Chemical Forums
Chemistry Forums for Students => High School Chemistry Forum => Topic started by: Byrne on January 01, 2006, 03:41:27 PM
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How are they determined? I'm having no luck on the Internet.
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the constants are derived from the critical point of the fluid.
the critical point is the pressure and temperature of the fluid at which the liquid state cannot be differentiated from the gaseous state.
if you plot a P-T graph, you will find that the critical point corresponds to the point of inflexion:
dP/dT = 0 and d2P/dT2 = 0.
By differentiating the VDW equation to find the first-order and second-order differentials, and plugging in the critical point values, the constants a and b are derrived.
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I see... I'm currently taking an introductory calculus course in high school so I think I understand most of what you said... now its only a matter of simplifying it so I can present it to a chemisty class. I'm wondering where I could find some data to perhaps plot of the graph that will show the point of inflection.
I also read somewhere that van der Waals constants can be determined empirically?
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This is the empirical method.
You can only get the values for the critical pressure and temperature by measurement - an act of experiment.
If you are not sure how to differentiate VDW equation, consult your calculus teacher. There is no physics/chemistry in this differentiation thingy. It is just mathematics.
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Ah I see...
Now what do you mean by "at which the liquid state cannot be differentiated from the gaseous state."
Is this something you would observe in an experiment? I don't understand exactly how something like this could be observed.
Thanks for your help by the way.
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both liquid and gas are fluid.
the difference between both phases is that the intermolecular distances are much larger in the cases of gas molecules, compared to that for liquid molecules.
as the temperature and pressure varies, the intermolecular distances for both the gas and liquid phases changes such that the intermoleculer distances becomes the same. At this state, one cannot differentiate liquid from gas. A fluid of such state is said to be a critical fluid.
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Thanks a lot for the help. I really appreciate it.
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One more thing. What pressure unit is most commonly expressed with the 'a' constant. I find it odd how the SI unit for pressure is the pascal, yet most tables I have come across express the 'a' value in L2 . atm / mol2.
Am I just looking at older charts or do chemistry handbooks of today also commonly express this info using atm? Why is the atm used anyway? I am much more accustomed to using kPa when pressure is involved.
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Hmm.. I am not sure why the old tables use the unit atm. (perhaps atm was a more popular unit than Pa)
This is the conversion ratio: 1 atm = 1.013 kPa
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Hmm.. I am not sure why the old tables use the unit atm. (perhaps atm was a more popular unit than Pa)
This is the conversion ratio: 1 atm = 1.013 kPa
I believe it is 1 atm = 101.3 kPa = 1.013 bar (= 760 mmHg = 760 torr).
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I believe it is 1 atm = 101.3 kPa = 1.013 bar (= 760 mmHg = 760 torr).
1 atm = 760 mmHg = 760 torr = 101325 Pa = 101.325 kPa = 1.0133 bar = 1013.3 = 14.0007 psi
Check EBAS ideal gas calculator, all these values are there (and it converts them if you need).
atm is a pre-SI unit. In early seventies I was teached atm, in the second half of seventies I was teached kPa.
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1 atm = 760 mmHg = 760 torr = 101325 Pa = 101.325 kPa = 1.0133 bar = 1013.3 = 14.0007 psi
Check EBAS ideal gas calculator, all these values are there (and it converts them if you need).
atm is a pre-SI unit. In early seventies I was teached atm, in the second half of seventies I was teached kPa.
I understand all this, but my main question is why is it that most of the data I'm finding on the internet is expressed using atm pressure units as opposed to kPa pressure units with regards to van der Waals constants.
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Apparantly van der Waals constants can be estimated through the relations viewable at the following link, scroll about a quarter of the page down. Where did these relations come from?
http://www.ccl.net/cca/documents/dyoung/topics-orig/eq_state.html
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the constants are derived from the critical point of the fluid.
dP/dT = 0 and d2P/dT2 = 0.
This is how they derive it. They use the critical values to substitute for values of P, T, and V.
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This is how they derive it. They use the critical values to substitute for values of P, T, and V.
Then where are those relations coming from?
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the relations come from the VDW equation.
If you plot the experimental data, you will find that the critical point is also point of inflexion (mathematical term).
assuming that the VDW equation is valid, then dP/dT = d2P/dT2 = 0 at the critical point, since the critical point is the point of inflexion.