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### Ideal gas Law video: the required conditions to be ideal?

Posted: Thu Jan 09, 2020 5:59 pm
Based on the ideal gas law (when you hold everything else constant -V), the pressure and Temperature are proportional (increased T increases the P due to more molecules colliding with the container's wall). But why would the required state to have an ideal gas law be LOW pressure and high Temperature? since you want it to be ideal and the ideal gas law states high P, high Temprature. Shouldn't you want the pressure to be high? How could you ever have a low pressure under a high Temperature?

### Re: Ideal gas Law video: the required conditions to be ideal?

Posted: Fri Jan 10, 2020 4:29 pm
So to figure this out, you don't want to worry about the prediction the ideal gas law makes (PV=nRT) but you want to concern yourself with WHY it makes this prediction.

So lets take a first glance at the original conditions for the ideal gas law:
Émile Clapeyron and friends wrote: 1. The gas particles have negligible volume.
2. The gas particles are equally sized and do not have intermolecular forces (attraction or repulsion) with other gas particles.
3. The gas particles move randomly in agreement with Newton’s Laws of Motion.
4. The gas particles have perfect elastic collisions with no energy loss.
Essentially these are saying that they have to be working like point-masses, infinitely small little balls, bouncing around and only colliding the way billiard balls would - not really attracting or repelling each other any other way.

And that turns out to be kinda true if a) the gas particles don't take up a lot of space relative to the total space available (low pressure) and b) are moving fast enough that what intermolecular interactions there are essentially don't matter or don't make a difference (high temperature).

The important idea is that the ideal gas law is a prediction based on a particular kind of model - a model that assumes that your gas particles are point-masses that don't take up any significant space (only the gas as a whole occupying a volume) and don't attract or repel each other. If those conditions aren't met, then the ideal gas law isn't going to be a very accurate tool to make predictions with. In those cases you would be better served using the Van der Waals equation of state, which you only need cursory familiarity with for the MCAT (it is reasonable to assume you won't be asked to have it memorized).

### Re: Ideal gas Law video: the required conditions to be ideal?

Posted: Wed Jan 15, 2020 12:41 pm
so there're 'kind of' 2 views that define high pressure, which is extremely confusing to me. One is that high pressure results from high rate of collision of molecules with the container's wall; the other is gas molecules clumping together (close space and a lot of molecules increase pressure). For the ideal gas law to work, Temperature should be high to minimize intermolecular interactions. But my understanding is high T would make more molecules collide with the walls, and thus pressure increases. This is the exact point of my confusion.
Also, which definition of pressure to go with?

### Re: Ideal gas Law video: the required conditions to be ideal?

Posted: Thu Jan 16, 2020 8:33 pm

### Re: Ideal gas Law video: the required conditions to be ideal?

Posted: Thu Jan 16, 2020 10:40 pm
I will get to all of them, although communicating the exact categorical and conceptual errors you're making here is fairly tricky.

Let's see if this clicks:
1. The ideal gas law is a set of predictions that only hold if certain conditions are met, that is pressure is fairly low and temperature is fairly high. This has nothing at all to do with the mathematical expression of the law.
2. And the mathematical expression itself just describes a relationship between four variables, which in no way at all means that if one of those increases a particular one must change. Any of them could change. This is why for systems on the MCAT where the ideal gas law is applicable, several of them will be held constant and you will be asked to predict the remaining one.

If that is not enough to work with (which I can understand, it can be a large leap to push oneself to completely re-conceptualize an idea), I will happily give this another shot.

### Re: Ideal gas Law video: the required conditions to be ideal?

Posted: Wed Jan 22, 2020 11:08 pm
Ohhh so you are trying to explain to me that the conditions for the ideal gas law to work-low pressure and high temperature has NOTHING to do with the proportional relationship between pressure and temperature (assuming everything else is constant). Is this correct?

For ideal gas law to work, the temperature has to be so high that the interaction between molecules is negligible. SEPARATELY, we want pressure to be low because the ideal gas don't take up a lot of space and thus wouldn't collide with a container's walls. THese are the 2 separate conditions for the ideal gas law to work and it DOESN'T mean that high temperature leads to high pressure because for the temperature to be high, we hold everything else constant and for the pressure to be low, we hold everything else constant.

Do you think I have got it yet? sorry it took me a while to respond back to your reply

### Re: Ideal gas Law video: the required conditions to be ideal?

Posted: Thu Jan 23, 2020 12:59 am
Bingo! That is absolutely right.
THese are the 2 separate conditions for the ideal gas law to work and it DOESN'T mean that high temperature leads to high pressure because for the temperature to be high, we hold everything else constant and for the pressure to be low, we hold everything else constant.
I am not sure by what you mean with 'hold everything else constant', but since you have grasped the general concept that the statements of the gas law are unrelated to the conditions under which it applies, I feel confident that there isn't a big misunderstanding here. My hangup here is just understanding that the initial state of the system follows no rules at all. There is however much gas in it (n) taking up however much volume (V) at whichever pressure (P) and temperature (T) as we say it is. Those 4 can be chosen almost entirely freely when deciding on an initial state of a system (after you pick 3, the fourth will be determined however). The ideal gas law only describes how those would relate to each other if we change that system (again: provided this is actually a system that fulfills the conditions for the ideal gas law to apply!).