Deviations from how ideal gases behave show us the limits of the Kinetic Molecular Theory (KMT).

KMT is a way to understand gases by making some basic guesses, like:

1. Gas molecules are always moving around randomly.
2. Molecules are tiny points with no size.
3. There are no forces pulling or pushing between them.

But when we look at real gases, especially when there is a lot of pressure or low temperature, these guesses don't always hold up:

• Size of gas particles: In real life, gas particles do take up space. When we increase pressure, the space between the particles becomes important, which isn’t what KMT assumes.

• Intermolecular forces: At low temperatures, these forces become stronger. This makes the particles attract each other, which KMT doesn’t consider. As a result, gases can turn into liquids, something KMT wouldn’t expect.

Also, the relationships shown in the ideal gas law ($PV = nRT$) don’t work as well in these conditions. For example, the Van der Waals equation helps us understand the effects of volume and attractions:

$[P + a(n/V)^2](V - nb) = nRT$

In this equation, $a$ and $b$ are specific numbers for each gas. They show us that real gases don't always fit into the simple predictions KMT gives us. By understanding these limits, we can better understand how real gases behave in different situations.