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10.8: Gas Density

Last updated

Mar 21, 2025
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- 10.7: Conversions Between Moles and Gas Volume
- 10.8: Mole Road Map

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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.

A colorful arrangement of balloons with one at the top displaying the word Congrats The balloons include shades of purple, red, green, yellow, orange, and blue, against a plain gray background. — Figure $\PageIndex{2}$ : Balloons filled with helium gas float in air because the density of helium is less than the density of air. (Public Domain; Photographer: Warren Denning, courtesy of the Pioneer Balloon Company via Wikipedia)

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?

Why does carbon dioxide sink in air?

Gas Density

Example 10.8.1\PageIndex{1}: Gas Density

Solution

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

Known

Unknown

Step 2: Calculate.

Step 3: Think about your result.

Example 10.8.2\PageIndex{2}: Molar Mass from Gas Density

Solution

Known

Unknown

Step 2: Calculate.

Step 3: Think about your result.

Summary

Review

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Example $\PageIndex{1}$ : Gas Density

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