At standard temperature and pressure (STP), which is defined as 298 K (25 degrees Celsius) and 100 kPa (1 atmosphere or 760 mmHg), the molar volume of a gas is approximately 22.4 liters/mol. This value is derived from the ideal gas law and the Avogadro's law.
According to Avogadro's law, equal volumes of gases at the same temperature and pressure contain an equal number of molecules. The ideal gas law combines several gas laws, including Avogadro's law, and can be expressed as:
PV = nRT
Where: P = Pressure (in Pascals or kilopascals) V = Volume (in cubic meters or liters) n = Number of moles of gas R = Ideal gas constant (8.314 J/(mol·K) or 0.0821 L·atm/(mol·K)) T = Temperature (in Kelvin)
At STP, we have: P = 100 kPa V = ? n = 1 mole R = 8.314 J/(mol·K) or 0.0821 L·atm/(mol·K) T = 298 K
Rearranging the ideal gas law to solve for V: V = (nRT) / P
Substituting the values: V = (1 mole * 0.0821 L·atm/(mol·K) * 298 K) / (100 kPa) ≈ 22.4 liters/mol
Therefore, at STP, the molar volume of a gas is approximately 22.4 liters/mol.