which conditions of P, T, and n, respectively, are most ideal?

Question

A) high P, high T, high n
B) low P, low T, low n
C) high P, low T, high n
D) low P, high T, high n
E) low P, high T, low n

Answer 1

To know what are the most 'ideal' conditions of a gas, you have to know what the ideal gas law leaves out. This is basically two things: the ideal gas law assumes that gas atoms have no volume themselves, and it also assumes that the atoms are never attracted to each other and just bounce around like ping pong balls. These are both false assumptions, but since the overall difference is small it's easier most of the time to use the simpler equations. So let's look at each factor separately:

Pressure is going to cram your atoms closer together. If you had an infinite pressure, your ideal gas would take up no space. BUT since the atoms do actually have volume, this is impossible! Thus a gas is more ideal the lower the pressure is.

Temperature is how fast the atoms are moving. If they are moving at zero speed, then even the small inter-atomic forces will have lots of time to come into play. On the other hand, if the atoms are zinging around at ridiculous speed then they can't stick together even if they want to (attraction will have to overcome that speed!). Thus a gas is more ideal the higher the temperature is.

If you had an idea gas, you could fit an infinite n into a finite container (see pressure, above). But we know we can't, because those atoms do actually have volume. Thus the lower the n, the more ideal it is.

Taken together, that means if you want to maximize ideal behaviour, you need minimum pressure, maximum temperature, and minimum n. This is answer E.

Answer 2

I agree with "Fermi of Borg's" reasoning, but I think it's a little tricky to decide whether n should be high or low. He decides it should be low. I disagree, based on the following reasoning:

The rationale that Fermi of Borg uses to decide on a low n is the same reasoning that he has already used to decide that the pressure should be low.

But if we've already made the pressure low, then a high n doesn't cause the problem that Fermi mentions (i.e., lots of molecules packed into the available space). Instead, a high value of n simply means that we have a proportionately larger volume. (Note that volume isn't mentioned in the problem, but you have to keep it in mind.)

A large volume means that the SIDES of the container have less effect on the gas (i.e., the molecules contact the sides less frequently). And this permits the gas to better approximate an ideal gas.

Conclusion: low P, high T, high n, which is answer D)

Comment: Often, the correct answer will consist of the values that are mentioned most frequently in the five available answers. In this case, low P occurs 3 times out of 5, and so do high T and high n, which suggests that the answer is low P, high T, and high n. This is very unscientific (or maybe it's just very "empirical," or very "inductive"), but it sometimes helps you find the right answer.

Answer 3

P of 1 atm is considered standard.
Lower T is easier to deal with (less molecular motion), and I don't think n makes a difference at all, really. Let's go B then.

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Answer 4

E...less interaction between the molecules in that configuration