Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

This statement is known as Avogadro's Law, named after the Italian scientist Amedeo Avogadro. It states that equal volumes of all gases, at the same temperature and pressure, have the same number of molecules.

Here's a step-by-step explanation:

1. Consider two gases A and B, each occupying a volume of V, at the same temperature and pressure.

2. According to Avogadro's Law, the number of molecules (or atoms, if the gas is atomic) in each volume of gas is the same. This is because the volume occupied by a gas is directly proportional to the number of molecules or atoms it contains, regardless of the nature of the gas.

3. Therefore, the volume V of gas A contains the same number of molecules as the volume V of gas B, given that the temperature and pressure conditions are the same.

4. This principle is fundamental in the development of the ideal gas law and the concept of the mole in chemistry.

5. It allows us to compare different gases under the same conditions of temperature and pressure, and know that we are dealing with the same number of particles (molecules or atoms).