The ideal gas law describes the relationship between the pressure, volume, temperature, and amount of gas in an idealized system. Under the assumptions of the law, gas particles are considered to occupy negligible volume, to experience no intermolecular forces, and to move randomly. Mathematically, the law relates these variables, establishing that the product of pressure and volume is directly proportional to the number of moles and the absolute temperature. This principle allows for the prediction and understanding of how gas characteristics change when subjected to changes in external conditions, forming a fundamental concept in physical chemistry and thermodynamics.