (atoms or molecules) that are in constant, random motion. The volume of a gas is largely empty space, with the particles moving freely and independently of one another. When the temperature and pressure are held constant, the average speed of gas particles is proportional to the square root of their temperature, and the frequency and force of collisions between gas particles and the walls of the container are proportional to the pressure.

Avogadro’s law can be explained by considering the fact that gas particles occupy the same amount of space regardless of their identity or size. This means that if we have two gases of different molecular weights and identical volumes, they will have different numbers of molecules, but the same number of collisions with the walls of the container. As a result, the pressure of the gases will be the same.

The law can be expressed mathematically as V = k n, where V is the volume of the gas, n is the number of molecules, and k is a constant of proportionality. This equation holds true for all ideal gases at a constant temperature and pressure. Therefore, it is possible to calculate the number of molecules in a given volume of an ideal gas, or to determine the volume occupied by a specific number of molecules of an ideal gas.

For example, let’s consider a sample of hydrogen gas (H₂) at a temperature of 25°C and a pressure of 1 atm. According to Avogadro’s law, the volume of the gas is directly proportional to the number of molecules it contains. If we have a volume of 22.4 dm^{3} of hydrogen gas, which is the molar volume of an ideal gas at standard temperature and pressure, we know that it contains 6.022 x 10²³ molecules of hydrogen. This number is known as Avogadro’s constant.

Questions

- What is Avogadro’s law and how does it relate to the volume of a gas?
- Who is the scientist credited with first proposing Avogadro’s law?
- Why is Avogadro’s law important in the study of chemistry?
- Can the ideal gas law be derived from Avogadro’s law? Why or why not?
- How does the kinetic molecular theory help explain the behavior of gases in relation to Avogadro’s law?
- What are some factors that may cause real-life gases to deviate from ideal gas behavior, and how does this impact Avogadro’s law?
- Suppose we have two gases, each with a volume of 2 liters at a temperature of 20 degrees Celsius and a pressure of 1 atmosphere. According to Avogadro’s law, how many molecules of each gas should be present?
- Can Avogadro’s law be used to compare the number of molecules of a gas at different temperatures or pressures? Why or why not?
- How does Avogadro’s law relate to the concept of molar volume?
- What is the significance of Avogadro’s number in relation to Avogadro’s law?