Final answer:
The ideal gas law is derived by combining Boyle's Law, Charles's Law, and Avogadro's Law, resulting in the equation PV = nRT, which describes the behavior of an ideal gas in terms of pressure, volume, temperature, and number of moles.
Step-by-step explanation:
The derivation of the ideal gas law can be understood by combining three empirical gas laws: Boyle's Law, Charles's Law, and Avogadro's Law. Boyle's Law states that the pressure (P) of a gas is inversely proportional to its volume (V) at constant temperature, mathematically represented as PV = constant. Charles's Law says that the volume (V) is directly proportional to its absolute temperature (T) at constant pressure, or V/T = constant. Avogadro's Law intimates that the volume (V) of a gas is directly proportional to the number of moles (n) at constant temperature and pressure, represented as V/n = constant.
Combining these relationships into a single expression that includes pressure (P), volume (V), temperature (T), and number of moles of gas (n), we derive the ideal gas equation PV = nRT. Here, R is known as the ideal (universal) gas constant, which provides the necessary proportionality to equate the variables.
An ideal gas is a hypothetical concept wherein the gas particles are considered to have no volume and experience no intermolecular forces. While no gas perfectly fits this definition, many real gases behave similarly to an ideal gas under a range of temperatures and pressures. The ideal gas law becomes less accurate at very high pressures or very low temperatures where the assumptions of the model deviate significantly from real gas behavior.