Density Calculations
A reformulation of the Ideal Gas Equation involving density allows us to evaluate the behaviors of ideal gases of unknown quantity.
Learning Objective

Apply the reformulated Ideal Gas Equation in your calculations
Key Points
 Density calculations allow us to evaluate the behaviors of gases of unknown volume.
 We can determine the density of an ideal gas using knowledge of three properties of the evaluated ideal gas.
 This reformulation of the Ideal Gas Equation relates pressure, density, and temperature of an ideal gas independent of the volume or quantity of gas.
Term

density
a measure of the amount of matter contained by a given volume
Full Text
The Ideal Gas Equation in the form
Astronomical applications of the Ideal Gas Law
The Taurus Molecular Cloud consists of dust and various gases, including hydrogen and helium. The density form of the Ideal Gas Equation may be of theoretical use when studying such astronomical phenomena as star formation.
Atmosphere composition
Atmospheric science offers one plausible reallife application of the density form of the ideal gas equation. Earth's atmosphere is composed of gases that support lifeāas the image shows, oxygen involved in the water cycle, sulfur emissions from oceans, methane from agriculture, and more. The density form of the Ideal Gas Law enables us to study the behavior of these gases without enclosing them in a container of known volume.
Derivation of the VolumeIndependent 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:
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.
Key Term Reference
 Pressure
 Appears in these related concepts: SI Units of Pressure, Physics and Engineering: Fluid Pressure and Force, and Surface Tension and Capillary Action
 gas
 Appears in these related concepts: Three States of Matter, Irreversible Addition Reactions, and Microstates and Entropy
 ideal gas
 Appears in these related concepts: Overview of Temperature and Kinetic Theory, Temperature, and Pressure
 ideal gas law
 Appears in these related concepts: The Effect of Intermolecular Forces, Collecting Gases Over Water, and Van der Waals Equation
 molar mass
 Appears in these related concepts: MasstoMole Conversions, Molar Mass of Gas, and Molar Mass of Compounds
 physical property
 Appears in these related concepts: Physical and Chemical Properties of Matter, Variation of Physical Properties Within a Group, and Isotopes
 system
 Appears in these related concepts: Free Energy Changes for Nonstandard States, Definition of Management, and Comparison of Enthalpy to Internal Energy
 temperature
 Appears in these related concepts: Extractive Metallurgy, Temperature, and Complex Ion Equilibria and Solubility
 volume
 Appears in these related concepts: Volumes, Volume and Density, and Shape and Volume
Sources
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