What is the ideal gas law? When is it useful?

Gas pressure is a fundamental concept within the study of gases and can be simply thought of like the force that gas exerts on the walls of its container. This force arises because gas particles are constantly moving and colliding with the container walls. The unit of pressure in the International System of Units (SI) is the pascal (Pa), though other units like atmospheres (atm), torr (mmHg), and bar are commonly used.
At a microscopic level, the force per collision may be small, but given the innumerable particles in a given volume, these collisions can sum up to exert considerable pressure. According to the ideal gas law, pressure is directly proportional to the temperature and the number of moles of gas present, while inversely proportional to the volume of the gas. Thus, increasing the gas volume leads to fewer collisions per wall area, and pressure decreases. When the temperature rises, the particles gain kinetic energy and hit the container walls more forcefully, increasing pressure.

Gas volume refers to the space occupied by the gas, typically measured in liters (L) or cubic meters (m³). An important characteristic of gases is their ability to expand to fill the available volume of their container. Unlike solids and liquids, a gas will change its volume in response to changes in temperature and pressure.
Under the ideal gas law, volume has an inverse relationship with pressure and a direct relationship with temperature and the number of moles: as pressure increases, volume decreases, and as temperature or the number of moles of gas increases, so does the volume. This relationship is crucial for understanding not just chemical reactions and processes in a lab but also in many real-world applications like the workings of engines and weather systems.

Gas temperature is a measure of the average kinetic energy of the gas particles and is usually measured in degrees Celsius (°C) or Kelvin (K). However, in the ideal gas law, temperatures must always be in Kelvin, as this is an absolute scale where 0 K, or absolute zero, represents the point at which particles theoretically stop moving.
Because temperature relates directly to the kinetic energy of gas particles, it plays a significant role in the behavior of gases. When the temperature of a gas increases, the particles move faster and collide more frequently and with more force against the container walls, which increases pressure, assuming that the volume remains constant. Consequently, at higher temperatures, if the pressure is kept constant, the volume of the gas will also increase.

Moles of gas, often symbolized as 'n' in equations, is a measure of the amount of substance or the number of particles in a given volume of gas. One mole is equivalent to approximately 6.022 × 10²³ particles, known as Avogadro's number. Whether these particles are atoms or molecules will depend on the gas.
According to the ideal gas law, the pressure and volume of a gas are directly proportional to the number of moles. Therefore, introducing more moles of gas into a container at constant temperature will result in an increase in pressure due to more particles colliding with the container walls (unless the volume is allowed to expand). The molar amount of a gas is critical to determining the mass of a sample and facilitates calculations in reactions involving gases.