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10.8: Gas Density

  • Page ID
    53772
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     Carbon dioxide sinks in air
    Figure \(\PageIndex{1}\) (Credit: CK-12 Foundation; Source: CK-12 Foundation; License: CK-12 Curriculum Materials license)

    Why does carbon dioxide sink in air?

    When we run a reaction to produce a gas, we expect it to rise into the air. Many students have done experiments where gases such as hydrogen are formed. The gas can be trapped in a test tube held upside-down over the reaction. Carbon dioxide, on the other hand, sinks when it is released. Carbon dioxide has a density greater than air, so it will not rise like the hydrogen gas.

    Gas Density

    As you know, density is defined as the mass per unit volume of a substance. Since gases all occupy the same volume on a per mole basis, the density of a particular gas is dependent on its molar mass. A gas with a small molar mass will have a lower density than a gas with a large molar mass. Gas densities are typically reported in \(\text{g/L}\). Gas density can be calculated from molar mass and molar volume.

    Balloons filled with helium floating.
    Figure \(\PageIndex{2}\): Balloons filled with helium gas float in air because the density of helium is less than the density of air. (Credit: Photographer: Warren Denning, courtesy of the Pioneer Balloon Company; Source: http://commons.wikimedia.org/wiki/File:Congrats_bqt.jpg(opens in new window); License: Public Domain)
    Example \(\PageIndex{1}\): Gas Density

    What is the density of nitrogen gas at ​​​​​​​STP?

    Solution
    Step 1: List the known quantities and plan the problem.
    Known
    • \(\ce{N_2} = 28.02 \: \text{g/mol}\)
    • \(1 \: \text{mol} = 22.4 \: \text{L}\)
    Unknown
    • density = ? g/L

    Molar mass divided by molar volume yields the gas density at STP.

    Step 2: Calculate.

    \[\frac{28.02 \: \text{g}}{1 \: \text{mol}} \times \frac{1 \: \text{mol}}{22.4 \: \text{L}} = 1.25 \: \text{g/L}\nonumber \]

    When set up with a conversion factor, the \(\text{mol}\) unit cancels, leaving \(\text{g/L}\) as the unit in the result.

    Step 3: Think about your result.

    The molar mass of nitrogen is slightly larger than molar volume, so the density is slightly greater than \(1 \: \text{g/L}\).

    Alternatively, the molar mass of a gas can be determined if the density of the gas at STP is known.

    Example \(\PageIndex{2}\): Molar Mass from Gas Density

    What is the molar mass of a gas whose density is \(0.761 \: \text{g/L}\) at STP?

    Solution

    Step 1: List the known quantities and plan the problem.

    Known
    • \(\ce{N_2} = 28.02 \: \text{g/mol}\)
    • \(1 \: \text{mol} = 22.4 \: \text{L}\)
    Unknown
    • molar mass = ? g/mol

    Molar mass is equal to density multiplied by molar volume.

    Step 2: Calculate.

    \[\frac{0.761 \: \text{g}}{1 \: \text{L}} \times \frac{22.4 \: \text{L}}{1 \: \text{mol}} = 17.0 \: \text{g/mol}\nonumber \]

    Step 3: Think about your result.

    Because the density of the gas is less than \(1 \: \text{g/L}\), the molar mass is less than 22.4.

    Summary

    • Calculations are described showing conversions between molar mass and density for gases.

    Review

    1. How is density calculated?
    2. How is molar mass calculated?
    3. What would be the volume of 3.5 moles of a gas?

    This page titled 10.8: Gas Density is shared under a CK-12 license and was authored, remixed, and/or curated by CK-12 Foundation via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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