# 10.8: Gas Density

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- 53772

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 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 \(\text{g/L}\). Gas density can be calculated from molar mass and molar volume.

Example 10.8.1

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 \(= ? \: \text{g/L}\)

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

*Step 2: Calculate.*

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

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 10.8.2

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 \(= ? \: \text{g/L}\)

Molar mass is equal to density multiplied by molar volume.

*Step 2: Calculate.*

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

*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.

## Contributors

CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon.