Question

What is the relationship between the ideal gas law and the Avogadro's law?

Answer 1

Avogadro's law states that, at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles present. In other words, equal volumes of gases at the same pressure and temperature contain the same number of molecules - this is true regardless of their physical properties or chemical nature.

This number of molecules is `6.022 * 10^23` and is known as Avogadro's number, `N_A`.

Matematically, Avogadro's law can be written like this

`V/n = const`, or, better yet, `V_1/n_1 = V_2/n_2`.

Avogadro's law, as well as Boyle's law and Charles' law, are special cases of the ideal gas law, `PV = nRT`. If temperature and pressure are kept constant, and knowing that `R` is of course constant, then

`PV = nRT -> (PV)/n = RT -> V/n = (RT)/P = const`, which represents Avogadro's law.

The ideal gas law can also be written to incorporate `N_A`, since the number of moles are actually the number of molecules divided by Avogadro's number

`PV = N/N_A *RT`, where `N` represents the number of molecules.