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Real-world gases exhibit behavior that significantly deviates from what we would expect based on the Ideal Gas Law, particularly under conditions of high pressure. When the pressure on a gas increases, molecules are forced closer together. This enhances the significance of the actual volume of the gas molecules compared to the space they are in.

Typically, the Ideal Gas Law doesn't consider the volume that gas molecules occupy, as it assumes them to be infinitesimally small. However, under high pressures, the 'excluded volume' – the space that gas particles themselves take up – can no longer be ignored. This results in the gas occupying more volume than predicted by the Ideal Gas Law, leading to a discrepancy that grows larger as the pressure increases.

Furthermore, increased pressure also causes enhanced interactions between the gas molecules, another factor ignored by the ideal model, which can lead to further deviations from ideal behavior, such as gas molecules sticking together instead of bouncing off perfectly elastic as the ideal model assumes.

At lower temperatures, gases also deviate from ideal behavior, but for reasons different than those at high pressures. As the temperature of a gas drops, the kinetic energy of the gas molecules decreases. This slowing down allows intermolecular forces—like Van der Waals forces—to become more prominent.

These forces can attract molecules to one another, significantly altering the gas's properties from what the Ideal Gas Law would predict. For instance, as the temperature decreases, gases may condense or liquefy, a phase change that the Ideal Gas Law does not account for. This is because the Ideal Gas Law assumes that there are no attractions or repulsions between molecules, which is not the case at low temperatures where these forces can be quite significant in dictating the behavior of gas molecules.

Understanding the intermolecular forces in gases is critical to grasping why real gases deviate from ideal behavior. Intermolecular forces are the forces of attraction or repulsion between molecules. In an ideal gas, these forces are assumed to be nonexistent; however, in reality, gases do experience weak, yet significant, interactions.

These include dispersion forces, which are present in all molecules and arise due to momentary asymmetries in electron distribution, and dipole-dipole interactions, which occur between polar molecules. There are also hydrogen bonds, which are particularly strong dipole-dipole interactions occurring in molecules containing hydrogen attached to a highly electronegative atom. When these forces come into play, the assumptions of the ideal gas model break down, which can affect everything from the gas’s pressure to its volume and temperature relationships.

The distinctions between real gases and ideal gases underscore much of what students need to grasp when studying gas behavior. An ideal gas is a theoretical construct that follows the Ideal Gas Law (PV=nRT) under all conditions. It assumes gas particles do not occupy space and do not interact with one another.

In reality, no gas perfectly fits this model, which is why real gases – the gases we observe and interact with – can behave in ways that deviate from the predictions of the Ideal Gas Law. These deviations are most pronounced at high pressures, where the volume of particles is non-negligible, and at very low temperatures, where intermolecular forces become influential. It's these deviations that lead to phenomena like the liquefaction of gases or the increased density and decreased compressibility of a gas under compression, which cannot be explained by the simple ideal model.

To account for this, scientists use the van der Waals equation and other real gas laws to describe gas behavior more accurately in these non-ideal conditions. These modifications include terms for particle volume and intermolecular force strength, providing a more comprehensive understanding of how gases behave in the real world.