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The equation describing osmotic pressure is

$\Pi=\frac{n}{V} RT $

which is just like the ideal gas equation law

$PV=nRT$

So how much of an analogy is there between ideal gases and solutes? Is there a extended version of the equation for osmotic pressure that matches the van der Waals equation of state?

If solutes can be in a state like a gas, can they also be in a state like a liquid? Is this distinct from a precipitate which would be the analog of a solid?

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The van t'Hoff equation for the osmotic pressure can be expanded by a virial expansion similarly to the extension of ideal gas equation. In the gas case, the coefficients of the virial expansion are related to the van der Waals constants a and b. Thus you can probably also obtain a similar equation of state for the osmotic pressure $\Pi$ of a solute. However, their interpretation will probably be different.

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  • $\begingroup$ The van der Waal equation has a liquid phase, so it makes me wonder that while ordinarily precipitates are solid, if there aren't substances that 'precipitate' out of an aqueous solution to a liquid form. $\endgroup$
    – David Elm
    Dec 6 '16 at 9:44
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    $\begingroup$ @David Elm - There are many examples of solutes "precipitating" as liquids that are, e.g., connected to a so-called miscibility gap. A simple example for phenol in water is given here chemistry.stackexchange.com/questions/23519/… $\endgroup$
    – freecharly
    Dec 6 '16 at 16:17
  • $\begingroup$ -Thanks. That's one of the things I looked for, but just didn't hit on the right key words to find. $\endgroup$
    – David Elm
    Dec 7 '16 at 7:56

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