Molar Volume Calculator
What is Molar Volume?
The Molar Volume (Vm) is the volume occupied by one mole of a gas under specific conditions.
STP: 22.4 L/mol (0°C, 1 atm)
SATP: 24.8 L/mol (25°C, 1 bar)
Key Terms:
- STP: Standard Temperature and Pressure (0°C, 1 atm)
- SATP: Standard Ambient T & P (25°C, 1 bar)
- Ideal Gas: Hypothetical gas that exactly obeys gas laws
Formulas
Molar Volume:
Vm = V / n
Vm = V / n
Calculate Gas Volume:
V = n × Vm
V = n × Vm
Calculate Molar Amount:
n = V / Vm
n = V / Vm
Ideal Gas Law:
PV = nRT
PV = nRT
R (Gas Constant): 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K)
Examples
Nitrogen (N₂) at STP
2 mol N₂ × 22.4 L/mol = 44.8 L
2 mol N₂ × 22.4 L/mol = 44.8 L
Carbon Dioxide (CO₂) at 25°C
1 mol CO₂ × 24.8 L/mol = 24.8 L
1 mol CO₂ × 24.8 L/mol = 24.8 L
Hydrogen (H₂) at STP
3 mol H₂ × 22.4 L/mol = 67.2 L
3 mol H₂ × 22.4 L/mol = 67.2 L
Oxygen (O₂) at STP
0.5 mol O₂ × 22.4 L/mol = 11.2 L
0.5 mol O₂ × 22.4 L/mol = 11.2 L
Chlorine Gas (Cl₂) at SATP
1.5 mol Cl₂ × 24.8 L/mol = 37.2 L
1.5 mol Cl₂ × 24.8 L/mol = 37.2 L
Ideal Gas Law Application
1 mol gas at 273 K, 1 atm → V = 22.4 L
1 mol gas at 273 K, 1 atm → V = 22.4 L
Technical Background
Ideal vs. Real Gas
The ideal gas law (PV = nRT) assumes that gas molecules have no volume and do not interact with each other. This is a good approximation at low pressures and high temperatures.
For real gases under extreme conditions, the van der Waals equation is more accurate.
Standards and Conditions
| Standard | Temperature | Pressure | Vm (L/mol) | Application |
|---|---|---|---|---|
| STP (old) | 0°C (273.15 K) | 1 atm | 22.4 | Classical chemistry |
| IUPAC STP (new) | 0°C (273.15 K) | 1 bar (100 kPa) | 22.71 | Modern definition |
| SATP | 25°C (298.15 K) | 1 bar (100 kPa) | 24.8 | Room temperature |
| NTP | 20°C (293.15 K) | 1 atm | 24.04 | Normal Temperature |
Practical Applications
- Stoichiometric Calculations: Conversion between gases and liquids/solids
- Laboratory Work: Measurement of gas volumes at different conditions
- Industry: Gas production and consumption in chemical plants
- Meteorology: Calculation of air volume and air density
- Respiration: Lung volume and gas exchange in humans
Note on Modern Standards
⚠️ Important: IUPAC changed the STP definition in 2019: New standard is 0°C and 1 bar (not 1 atm). The new molar volume is therefore 22.71 L/mol (instead of 22.4 L/mol). Check which standard is used in your school/university!
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