Gases are a state of matter defined by their lack of fixed shape or volume, expanding to fill any container they occupy. In introductory science, gas behavior is simplified through the “ideal gas” concept, which operates under theoretical assumptions. This model provides an accurate approximation for many common scenarios, such as air at room temperature and standard atmospheric pressure. However, actual gases, referred to as “real gases,” exhibit behaviors that deviate from this simple model, particularly when subjected to certain environmental conditions. Understanding this difference is necessary for accurate prediction.
The Theoretical Ideal Gas Model
The theoretical framework for the ideal gas is built upon two core assumptions that simplify molecular interactions. The first assumption is that gas particles occupy a negligible amount of volume compared to the container’s total volume. In this model, molecules are treated as point masses with no size.
The second assumption posits that there are zero attractive or repulsive forces acting between the gas particles, except during instantaneous, perfectly elastic collisions. This means the molecules move independently, following straight-line paths until they strike another molecule or the container wall. The Ideal Gas Law, \(PV=nRT\), perfectly describes a gas that adheres to these two assumptions. This relationship is used for calculating gas properties when molecules are far apart and moving rapidly.
The Intrinsic Properties of Real Gases
The difference between an ideal gas and a real gas lies in the physical reality of gas molecules. Unlike the point masses assumed in the ideal model, real gas molecules possess a finite, non-zero volume. When a gas is compressed, the space available for the molecules to move around is the container volume minus the volume occupied by the gas particles themselves.
The second intrinsic property causing deviation is the existence of intermolecular forces between molecules. These forces include weak, temporary Van der Waals forces, as well as dipole-dipole attractions in polar molecules. These forces influence molecular movement and collisions. Attractive forces pull molecules toward one another, slightly reducing the force and frequency of their collisions with the container walls. Repulsive forces, which become dominant when molecules are forced very close together, resist further compression.
External Conditions Causing Deviation
The intrinsic properties of molecular volume and intermolecular forces cause measurable deviation from ideal behavior under specific external conditions. High pressure is one condition, which dramatically reduces the container’s total volume. As the gas is compressed, the actual volume of the molecules becomes a much larger percentage of the available space, invalidating the ideal assumption of negligible particle volume.
Another condition is low temperature, which reduces the kinetic energy of the gas molecules. When molecules move slower, attractive intermolecular forces have a greater opportunity to influence their path, causing them to linger near one another. This results in a lower measured pressure than the Ideal Gas Law would predict. Real gases only approximate ideal behavior when the pressure is low and the temperature is high.
Modeling Real Gas Behavior
To accurately model real gas behavior across a wider range of conditions, scientists use equations that adjust the Ideal Gas Law to account for the physical realities of real molecules. The most recognized is the Van der Waals equation, which was the first to introduce correction factors. This equation adds two specific terms to \(PV=nRT\) to correct for the finite volume of the particles and the intermolecular forces.
The Van der Waals equation includes a constant, designated ‘b’, which is subtracted from the volume (V) to account for the space occupied by the gas molecules. This ‘b’ value is characteristic of each specific gas and represents the excluded volume. A second constant, ‘a’, is added to the pressure term (P) to compensate for the attractive intermolecular forces that reduce the pressure exerted on the container walls. The constant ‘a’ is also specific to the type of gas, with larger values indicating stronger attractive forces.