The Ideal Gas Law: PV = nRT
The ideal gas law PV = nRT relates pressure (P), volume (V), number of moles (n), and temperature (T) for ideal gases. R is the gas constant (8.314 J/(mol?K) or 0.0821 L?atm/(mol?K)). The equation combines Boyle's law (P?1/V), Charles's law (V?T), and Avogadro's law (V?n). At standard temperature and pressure (STP: 273.15 K, 101,325 Pa), one mole of any ideal gas occupies 22.4 L.
When Gases Behave Ideally
Ideal gas law works best at low pressure and high temperature where gas particles are far apart and interactions are negligible. Real gases deviate at high pressure (molecules get close) and low temperature (intermolecular forces become significant). Noble gases behave nearly ideally under most conditions. For precise calculations with real gases, use the van der Waals equation. Despite limitations, the ideal gas law is remarkably accurate for most everyday applications.
Applications in Science and Engineering
The ideal gas law is essential in chemistry, physics, and engineering. Chemists calculate reactant and product amounts in gas-phase reactions. Engineers design pressure vessels, pneumatic systems, and HVAC systems. Meteorologists use modified versions for atmospheric predictions. Scuba divers apply it to understand air consumption at depth. The law explains why tires lose pressure in cold weather, why hot air balloons rise, and how internal combustion engines work. It's fundamental to understanding respiratory physiology, industrial gas processes, and atmospheric chemistry.
Quick Tips
- Always verify units are consistent
- Use scientific notation for very large/small numbers
- Results are approximations — real conditions may vary
Frequently Asked Questions
Standard Temperature and Pressure (STP) is 273.15 K (0 degreesC) and 101,325 Pa (1 atm). At STP, one mole of ideal gas occupies 22.4 L. Note: IUPAC now defines STP at 100 kPa instead of 101.325 kPa.
R is 8.314 J/(mol?K) or 0.0821 L?atm/(mol?K), depending on units. It relates energy to temperature on a per-mole basis and appears in many equations beyond ideal gas law.
Real gases deviate at high pressure (molecules close together) and low temperature (intermolecular forces significant). Small, nonpolar molecules (H?, He) behave most ideally. Large, polar molecules deviate more.
At constant volume, pressure is directly proportional to absolute temperature (Gay-Lussac's law): P/T = constant. Doubling absolute temperature doubles pressure. Always use Kelvin for gas law calculations.
Gas laws involve ratios and proportions that only work with absolute temperature. Kelvin starts at absolute zero (0 K = -273.15 degreesC). Using Celsius or Fahrenheit gives incorrect results because they don't start at zero energy.