# Clarification of textbook concepts relating to "perfect", "ideal", and "real" gases

My textbook, Atkins' Physical Chemistry, 11th edition, by Atkins, de Paula, and Keeler, says the following:

The resulting expression

$$pV = nRT \tag{1A.4}$$

is the perfect gas law (or perfect gas equation of state). It is the approximate equation of state of any gas, and becomes increasingly exact as the pressure of the gas approaches zero. A gas that obeys eqn 1A.4 exactly under all conditions is called a perfect gas (or ideal gas). A real gas, an actual gas, behaves more like a perfect gas the lower the pressure, and is described exactly by eqn 1A.4 in the limit of $$p \to 0$$. The gas constant $$R$$ can be determined by evaluating $$R = pV/nT$$ for a gas in the limit of zero pressure (to guarantee that it is behaving perfectly).

A note on good practice Despite 'ideal gas' being the more common term, 'perfect gas' is preferable. As explained in Topic 5B, in an 'ideal mixture' of A and B, the AA, BB, and AB interactions are all the same but not necessarily zero. In a perfect gas, not only are the interactions all the same, they are also zero.

My questions here relate to this part:

A note on good practice Despite 'ideal gas' being the more common term, 'perfect gas' is preferable. As explained in Topic 5B, in an 'ideal mixture' of A and B, the AA, BB, and AB interactions are all the same but not necessarily zero. In a perfect gas, not only are the interactions all the same, they are also zero.

1. It seems that the authors here are implying that a "perfect gas" and an "ideal gas" are synonymous, but my research indicates that they are actually different concepts. Are these two concepts the same, or are they different? How should one think about (distinguish) these two concepts?

2. What do the authors mean when they say that "in an 'ideal mixture' of A and B, the AA, BB, and AB interactions are all the same but not necessarily zero"? And what is meant by the interactions being "zero" here?

3. What do the authors mean when they say that "in a perfect gas, not only are the interactions all the same, they are also zero"? And what is meant by the interactions being "zero" here?

I would greatly appreciate it if people would please take the time to clarify these points.

The authors attempt to explain that in many sources the term "ideal gas" is used in place of "perfect gas" to indicate a gas following the ideal gas law and which has the property that the molecules do not interact. They equate the absence of an intermolecular interaction with the statement that the "interactions are zero". In other words, there is no intermolecular potential between the idealized gas molecules in a "perfect gas". These idealized molecules lack a volume, so that even steric (excluded volume) interactions expected for hard spheres are absent. They are "point particles".

The authors further explain that it is preferable to use the word "perfect" rather than "ideal" because the word "ideal" is used in other contexts where the condition of no interaction is not observed, ie during ideal mixing. Ideal mixing occurs when different molecules have the same volume and intermolecular potential in the pure and in the mixed states.

Opinion-based aside

BTW I've always been partial to the term "ideal gas". IMHO the term "perfect" seems to imply that the molecules excel in some way, whereas "ideal" simply means that it is the product of human minds, an abstraction, and not necessarily a real thing.

IUPAC does not to have any qualms about continued use of the term "ideal gas", so I don't see reason to stop using this term.

• A search for the term "perfect gas" and "IUPAC" leads straight back to IUPACs definition of "ideal gas". Feb 19, 2020 at 14:09
• Thanks for the answer, Buck. I'm guessing you're referring to 1A.4 as the "ideal gas law"? The authors actually explicitly label this as the "perfect gas law". Feb 19, 2020 at 14:19
• Yes. If you search for the "perfect gas law" online you will obtain a lot of hits for "ideal gas law" (including for the wikipedia) and a few for "perfect gas law". Another opinion-based aside: Atkins et al are heavyweights in the pchem education world but are on what I would consider a quixotic quest in attempting to alter terminology preferences. There are plenty of confusing topics in pchem and I don't think this one merits so much special attention, although it is good to bring attention to the fact that "ideal" can mean different things in slightly different contexts. Feb 19, 2020 at 14:25
• Interesting. Thanks for the clarification. Feb 19, 2020 at 14:27
• I'm old, but in 2 semesters of intense Chemical Engineering thermodynamics (back in the 1970s), I never once heard of a perfect gas - only ideal gases. Ideal gas is part of the standard assumptions you make when solving most problems. You have to get pretty from standard conditions before pV = nRT breaks down. Feb 20, 2020 at 0:33