When is 500 psi not 500 psi?

[rsterne]

I revisited this phenomenon yesterday, and made up a graph which shows the overall VanDerWaals effect, and also the effect for each 500 psi increment.... This chart is for air, other gasses show different results....



I used this calculator to determine the air density at each pressure....  http://www.peacesoftware.de/einigewerte/luft_e.html

and then plotted how that compared to that predicted by Boyle's Law for ideal gasses in the red line above.... I then looked at the drop in density for each 500 psi increment, and compared that to the drop in density predicted by Boyle, which should be a constant (100%).... Those results are plotted in the blue line.... The percent value plotted for each pressure is the value for a 500 psi drop from that pressure.... ie for a drop from 4500 psi to 4000 psi, the drop in mass is only 69% that predicted by Boyle.... As you can see, Boyle's Law works for air within a small percentage up to about 2500 psi, but above that the VanDerWaals effect becomes significant....

For those of you who want to do more reading on VanDerWaals, and see the equations it is based on.... Travis supplied this link....

http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/deviation5.html

That site has the values of the two VanDerWaals constants for a number of gasses, and an explanation of the reasoning behind their use....

Bob

[anti-squirrel]

Thank you for putting in the legwork on this.  If nothing else, it's a good mental exercise.

My only beef is the second link goes into some great math regarding molar mass, but the title itself has a typo 

If one thinks about the Van der Waals force, as molecular weight increases, the VdW force increases.  For some real head-smushing information read this

[Kid Shelleen]

Bob, this whole discussion is very interesting and reminded me of a joke.

Albert Einstein gets invited to a cocktail party and is mingling around the crowd.  He meets a  physicist and he starts discussing the wave function which provides information about the probability amplitude of position, momentum, and other physical properties of a particle.

He next begins a conversation with a college English literature professor and they talk about the differences and similarities between T.S. Eliot and James Joyce.

Einstein then meets another man and asks what his profession is.  The man says he is a police officer.  Einstein replies.  “Hey, how bout them Mets”. 

After reading this thread, I feel like the police officer.  Lol.

[rsterne]

Yeah, Peter, that typo in the title is amusing.... *LOL*....

There are actually two, opposing forces, that VanDerWaals deals with.... His "a" constant is the attractive force between molecules (high in the case of CO2), and causes a reduction in pressure as you compress the gas compared to Boyle's prediction.... Low boiling point gasses have a smaller value of "a", and that relationship is almost linear vs. absolute temperature.... His "b" constant is dependant on the volume of the molecules themselves, and smaller molecules (atoms) like Helium have a smaller value of "b".... The "b" constant causes an increase in pressure as the volume trends towards the residual volume of the molecules themselves.... It puts a lower limit on the volume that a given molar volume can be compressed to.... The first diagram in the 2nd link above does a good job explaining that effect, which is the major one we deal with in air at high pressures.... It is the effect of the "a" (attractive) constant that causes the little bump above 100% between 500-2000 psi on the graph I posted....

Different gasses act totally different.... Here is a drawing I borrowed from the 2nd link to show that....



Helium is similar to Hydrogen, and air is similar to Nitrogen, on that drawing.... Note that at anything below ~500 bar, CO2 gas develops less pressure than you would expect, because of the strong attractive force between its molecules....

Bob