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Gas Density

Calculations of conversions between molar mass and the mass per unit volume of gases

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Gas Density

Carbon dioxide sinks in air

Credit: Image copyright md8speed, 2014
Source: http://www.shutterstock.com
License: CC BY-NC 3.0

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 that air, so it will not rise like these other gases would.

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 g/L.  Gas density can be calculated from molar mass and molar volume.

Balloons float because they contain helium, which is lighter than air

Credit: Photographer: Warren Denning, courtesy of the Pioneer Balloon Company
Source: http://commons.wikimedia.org/wiki/File:Congrats_bqt.jpg
License: CC BY-NC 3.0

Balloons filled with helium gas float in air because the density of helium is less than the density of air. [Figure2]

Sample Problem One: Gas Density

What is the density of nitrogen gas at STP?

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

Known

  • N 2 = 28.02 g/mol
  • 1 mol = 22.4 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} / \text{L}

When set up with a conversion factor, the mol unit cancels, leaving 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 g/L.

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

Sample Problem Two: Molar Mass from Gas Density

What is the molar mass of a gas whose density is 0.761 g/L at STP?

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

Known

  • N 2 = 28.02 g/mol
  • 1 mol = 22.4 L

Unknown

  • molar mass = ? g/L

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} / \text{mol}

Step 3: Think about your result.

Because the density of the gas is less than 1 g/L, the molar mass is less than 22.4.

Summary

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

Practice

Questions

Use the link below to answer the following questions:

http://employees.oneonta.edu/viningwj/sims/gas_density_s.html

  1. Which of the gases has the highest density?
  2. Which gas has the lowest density?
  3. Would you expect nitrogen to have a higher or lower density that oxygen? Why?

Review

Questions

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

Image Attributions

  1. [1]^ Credit: Image copyright md8speed, 2014; Source: http://www.shutterstock.com; License: CC BY-NC 3.0
  2. [2]^ Credit: Photographer: Warren Denning, courtesy of the Pioneer Balloon Company; Source: http://commons.wikimedia.org/wiki/File:Congrats_bqt.jpg; License: CC BY-NC 3.0

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