Ask an Expert: Ideal gas constant versus osmotic constant
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Ideal gas constant versus osmotic constant
Hello
This may sound very elementary but why is the ideal gas constant R=8,31... found in PV=nRT the same constant in the osmotic pressure formula pi = nRT . Since the osmotic pressure is within liquids and not gases.
It would really clear things up for me
Thanks
This may sound very elementary but why is the ideal gas constant R=8,31... found in PV=nRT the same constant in the osmotic pressure formula pi = nRT . Since the osmotic pressure is within liquids and not gases.
It would really clear things up for me
Thanks

 Former Expert
 Posts: 932
 Joined: Wed Oct 03, 2007 12:24 am
Re: Ideal gas constant versus osmotic constant
Hi
You ask a profound but obscure question. The mystery is even more profound than you state  the same constant keeps reappearing in a whole bunch of places, equations describing thinks like the voltages of batteries(http://www.science.uwaterloo.ca/~cchieh ... nsteq.html) , the “colligative” properties of liquids(http://hyperphysics.phyastr.gsu.edu/hb ... ollig.html), reaction rates, and statistical mechanics and boltzman statistics.
The best answer I can give is that the reason lies in the theories of thermodynamics, specifically in the concept of Gibbs Free Energy( see link below). I apologize in advance if this answer seems to raise more questions than it answers. I think the answer my quantum mechanics professor gave to one his students forty years ago applies: “Some questions seem unanswerable. You just have to think about them until you no longer worry about them.” I hated the answer at the time, and still don’t like it, but I am afraid it is the way it is in this case.
Congratulations. Your question strongly suggests to me you have a brilliant career ahead of you in scientific inquiry. Keep the faith!
Here is a paper on the determination of R:
http://arxiv.org/ftp/arxiv/papers/0711/0711.0740.pdf
Here is a brief survey of physics including thermodynamics:
http://physics.about.com/od/thermodynam ... namics.htm
Here is a discussion of Gibbs Free Energy:
http://en.wikipedia.org/wiki/Gibbs_free_energy
Best Regards,
Barrett Tomlinson
You ask a profound but obscure question. The mystery is even more profound than you state  the same constant keeps reappearing in a whole bunch of places, equations describing thinks like the voltages of batteries(http://www.science.uwaterloo.ca/~cchieh ... nsteq.html) , the “colligative” properties of liquids(http://hyperphysics.phyastr.gsu.edu/hb ... ollig.html), reaction rates, and statistical mechanics and boltzman statistics.
The best answer I can give is that the reason lies in the theories of thermodynamics, specifically in the concept of Gibbs Free Energy( see link below). I apologize in advance if this answer seems to raise more questions than it answers. I think the answer my quantum mechanics professor gave to one his students forty years ago applies: “Some questions seem unanswerable. You just have to think about them until you no longer worry about them.” I hated the answer at the time, and still don’t like it, but I am afraid it is the way it is in this case.
Congratulations. Your question strongly suggests to me you have a brilliant career ahead of you in scientific inquiry. Keep the faith!
Here is a paper on the determination of R:
http://arxiv.org/ftp/arxiv/papers/0711/0711.0740.pdf
Here is a brief survey of physics including thermodynamics:
http://physics.about.com/od/thermodynam ... namics.htm
Here is a discussion of Gibbs Free Energy:
http://en.wikipedia.org/wiki/Gibbs_free_energy
Best Regards,
Barrett Tomlinson
Re: Ideal gas constant versus osmotic constant
Thanks a lot !!
I'll go check out those links and see if I can forget about it. lol
Thanks for your time
I'll go check out those links and see if I can forget about it. lol
Thanks for your time

 Former Expert
 Posts: 932
 Joined: Wed Oct 03, 2007 12:24 am
Re: Ideal gas constant versus osmotic constant
Some further clarification of the question of R appearing many equations describing physical and chemical phenomena. The common link lies in the Maxwell Boltzmann distribution law, found in the study of statistical mechanics.
See:
http://en.wikipedia.org/wiki/Maxwell%E2 ... stribution
Also a better book reference:
The Principles of Statistical Mechanics
Richard C. Tolman
Oxford University Press 1962
R= N *k
Where
R = the gas constant
N = Avogadros number, the number of molecules in a mole
k = Boltzmann constant, a constant of the universe whose measured value scales our measuring system units to the natural order of things.
See:
http://en.wikipedia.org/wiki/Maxwell%E2 ... stribution
Also a better book reference:
The Principles of Statistical Mechanics
Richard C. Tolman
Oxford University Press 1962
R= N *k
Where
R = the gas constant
N = Avogadros number, the number of molecules in a mole
k = Boltzmann constant, a constant of the universe whose measured value scales our measuring system units to the natural order of things.

 Former Expert
 Posts: 1297
 Joined: Mon Oct 16, 2006 11:47 am
Re: Ideal gas constant versus osmotic constant
The answers aren't all that difficult to comprehend when you think about things as mathmatical models. Liquids and gasses are fluids and different states often coexist at the same pressure, temperature, and volume. Why wouldn't there be some comonality in the thermodynamic models? The mathmatical model for a difusion gradient is independent of what is being difused if you factor out the permubility properties of the difusion media wrt what is being difused. Why wouldn't you expect similar constants to come up when you've already factored out the other differences?
Craig