**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.

#### 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

- N
_{2}= 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.*

\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.

*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 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

- N
_{2}= 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.*

\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*}

*Step 3: Think about your result.*

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

- How is density calculated?
- How is molar mass calculated?
- What would be the volume of 3.5 moles of a gas?