Real Gas Formula - Confusion

[mcat411]

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I am confused on the real gas formula. I was provided:

[P+a(n^2)/(V^2)]*(V-nb)=nRT

From my understanding, at low temperatures and high pressures gas behaves less ideal:
- Pressure of a real gas should be LOWER than the pressure of an ideal gas (due to IM interactions).
- And volume occupied by a real gas should be HIGHER than the volume of an ideal gas (because the volume of the particles are no longer negligible).

Why, then, in the real gas formula (aka van der Waals equation) is it (P+a)(V-b)

Shouldn't it be (P-a)(V+b) at low temperatures and high pressures?
- I can understand V-b if you consider volume to be the "free space" in the container (i.e. the volume not occupied by the molecules themselves)
- But what I really don't understand is why is it P+a instead of P-a since IM forces should reduce the frequency/probability of the molecules colliding with the walls of the container (thus reducing pressure).

Many websites even show that experimental data indicate a higher "a" value for gasses that are more likely to be non-ideal (ex: higher "a" value for NH3 than H2). This makes no sense to me. Why should pressure be HIGHER in molecules more likely to deviate due to IM forces?

Also...can someone explain this graph to me? http://imgur.com/5Zgb9
-Why does PV/RT increase or deviate from the ideal gas line?
-What is this graph showing?

I'm pretty confused....I thought I understood real v. ideal gasses until my TPR professor confused the hell out of me.

If SDN could help me out on this, I'd REALLY appreciate it. I tried talking to my professor but he seemed just as confused as I was....

Thanks a lot everyone!

 

[ikjadoon]

Wikipedia the derivation of the Van der Waals...I think, through some funky algebra, "a" is subtracted, but you combine some terms and it comes up positive. Unsure...pressure should be reduced because of attractive IM forces...but, I don't think the MCAT will be asking you the exact derivation.

PV deviation: at a constant mole #, PV/RT should equal one number right? In that pic, they're using n = 1.

It's showing positive/negative deviation of PV/RT. If it's positive, it's because the volume is actually higher than what ideal gases would predict (because gas molecules have volume) and THAT plays a larger role than pressure deviation (which is negative). If it's negative deviation, it's because the pressure is lower than what ideal gases would predict (because of attractive IM forces) and THAT plays a larger role than volume deviation (which is positive).

 

[mcat411]

WOW. Thank you! That last part was so simple I dunno why I had such a tough time analyzing that....



I'm only worried about the Van der Waals equation in case it comes up in a dense PS passage. I'll look more into it when I get some spare time. Thanks!

 

[ikjadoon]

oh, lol, it's all good: that was basically straight from my EK chemistry book, so I can't claim super-awesome intuitiveness skills, 😀

Ah, right, right. If you can't figure it out after checking out Wikipedia or other websites, put up a thread at Physics Forums. They've helped me many a times in weird physics stuff like this...it's like a little haven for physics PhDs.