Why is the ideal gas law called ideal?

Answer 1

The ideal gas law is called ideal because it is a mathematical idealization and not meant to be exactly descriptive and any real gas.

It is famous because it does an excellent job of describing real gasses and it is something to which you can use with a real gas.

The ideal gas law is used very often because it works the same for all gasses once the temperature is high enough and the gas dilute enough. One does not need to know what kind of gas one is describing in those circumstances and so it saves having to keep track of different gas laws and properties for many different types of atoms and molecules. The trick is to know that for any particular gas, you are at a high enough temperature and low enough pressure. It turns out that normal temperatures and pressures that humans live with is already good enough for many common gasses, like those that make up air and methane and butane that we burn for fuel and many others.

If you want to know the ideal gas equation, one common way of stating it is as follows.

PV=nRT.

P is pressure. V is volume, T is (absolute) temperature, n is the number of gas particles (measured as moles in chemistry) and R is the universal gas constant. It is called universal because it is the same constant for all gasses.

Those are the basic facts. Now, here is a bit more about it.

The ideal gas law works well when a gas has a very low density and a high enough temperature that the forces between gas particles are insignificant. The trick is that you need to know the temperatures and the densities (or pressures) where it starts working. The accuracy of the comparison between the ideal gas law and the behavior of a real gas depend on staying at the higher temperatures and lower densities.

For all neutral atoms and molecules that form gasses, there is an weak attractive force when they are far apart and a strong repulsive force when they get very close. In between, complicated things happen which are different for different types of atoms and molecules. In any case, that is why the gas density has to be low, so these interactions between gas particles are very rare.

What is really amazing is that if you can get a material to form a gas, then it pretty much follows the ideal gas law for all the temperatures and pressures and volumes that it takes as long as you stay away from the temperatures and pressures where it will convert back to its original condensed form which is usually a liquid. Even water follows the gas law when it is in the form of water vapor or steam and water turns out to be one of the types of materials that are a little uncooperative.

As an aside, it is worth mentioning that many materials will not form a gas because if they are heated to the point of vaporizing, they will undergo chemical change. Large molecules in particular tend to break apart before they can be heated enough that the temperature can supply enough energy to separate the molecules from each other. After the chemical change occurs, then the new chemical will often easily form a gas.

Answer 2

No-one knows why, science is there to observe, measure and predict, and the gas laws apply to a ideal gas and are a good approximation for the behaviour of real gases. Why that is, is a theological question :)

Answer 3

Because it's the mathematical relationship between those properties in an ideal gas.

It's not the mathematical relationship between those properties in actual real gasses, because actual real gasses have intermolecular forces that the ideal gas law doesn't take into account and liquify or solidify when the temperature gets low enough. The relationship for real gasses is described by a more complicated (and usually at least semi-empirical) expression such as van der Waal's equation.