# 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.

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.