The kinetic theory of gases and gas laws
The molecules of any gas, such as in air, are in constant and very fast motion. The observation that lead to the kinetic theory of gases was Brownian motion. In the original experiment in 1827 Brown observed pollen grains in water and saw tiny particles dancing around without any apparent cause. In gases we demonstrate the same sort of thing by looking at smoke particles in air (free video here). The complete explanation has to wait until 1905 when Einstein explained that it was fast moving molecules hitting the particles so hard that they jumped or vibrated.
The first sheet of notes explains brown motion and how to observe it in detail.
The second sheet explains Boyle's Law (the pressure of a gas is inversely proportional to the volume at a fixed temperature) in terms of the kinetic theory. The third sheet similarly explains Charles's Law (the volume of a gas is directly proportional to the temperature if the temperature remains constant).
The final five sheets of notes explain a detailed derivation of the main gas equations from the kinetic theory and the assumptions we have to make. The equations and laws that are derived from it are explained including Avogadro's Law and Avogadro's number.