Question

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

Answer 1

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.

`PV` = constant

`V/T` = constant

`P/T` = constant

The Combined Gas Law joins these to make

`(PV)/T` = constant or `(P_1V_1)/T_1 = (P_2V_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".

`V/n` = constant

Then the Combined Gas Law becomes

`(PV)/(nT)` = constant

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

`(PV)/(nT) = R`

When we rearrange this equation, it becomes

`PV = nRT`

We call this equation the Ideal Gas Law.