[big]

An unknown gas is placed in a sealed container with a fixed volume. Which of the characteristics listed change(s) when the container is heated from 25°C to 250°C?

I. The density of the gas
II. The average kinetic energy of the molecules
III. The mean free path between molecular collisions

A) I only
B) II only
C) III only
D) I and II only

I can see that I definitely does not change and that II obviously does, so that would eliminate all answer choices except B. But doesn't mean free path change with a change in temperature too? I did a google search and found this: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/menfre.html, where temperature IS a factor in the refined version of the mean free path equation. So how come in this case, there isn't an option for II and III?

[fledarmus]

With constant volume and a constant number of moles (sealed container), T/P is a constant - an increase in T gives a corresponding increase in P. Since the change in T is offset by a change in P, the mean free path does not change with changes in T.

[juanrga]

An unknown gas is placed in a sealed container with a fixed volume. Which of the characteristics listed change(s) when the container is heated from 25°C to 250°C?

I. The density of the gas
II. The average kinetic energy of the molecules
III. The mean free path between molecular collisions

A) I only
B) II only
C) III only
D) I and II only

I can see that I definitely does not change and that II obviously does, so that would eliminate all answer choices except B. But doesn't mean free path change with a change in temperature too? I did a google search and found this: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/menfre.html, where temperature IS a factor in the refined version of the mean free path equation. So how come in this case, there isn't an option for II and III?

That "refined version of the mean free path equation" depends on molecular size d and number of molecules per unit volume n_V. Both are constants in your example.