# What is the relationship between the combined gas law and the ideal gas law?

May 18, 2014

The Combined Gas Law and the Ideal Gas Law are the same relationships written in different ways.

The Combined Gas Law is a combination of Boyle's, Charles' and Gay-Lussac's laws.

$P V$ = constant

$\frac{V}{T}$ = constant

$\frac{P}{T}$ = constant

The Combined Gas Law joins these to make

$\frac{P V}{T}$ = constant or $\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$

The Combined Gas Law should also include Avogadro's Law: "The volume of a gas is directly proportional its number of moles".

$\frac{V}{n}$ = constant

Then the Combined Gas Law becomes

$\frac{P V}{n T}$ = constant

If we call the constant $R$, the Combined Gas Law becomes

$\frac{P V}{n T} = R$

When we rearrange this equation, it becomes

$P V = n R T$

We call this equation the Ideal Gas Law.