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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

Credit: Image copyright md8speed, 2014
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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.

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

• N2 = 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.

28.02 g1 mol×1 mol22.4 L=1.25 g/L\begin{align*}\frac{28.02 \ \text{g}}{1 \ \text{mol}} \times \frac{1 \ \text{mol}}{22.4 \ \text{L}}=1.25 \ \text{g} / \text{L}\end{align*}

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

• N2 = 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.

0.761 g1 L×22.4 L1 mol=17.0 g/mol\begin{align*}\frac{0.761 \ \text{g}}{1 \ \text{L}} \times \frac{22.4 \ \text{L}}{1 \ \text{mol}}=17.0 \ \text{g} / \text{mol}\end{align*}

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.

### 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?

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