Molar volume.

Step 1 of 5

Counting moles

For a gas it is easier to measure volume than mass. The ideal gas equation, $pV = nRT$⁠, links the volume to the number of moles, $n$⁠, so you can count the molecules of a gas with a pressure gauge, a thermometer and a ruler.

To use it with $R = 8.314\ \mathrm{J/(mol \cdot K)}$$R =$$8.314\ \mathrm{J/(mol \cdot K)}$⁠, every quantity has to be in SI units: pressure in pascals, volume in cubic metres, and temperature in kelvin. The box in the Scene is at 300 K, 2 L and one atmosphere.

Step 2 of 5

One mole

The molar volume, $V_m$⁠, is the volume one mole of gas takes up: $V_m = \dfrac{V}{n}$⁠. From the equation, $V_m = \dfrac{RT}{p}$⁠, so it depends only on temperature and pressure, not on which gas it is.

Step 3 of 5

Standard conditions

At 0 °C and one atmosphere, standard conditions, the molar volume is 22.4 L/mol. At room temperature, 20–25 °C, it is about 24 L/mol. The box has now been cooled to 273 K, and the pressure has dropped.

Step 4 of 5

Avogadro’s law

Notice that the kind of gas never came into the working. In 1811 Amedeo Avogadro proposed that equal volumes of different gases, at the same temperature and pressure, hold equal numbers of particles. The reason is that the molecules are tiny compared with the gaps between them: their size hardly matters. And a heavy molecule moves more slowly but hits harder, so the pressure comes out the same.

Show the speed curve is at Speed curve: this is how the speeds of the nitrogen spread at 300 K.

Step 5 of 5

From grams to litres

Now you can go from the mass of a gas to its volume in two steps: from mass to moles with the molar mass, $n = \dfrac{m}{M}$⁠, and from moles to volume with the molar volume, $V = n V_m$⁠.