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

Dec 23, 2014

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 $6.022 \cdot {10}^{23}$ and is known as Avogadro's number, ${N}_{A}$.

Matematically, Avogadro's law can be written like this

$\frac{V}{n} = c o n s t$, 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, $P V = n R T$. If temperature and pressure are kept constant, and knowing that $R$ is of course constant, then

$P V = n R T \to \frac{P V}{n} = R T \to \frac{V}{n} = \frac{R T}{P} = c o n s t$, 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

$P V = \frac{N}{N} _ A \cdot R T$, where $N$ represents the number of molecules.