Gases consist of molecules in constant, rapid, and random motion. To understand how these substances behave, scientists use equations of state, the simplest being the Ideal Gas Law. This law describes a theoretical “ideal gas,” but real gases do not perfectly follow this simplified model. Developed in 1873 by Johannes Diderik van der Waals, the Van der Waals equation serves as a refined equation of state to bridge the gap between the theoretical ideal and the measurable reality of actual gases.
Why Real Gases Deviate from Ideal Behavior
The Ideal Gas Law is built on assumptions that simplify molecular interaction. It assumes gas molecules are tiny, point-like particles that occupy no significant volume and that there are no attractive forces between them. These assumptions hold true only for gases at very low pressures and high temperatures.
When pressure increases, molecules are forced closer, and their finite size consumes a noticeable fraction of the container volume. When temperature drops, molecules slow down, allowing attractive forces between them to become significant. These two phenomena—molecular volume and intermolecular attraction—cause real gases to deviate from the Ideal Gas Law. The Van der Waals equation corrects for these failures using two substance-specific constants: ‘\(b\)‘ for molecular volume and ‘\(a\)‘ for intermolecular forces.
What the ‘a’ Coefficient Represents
The Van der Waals coefficient ‘\(a\)‘ is the correction factor that accounts for the attractive forces, known as cohesive forces, acting between gas molecules. These forces—which include dispersion forces, dipole-dipole interactions, and hydrogen bonds—cause a real gas to exert less pressure than an ideal gas would under the same conditions. As a molecule moves toward the container wall, neighboring molecules pull it inward, reducing the force and frequency of its collision. This inward pull lowers the measured pressure of the gas.
To compensate for this “lost” internal pressure, the Van der Waals equation adds a correction term to the experimentally measured pressure, \(P\). This correction term is \(a(n/V)^2\), where \(n\) is the number of moles and \(V\) is the volume. The ‘\(a\)‘ constant is the proportionality factor, serving as a quantitative measure of the strength of the attractive forces for a specific gas. Because the attractive force is dependent on the concentration of molecules, the correction is proportional to the square of the concentration.
Using the ‘a’ Value to Characterize Gases
The numerical value of the ‘\(a\)‘ coefficient is characteristic of a specific gas and provides direct insight into its properties. A large ‘\(a\)‘ value signifies that the gas molecules have strong attractive forces acting between them. For instance, gases composed of polar molecules or large, complex molecules typically have higher ‘\(a\)‘ values than small, non-polar gases like helium or neon.
The magnitude of ‘\(a\)‘ is directly related to a gas’s tendency to condense into a liquid. Gases with a high ‘\(a\)‘ value are easier to liquefy because their molecules already possess significant natural attraction, requiring less external cooling or compression. Conversely, gases with a very low ‘\(a\)‘ value, such as helium, are difficult to liquefy because their intermolecular forces are weak, requiring extremely low temperatures. The ‘\(a\)‘ constant is therefore a fundamental parameter used in predicting the physical behavior of a gas.