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

Derive the Ideal Gas Law for gases of unknown volume

Make calculations using the reformulated Ideal Gas Equation.
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
Example

The form of the Ideal Gas Equation involving density helps make determinations about gases that are not enclosed in a container, such as the gases in our atmosphere or outer space.
Full Text
The Ideal Gas Equation in the form
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.
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Key Term Reference
 atmosphere
 Appears in this related concepts: Emission Spectrum of the Hydrogen Atom, Environmental Problems Associated with Fossil Fuel Use, and Earth's Atmosphere
 gas
 Appears in this related concepts: Oxidation Numbers of Metals in Coordination Compounds, Microstates and Entropy, and Three States of Matter
 ideal gas
 Appears in this related concepts: Kelvin Scale, Isotherms, and The Ideal Gas Equation
 ideal gas law
 Appears in this related concepts: The Effect of Intermolecular Forces, Collecting Gases Over Water, and Van der Waals Equation
 molar mass
 Appears in this related concepts: Molar Mass of Gas, Converting between Mass and Number of Moles, and MasstoMole Conversions
 mole
 Appears in this related concepts: Percent Composition of Compounds, Equations of State, and Gas Exchange across the Alveoli
 physical property
 Appears in this related concepts: Physical and Chemical Properties of Matter, Variation of Physical Properties Within a Group, and Isotopes
 system
 Appears in this related concepts: Free Energy Changes for Nonstandard States, A Definition of Management, and Comparison of Enthalpy to Internal Energy
 temperature
 Appears in this related concepts: Complex Ion Equilibria and Solubility, Extractive Metallurgy, and Temperature
 volume
 Appears in this related concepts: Cylindrical Shells, Volume and Density, and Shape and Volume
Sources
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Cite This Source
Source: Boundless. “Density Calculations.” Boundless Chemistry. Boundless, 25 Nov. 2014. Retrieved 20 Mar. 2015 from https://www.boundless.com/chemistry/textbooks/boundlesschemistrytextbook/gases5/theidealgaslaw52/densitycalculations2581026/