How ideal gas combines Boyle, Charles, and Avogadro
The ideal gas law, PV = nRT, is a unified statement of three earlier observations. Boyle's law says pressure and volume are inversely related at constant temperature; Charles's law says volume increases with temperature at constant pressure; Avogadro's law says volume is proportional to the number of moles. The ideal gas law wraps all three into one equation where R is a universal constant (0.0821 L atm/mol K), and temperature must be in Kelvin.
Real gases deviate from ideality at high pressure or low temperature when molecules are forced close enough that their size becomes significant, or when intermolecular forces (van der Waals attractions) matter. The ideal gas law is highly accurate for most gases at room temperature and atmospheric pressure, which is why it is so widely used.
Using PV = nRT to solve problems
The law is algebraically flexible. Rearrange to find any unknown: n = PV/RT to find moles, P = nRT/V to find pressure, or T = PV/nR to find temperature. Units must be consistent; if you want pressure in atmospheres and volume in liters, use R = 0.0821. If you want pressure in pascals and volume in cubic meters, use R = 8.314 J/(mol K). A common pitfall is forgetting to convert Celsius to Kelvin; subtracting 273 or 274 is essential.
Practical limits and corrections
At very high pressures (above 10 atm) or very low temperatures (approaching liquefaction), the van der Waals equation is more accurate because it accounts for molecular volume and intermolecular attractions. For most lab and real-world scenarios with air, nitrogen, oxygen, or other common gases at moderate conditions, the ideal gas law is sufficient. Understanding when it breaks down helps avoid calculation errors in engineering and industrial applications.