Why Ideal Gas Law Is Not That Ideal


By Don Lincoln, Ph.D., University of Notre Dame

Let’s analyze the different conditions required of an ideal gas, and how ideal gases don’t remain so ideal under the scrutiny of varying temperatures and pressures.

An image displaying the different state and volume of molecules in different states of matter.
Pressure and temperature play a defining role in the states of matter and its form; hence, under certain conditions, they can undermine the ideal gas law. (Image: KRPD/Shutterstock)

What is the ideal gas law? Well, it describes the relationship between pressure, volume, temperature, and the number of moles of molecules for an ideal gas. But what is an ideal gas?

Ideal Gas Is Needed for the Ideal Gas Law

An ideal gas is a collection of molecules that are just bouncing around inside some sort of container and for which the molecules don’t interact except for bouncing off one another in what is called an elastic collision. An elastic collision is just a fancy term for a collision in which the objects don’t lose any energy.

The ideal gas law is taught in high school chemistry. If you took chemistry, it’s likely that you even remember it, because it’s drilled into student’s heads and it’s a relatively simple equation. Even the equation is somehow catchy: PV=nRT just has a memorable ring to it.

What it means is pretty straightforward. Double something on the left-hand side of the equation, and you have to double something on the right-hand side. Or you could change two things on the right-hand side, but they’d have to combine to effectively double.

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The ideal gas law does work pretty well, but it’s not perfect. It assumes non-interacting molecules. If the molecules interact, the whole thing falls apart. The ideal gas law, while easy to understand, remember, and use, has an obvious limitation. It describes an ideal gas. Gases aren’t ideal. Now, this isn’t to say that the gases are terribly different from the ideal.

The ideal gas law works quite well, but it has limitations. Remember that an ideal gas is one in which the molecules interact only elastically.

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Conditions of an Ideal Gas

The crucial conditions of an ideal gas are the following. First, the gas has to be at relatively low pressure. This is because the molecules are pretty far apart and run into one another only occasionally. Because the molecules interact only occasionally, their interactions can be generally ignored. Being able to ignore those interactions is part of what goes into making a gas ideal. You can’t ignore those interactions at high pressure or density.

Another condition in which gases aren’t ideal is at low temperature. In an ideal gas, there are no interactions between molecules except bouncing off from one another. But, obviously, molecules do interact in other ways. For example, it’s possible for gas molecules to come together and interact. The steam cools down and becomes water.

The water molecules in steam are the same molecules as in liquid water and we know for a fact that water molecules interact with one another in a pool or a bathtub. So, that means that similar interactions must be occurring in steam. It’s just that those interactions must be very weak when water is heated in the form of steam.

In steam or, indeed, in any gas, the molecules are zooming around at high speed. So even if a molecule experiences a weak interaction, it doesn’t change things very much. But if you slow down the molecules, when they pass by one another, their interactions start to come into play.

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Limitations of Ideal Gas Law: Low Temperature

The interaction between water molecules becomes important when the temperature gets lowered. In fact, it’s worth taking just a moment to delve into how that interaction works.

An illustration showing the dipole nature of water or H2O molecules.
Dipole or polar nature of water molecules under lower temperature leads to condensation and departure from the ideal gas law. (Image: Magnetix/Shutterstock)

So, everyone knows the molecular formula for water, H2O, which means that there are two hydrogen atoms and one oxygen atom. And you may know that when a water molecule forms, it’s electrically neutral, which means it has equal amounts of positive and negative electrical charge.

Normally, electrically neutral objects don’t interact with one another. Yet water molecules do. This is because of the shape of the molecule. In water, the two hydrogen atoms are on one side of the molecule and the oxygen is off on the other side.

This shape and how the atoms join together has an interesting consequence. Hydrogen atoms are just one proton and one electron, which is to say one positive and one negative electric charge. When the hydrogen atom attaches to the oxygen, it does so by sharing electrons. This brings the electron, which is to say the negative charge, closer to oxygen. That means the proton is, on average, further away from the water molecule than the electrons are.

And since the proton is a positive electrical charge, that means that the hydrogen side of the water molecule is a little more positive. For water molecules to be electrically neutral, that means that the oxygen side is a little more negative.

So, a water molecule is electrically neutral, but the charge is separated just a little bit. Scientists have a name for this configuration, we call it a dipole, which is just when two objects that should cancel one another are separated by a small distance.

We know that positive and negative charges cancel one another out, but we also know that distance from a charge matters. If a molecule has separated charges, when you get close to one side, you’ll be closer to the positive or negative charge and that one will have a greater influence than the other.

And when two atoms are separated by a larger distance, the difference in distances between you and the separated charges is very small, so the influence from the two charges is more nearly equal. The effect I am describing is very small and only matters if two objects get close to one another and aren’t moving very fast.

Now this mechanism, this polar molecule thing, isn’t true for all molecules, so don’t think it’s universal. It’s not. But for other molecules, they have their own set of unique peculiarities.

Remember a gas is where the molecules are well separated and moving quickly. But these peculiar effects start to matter when you decrease the distance between the molecules or slow them down.

Limitations of Ideal Gas Law: Increasing Pressure

An image displaying the volume of the molecules decreasing with increasing pressure.
The impact of increasing pressure on the molecules challenges the Ideal Gas Law. (Image: Fouad A. Saad/Shutterstock)

One of the assumptions of an ideal gas is that the size of individual molecules is much smaller than the distance between molecules. The idea is that tiny and negligibly small molecules are zipping around in a ginormous space. In that environment, if you decrease the volume a bit, the molecules can still zoom around without too much of a problem.

The same thing can happen for molecules. Molecules really do have a size. For instance, water molecules are about a tenth of a nanometer in size, a tenth of a billionth of a meter. In contrast, at 100° centigrade and at standard atmospheric pressure, when steam is just forming, the distance between adjacent water molecules is about 30 times greater than that, ballpark three nanometers.

If you decrease the volume and thereby increase the pressure, individual water molecules are still pretty far apart and there’s no problem. However, when you compress a gas enough, the size of the molecules, which we completely ignore in the case of an ideal gas, starts to matter. At some point, it actually becomes harder and harder to compress the gas. The ideal gas law then starts to break down.

Common Questions about Ideal Gas Law

Q: Why is the ideal gas law inaccurate?

The ideal gas law is inaccurate because the ideal gas law accounts for no or negligible molecular interaction, while the real gases do have molecular interaction under certain conditions.

Q: What is not an ideal gas?

Every substance, even ideal gas, does condense when it is cooled and compressed enough, so attractive forces do exist between molecules under certain conditions in nearly all elements.

Q: Why does the ideal gas law fail at low temperatures?

The ideal gas law fails at low temperature and high-pressure because the volume occupied by the gas is quite small, so the inter-molecular distance between the molecules decreases. And hence, an attractive force can be observed between them.

Q: Can an ideal gas condense?

Yes, in most cases, under high pressure and low temperature the real gases do condense.

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