# Assumptions and limitations for ideal gas

Assumption: In the assumption for ideal gas law, it is stated:"The time it takes to collide is negligible compared with the time between collisions." For, this assumption, can i just say there is only one collision "per time"?

Limitation: I collected following comparisons between ideal gas and real gas：1 Molecules do occupy volume, which means real gas particle will have relatively smaller space for random motion compare to ideal gas if the total volume of the "container" is the same, this fact causes the deviation between ideal gas pressure and real gas pressure. Where real gas has higher pressure than ideal gas. But it is noticeable that there is also a increase in deviation as volume become lower, what is the reason for this? Can it be explained as following?----" the molecules of gas are so compressed that their volume becomes a significant fraction of the total volume of the gas. Since the volume of the molecules stay constant, as the total volume of gas decrease further, the volume of molecules will become a even higher fraction of the total volume, as this increase in fraction continues on. It will some how results in a " near " exponential increase of the pressure of the real gas, hence a increase in deviation.

At the mean time, in extremely small volume, will "space for random motion of the particles" be the main reason causing such deviation in pressure? Do we also have to consider the repulsive part of molecular interaction(intermolecular force) and as illustrated by something such as "Lennard-Jones potential"? And won't this also enlarge the deviation between real gas pressure and ideal gas pressure?

2 Forces of attraction do exist between molecules, it is stated in my textbook: "This factor significantly increases deviations from ideal behavior at low temperatures, at low temperature the molecules have less kinetic energy and thus more slowly. The intermolecular forces have more effect because of the slower speed of the molecules" Can i interpret this statement in the following way?----- As the temperature decreases, the speed of the molecules decrease(average speed). Hence in a particular instance, the relatively separation between particles is somehow smaller? And this will result in a increase in intermolecular force( attraction part) and then a decrease in pressure exerted by the real gas to exterior surface( then of course real gas will have lower pressure compare to the ideal gas). Now, if we only consider the case for the real gas, and if my interpretation is right, then why is the increase in the intermolecular force only subjected to the decrease in temperature? Why can't it also be related to the decrease in volume as in 1? As the volume of the real gas decrease, the separation between molecules decrease, hence within a certain range of compression (the volume is not too low= repulsive part of intermolecular force is not considered), the intermolecular force will become more attractive and causes a decrease in pressure of the real gas? But we also stated in limitation 1 that this decrease in volume will also cause increase in percentage occupied by molecules in the total volume of gas, and therefore there will be less space for random motion hence a increase in pressure of real gas? And won't the "decease" and "increase" make a contradiction? And how does it achieve a "net decrease in pressure in the P, T graph as below?

And further more, how can i explain the increase in deviation between two pressure as temperature decrease in $$P$$-$$T$$ graph? How should i explain the exponential line at the end of $$P$$-$$T$$ graph? Sorry for my lack of knowledge at my current level, i am really confused by these and can some one please help me?

• Your "question" is really a lot of questions. I believe you would be able to get more people to help you if you just ask one particular shorter question per post. – Daniel Duque Mar 18 '19 at 13:58
• Yeah that’s true.. just come across these stuff and I think it’s just better to put it as a whole. I mean there are lots of relations in there which might be more confusing if I just break it apart....... – Wang Rui Mar 18 '19 at 14:03