# 10.8: Gas Density

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. Figure 10.8.1: Balloons filled with helium gas float in air because the density of helium is less than the density of air.

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.

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.

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

Because the density of the gas is less than $$1 \: \text{g/L}$$, the molar mass is less than 22.4.