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
Rearranging the above equation, we get:
Now, recall that density is equal to mass divided by volume:
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.