A gas is a state of matter characterized by widely separated particles in constant, random motion. To study and predict this behavior mathematically, scientists use simplified conceptual frameworks called gas models. The ideal gas model represents a theoretical benchmark, describing how a gas would behave under perfect conditions. This model allows for straightforward calculations that approximate the behavior of most gases under typical laboratory conditions. However, every gas in the physical world is a real gas, and these complexities cause them to deviate from the simplified ideal model.
The Core Assumptions of Ideal Gas Behavior
The foundation for the ideal gas model is the Kinetic Molecular Theory (KMT), which establishes simplified, theoretical rules for how gas particles interact. One primary assumption is that the gas particles themselves occupy zero volume. The KMT treats individual gas molecules as “point masses” whose physical volume is considered negligible compared to the vast empty space between them. This assumes the entire volume of a container is available space for the gas particles to move.
Another central pillar of the ideal gas concept is the assumption that there are no forces of attraction or repulsion between the particles. In this theoretical model, particles move completely independently, and their paths are only altered by perfectly elastic collisions. A perfectly elastic collision means that when particles bounce off each other or the container walls, the total kinetic energy of the system is conserved.
The KMT also assumes that particle motion is entirely random and continuous, moving in straight lines until a collision occurs. The average kinetic energy of the gas particles is directly proportional to the gas’s absolute temperature. These simplified rules provide a predictable, easily calculable description of gas behavior.
The Ideal Gas Law
The theoretical assumptions of the Kinetic Molecular Theory are translated into the Ideal Gas Law. This equation, often written as PV = nRT, links the macroscopic, measurable properties of a gas. The variables involved are pressure (P), volume (V), the number of moles of gas (n), and temperature (T), while R is the universal gas constant.
The law describes proportional relationships that must hold true if a gas is truly ideal. For instance, if temperature and the amount of gas remain unchanged, increasing the pressure results in a proportional decrease in volume. If the volume is held constant, increasing the temperature causes the pressure to rise because particles hit the container walls more forcefully.
This equation allows scientists to predict one property of a gas if the other three are known, provided the gas behaves ideally. The simplicity and accuracy of the Ideal Gas Law under normal conditions have made it a widely used tool in chemistry and physics. It serves as the standard against which the behavior of all real gases is measured.
Conditions that Cause Deviation
Real gases deviate from the Ideal Gas Law primarily under high pressure and low temperature. These conditions cause the two main assumptions of the KMT to break down. Deviations are noticeable when the gas is subjected to pressures significantly above atmospheric pressure or temperatures near the point of condensation.
Under high pressure, gas particles are forced into a much smaller volume, reducing the empty space between them. When particles are packed closely, the physical size of the individual gas molecules can no longer be ignored relative to the total container volume. The volume occupied by the particles makes the actual free space available less than the measured container volume, causing the gas to be less compressible than an ideal gas.
At low temperatures, the average kinetic energy and speed of the gas particles decrease significantly. This slower movement allows weak, temporary attractive forces between molecules, such as van der Waals forces, to become influential. These intermolecular forces are negligible at high speeds, but they begin to pull the particles toward one another at low temperatures.
This attraction causes the gas particles to strike the container walls with less force than they would otherwise. Consequently, the measured pressure of the real gas is lower than the pressure predicted by the Ideal Gas Law. High pressure and low temperature conditions expose the inaccuracies of the KMT assumptions, demonstrating that real gas particles have finite volume and exert forces on one another.
Accounting for Real Gas Behavior
Since the Ideal Gas Law is insufficient for accurately modeling gas behavior under non-ideal conditions, scientists developed corrected equations. These equations introduce specific adjustment factors to account for the physical realities of real gases. The need for a corrected model arises directly from the failure of the two core KMT assumptions under stress.
One recognized corrected model is the Van der Waals equation, which modifies the Ideal Gas Law with two added terms. One correction factor, specific to each gas, is subtracted from the volume term to account for the finite volume occupied by the gas molecules. This adjustment calculates the true available volume for the particles to move within.
A second correction factor is added to the pressure term to account for the attractive forces between the particles. This term adjusts the measured pressure upward to represent the pressure the gas would exert without attractive forces slowing the particles before impact. By incorporating these two factors, the Van der Waals equation provides a more accurate description of real gas behavior across a broader range of temperatures and pressures.