A gas is a state of matter characterized by particles that are widely separated, moving rapidly, and filling the entire volume of their container. A simplified theoretical construct known as the “ideal gas” is used to model this behavior for ease of calculation. Real gases, which are the ones we encounter in the physical world, deviate from this theoretical behavior, particularly when subjected to extreme conditions. Understanding the difference between the theoretical ideal gas and the physical real gas is fundamental to accurately predicting how gases behave in industrial and natural settings.
The Ideal Gas Model: Core Assumptions
The concept of an ideal gas is built upon the Kinetic Molecular Theory, which makes several specific assumptions about the nature of the gas particles. The primary assumption is that the gas particles occupy a negligible volume compared to the total volume of the container. They are treated as point masses, meaning their size is essentially zero.
The second assumption is that there are no attractive or repulsive forces acting between the gas particles or the container walls. Collisions between particles and with the container walls are assumed to be perfectly elastic, ensuring that no total kinetic energy is lost during these interactions. These assumptions describe a gas that perfectly obeys the simple relationship known as the Ideal Gas Law (\(PV=nRT\)). This simplified framework allows for straightforward calculations but only holds true under a limited set of physical conditions.
Real Gas Characteristics: Violations of the Ideal Model
Real gases fundamentally violate the two main assumptions of the ideal model. The first violation is that real gas molecules possess a measurable, finite volume. When a gas is compressed, the space occupied by the molecules themselves becomes a significant portion of the total container volume, meaning the available free space for movement is reduced.
The second major deviation involves intermolecular forces, which are not negligible in real gases. Gas molecules experience weak attractive forces, such as London dispersion forces. This attraction pulls the molecules closer together as they approach the container walls, reducing the force and frequency of their collisions. Because of these forces, the pressure exerted by a real gas is often lower than what the Ideal Gas Law predicts, as the molecules are slightly held back from the walls.
When Reality Diverges: The Impact of Pressure and Temperature
Deviations of a real gas from ideal behavior become most apparent under specific conditions of pressure and temperature. When pressure is high, gas molecules are forced into close proximity. This crowding causes the finite volume of the particles to become significant, reducing the total free volume available for movement.
At high pressures, the volume occupied by the particles makes the actual volume of the gas larger than what the ideal law predicts, increasing the pressure beyond the theoretical ideal value. Conversely, when the temperature is very low, the average kinetic energy of the particles decreases significantly. This reduction in speed allows the weak intermolecular attractive forces to become influential. These attractive forces reduce the number and intensity of collisions with the container walls, leading to a pressure that is lower than the ideal prediction. Therefore, a real gas most closely approximates an ideal gas only under the conditions of low pressure and high temperature.
Adjusting the Model: The Van der Waals Equation
Since the simple Ideal Gas Law (\(PV=nRT\)) is insufficient for accurately describing real gas behavior under non-ideal conditions, scientists employ modified equations of state. The most widely recognized of these is the Van der Waals equation, developed to mathematically account for the two primary ways a real gas differs from an ideal one. This equation incorporates correction factors into the pressure and volume terms of the ideal gas law.
The volume correction factor, denoted by the constant ‘\(b\)‘, is subtracted from the total container volume (\(V\)) and accounts for the physical space occupied by the gas molecules themselves. This term effectively reduces the available free volume for the particles to move within. The pressure correction factor, which uses the constant ‘\(a\)‘, is added to the measured pressure (\(P\)) to compensate for the pressure lost due to intermolecular attractive forces.
The constant ‘\(a\)‘ is specific to each gas and quantifies the strength of the attractive forces between its molecules, while ‘\(b\)‘ accounts for the size of the molecules. By including these empirically determined constants, the Van der Waals equation allows for a much more accurate prediction of a real gas’s behavior, especially under the high-pressure and low-temperature conditions where the ideal model fails.