The molar volume is the volume occupied by one mole of gas, whatever the type of gas, at a given temperature and pressure. It is expressed in |\text{L/mol}|.
According to Avogadro's law, the volume of a gas is directly proportional to its quantity of mole under constant temperature and pressure conditions, regardless of the gas in question. The space occupied by a gas does not therefore depend on its nature. Rather, it is determined by the quantity of particles it contains.
Experimental measurements have made it possible to determine the molar volume of a gas at standard experimental conditions (STP and SATP):
| Experimental conditions | Temperature | Pressure | Molar Volume |
| STP (standard temperature and pressure) |
|0\ \text{°C}| or |273\ \text{K}| | |101.3\ \text{kPa}| | |22.4\ \text{L/mol}| |
| SATP (standard ambient temperature and pressure) |
|25\ \text{°C}| or |298\ \text{K}| | |101.3\ \text{kPa}| | |24.5\ \text{L/mol}| |
The molar volume of a gas can be useful for converting a number of moles or a mass of a certain gas into units of volume, or vice versa. To do this, the gas must be at STP or SATP.
At STP, what is the volume occupied by |8.0\ \text{g}| of nitrogen dioxide (|\text{NO}_{2}|)?
- Identification of problem data
|n = \displaystyle \frac {m}{M} = \frac {8.0\ \text{g}}{46.01\ \text{g/mol}} = 0.174\ \text{mol of NO}_{2}| - Calculation of the volume occupied by |\text{NO}_2|
At STP: |1\ \text{mol} = 22.4\ \text{L}|
By cross-product:
|\displaystyle \frac{22.4\ \text{L}}{1\ \text{mol}}=\frac{x}{0.174\ \text{mol}}|
|x = 3.9\ \text{L}|
Answer:
The volume occupied by |8.0\ \text{g}| of nitrogen dioxide |(\text{NO}_2)| is |3.9\ \text{L}|.
How many bottles of |2\ \text{L}| could be filled with |2\ 225.6\ \text{g}| of carbon dioxide |(\text{CO}_{2})| at SATP?
- Identification of problem data
|n = \displaystyle \frac {m}{M} = \frac {2\ 225.6\ \text{g}}{44.01\ \text{g/mol}} = 50.57\ \text {mol of CO}_{2}| - Calculation of the volume occupied by |\text{CO}_{2}|
At SATP: |1\ \text{mol} = 24.5\ \text{L}|
By cross-product :
|\displaystyle \frac{24.5\ \text{L}}{1\ \text{mol}}=\frac{x}{50.57\ \text{mol}}|
|x = 1\ 238.97\ \text{L}|
Answer:
The volume occupied by |2\ 225.6\ \text{g}| of carbon dioxide |(\text{CO}_2)| corresponds to a volume of |1\ 238.97\ \text{L}|, i.e. |619| full bottles of |2\ \text{L}|, and |1| partially filled bottle.
Under other conditions, the molar volume of a gas can be determined using the ideal gas law and the following mathematical relationship:
||\frac{V}{n\,(1\ \text{mole})}=\frac{R T}{P}||
What is the molar volume of an unknown gas which is contained in a sphere containing |1.3\ \text{L}| at |32.7\ \text{ºC}| and a pressure of |1.2\ \text{atm}|?
- Identification of problem data
|V = ?|
|n = 1.0\ \text{mol}| (we want to find the volume occupied by one mole of this unknown gas)
|R = 8.314\ \text{L} \cdot\text{kPa} /\text{mol} \cdot\text{K}|
|T = 32.7\ \text{ºC} + 273.15 = 305.15\ \text{K}|
|P = 1.2\ \text{atm} \times 101.3\ \text{kPa} = 121.56\ \text{kPa}|
- Calculation of the molar volume of the unknown gas
From the relation of the ideal gas law, we obtain :
|\displaystyle \frac{V}{1\ \text{mol}}=\frac{R T}{P}=\frac{(8.314\ \text{L} \cdot \text{kPa}/ \text{mol} \cdot \text{K}))\times(305.15\ \text{K})}{121.56\ \text{kPa}}=\frac{20.9\ \text{L}}{\text{mol}}|
Answer:
The volume of one mole of the unknown gas is |20.9\ \text{L}|.