The Ideal Gas Equation in the form

## Derivation of the Volume-Independent Ideal Gas Law

We know the Ideal Gas Equation in the form

If we substitute *n*:

Rearranging the above equation, we get:

Now, recall that density is equal to mass divided by volume:

The term

Rearranging in terms of D, we have:

This derivation of the Ideal Gas Equation allows us to characterize the relationship between the pressure, density, and temperature of the gas sample independent of the volume the gas occupies; it also allows us to determine the density of a gas sample given its pressure and temperature, or determine the molar mass of a gas sample given its density.