issue with real/ideal gases

[johndoe3344]

---

Members don't see this ad.

This has been discussed many times in old threads. In general,

Vreal > Videal (because of molecular volume)
Preal < Pideal (because of intermolecular attractions)

But conditions for deviation is generally high P/low T, so I have a few questions, in bold:

1) Under high P/low V or low T, is it ALWAYS true that Vreal>Videal AND Preal<Pideal?

And a follow up question,

2) Under low P/high V or high T, is it ALWAYS true that Vreal<Videal AND Preal>Pideal?

Also, I have a semi-unrelated question. The van der Waals Equation is given by (P+f(a))(V-g(b)) = nRT

Where I denoted f(a) as a function of a, and g(b) as a function of b. From what I understand, a is a measure of intermolecular attractions, and b is a measure of molecular volume.

3) In the VDW equation for a real gas, is it P PLUS f(a) and V MINUS g(b)? Shouldn't it be P MINUS f(a) and V PLUS g(b)?

My reasoning is that if you increase a, meaning you increase the intermolecular attractions, shouldn't that result in a DECREASE in pressure of the real gas, thus P-f(a)? And vice versa for V+g(b)?

 

[Dr Gerrard]

I always thought that in your second condition, gases tend to behave ideally and thus there is no deviation.

EDITED --- Because deviations occur due to intermolecular forces, and when there is low pressure and high volume, the intermolecular forces are ignorable.

Thus, if there is any deviation at all, it will be that Vreal > Videal and Preal < Pideal.

I think this is correct, but I am not by any means 100% confident.

Finally, in the VVW equation, my only guess is that the entire P term and the entire V term are meant to represent the ideal values. Thus, if you replaced the P with Preal and V with Vreal, it might make more sense.

(Preal+f(a))(Vreal-g(b)) = nRT

This is a modification of the ideal gas law, and thus you want to change the real pressure and volume to fit the ideal gas law, so you add and subtract, respectively, in order to take the real qualities into consideration.

 

[johndoe3344]

(Preal+f(a))(Vreal-g(b)) = nRT <-- This makes sense to me. I hope it's right 🙂


Regarding your statement about:
Thus, if there is any deviation at all, it will be that Vreal > Videal and Preal < Pideal.

Then it would seem as if, under any and all cases whatsoever, the volume of a real gas will ALWAYS be greater than the volume of an ideal gas, and same with pressure of a real gas being less than the pressure of an ideal gas.

But look at a graph of PV/RT vs P in any of the prep books. You see the dip below 1 and then a rise again. One of the questions I came across was:

According to the graph, which of the following would be true, if the ideal gas law were used to calculate the volume of a sample of gas from measured variables at (the condition where the line dips below 1) and again at (the condition where the line rises above 1)?

A. The calculated volume would be less than the real volume for both calculations.
B. The calculated volume would be greater than the real volume for both calculations.
C. The calculated volume would be less than the real volume for the first case, and greater than the real volume for the second case.
D. The calculated volume would be greater than the real volume for the first case, and less than the real volume for the second case.

I put B, saying that no matter what, the ideal volume > real volume, but the correct answer was D.

How do you explain that?

 

[Dr Gerrard]

http://www.chem.ufl.edu/~itl/2045/lectures/lec_e.html

I am lost, but let me give it a shot again.

Even when it dips below 1, the pressure is still relatively high (around 100 atm), so I think it is safe to say that at low pressure, deviation is always less significant.

Also, as temperature increases, the deviation from ideal behavior decreases, and this must be due to the fact that at higher temperatures, there is less intermolecular forces.

I still do not know why the dip occurs, thus I can't really answer your question. Sorry for rambling on..