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Gas Density
If you start out with the ideal gas equation and substitute grams/molar mass for moles, then rearrange to get
,
and then substitute d (density) for g/V, we have the relationship

You can use this equation to calculate the density of a gas from the pressure, temperature, and molar mass, or obviously the molar mass can be calculated if the density, pressure, and temperature are known. The equation above also tells us two important facts about the density of an ideal gas:
1. At constant temperature and pressure, the density of a gas is directly proportional to the molar mass. This means that the density of methane (CH4, molar mass = 16 g/mol) is four times the density of helium (atomic weight = 4 g/mol) if the two gases are at the same T and P.
2. At constant molar mass (i.e., for a given gas) and pressure, density is inversely proportional to the absolute temperature. This explains the common observation that warm air rises and cold air falls.

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