10.8: Gas Density
- Page ID
- 53772
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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.
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
- How is density calculated?
- How is molar mass calculated?
- What would be the volume of 3.5 moles of a gas?