Regardless of conditions, gases have nearly the same volume per 1 mol. This is a useful property unique to gases.
Basic Knowledge
Regardless of the type of gas, gases have the same volume when they have the same amount of substance at the same temperature and pressure (Avogadro's law).
At standard temperature and pressure (0 ℃ = 273 K, 1.013×105 Pa), 1 mol of gas has a volume of approximately 22.4 L. This is called molar volume.
・Volume (L) = amount of substance (mol) × 22.4 (L/mol)
・Amount of substance (mol) = volume (L) ÷ 22.4 (L/mol)
Example: 11.2 L of O2 (at standard conditions) is 11.2 ÷ 22.4 = 0.50 mol.
Avogadro's law (Gases with the same volume at the same temperature and pressure contain the same number of molecules, regardless of type)
Standard state (0 ℃, 1.013×105 Pa. Abbreviation STP)
Molar volume (Volume of 1 mol of gas. 22.4 L/mol at standard conditions)
Density of a gas (Molar mass ÷ molar volume = g/L)
Average molecular mass of a gas (Apparent molecular mass of a gas mixture. Air is approximately 28.8)
Further Exploration (Background and Significance)
Because the distances between gas molecules are large, differences in molecular size and type have little effect. Therefore, even different gases have nearly the same volume of 22.4 L per 1 mol. This convenient property is unique to gases and does not hold for solids and liquids.
The density of a gas is found using density (g/L) = molar mass (g/mol) ÷ 22.4 (L/mol). Conversely, if the density is known, the molar mass (= molecular mass) can be estimated. Whether a gas is heavier or lighter than air can be determined immediately by comparing its molecular mass with the average molecular mass of air, 28.8 (for example, CO2=44 is heavier, while H2=2 is lighter).
- At standard conditions (0 ℃, 1.013×105 Pa), 1 mol of gas = 22.4 L
- Avogadro's law: same temperature and pressure, same volume, same number of molecules
- Volume (L) = amount of substance (mol) × 22.4
- Amount of substance (mol) = volume (L) ÷ 22.4
- Gas density = molar mass ÷ 22.4 (g/L)
- Molar volume is nearly the same regardless of the type of gas
- Average molecular mass of air ≒ 28.8 → compare to determine whether a gas is lighter or heavier
Points of Caution (Common Confusions)
① 22.4 L/mol applies only at standard conditions. The value changes if the temperature or pressure is different. ② 22.4 L/mol cannot be used for solids and liquids. It is limited to gases. ③ 0 ℃ = 273 K (be careful with absolute temperature). ④ Avogadro's law can be used only at the same temperature and pressure.
Practice
- How many mol is 5.6 L of nitrogen N2 at standard conditions?
- What is the volume in liters of 0.25 mol of CO2 at standard conditions?
- Find the density of O2 at standard conditions. (Use O=16 and 22.4 L/mol)