🚀 go-pugleaf

In article <1990Nov14.171839.12177@ux1.cso.uiuc.edu> mcdonald@aries.scs.uiuc.edu (Doug McDonald) writes:
>In article <4171@kitty.UUCP> larry@kitty.UUCP (Larry Lippman) writes:
>>In article <1748@ruunsa.fys.ruu.nl>, hooft@ruunsa.fys.ruu.nl (Rob Hooft) writes:
>>> I've got enough osmosis-nonsense today.
>>> Please stop using all this empirical nonsense and start using plain 
>>> thermodynamics. The effect is so simple to understand once you know the
>>> fundamental laws of thermodynamics.
>>
>
>Sure. No problem.
>
>But that begs the question very seriously. The "usual" thermodynamic
>formulation ASSUMES ideal solutions. Are the big polymer solutions ideal?
>If so, this will work. Under what conditions ARE they ideal - 
>does big size prevent ideality (yes, this is answered clearly in
>undergrad texts)? If they are not ideal WHY not - is it an entropic
>or energetic effect. What is the physical basis behind this?
>
>I don't know. But I will ask a genuine expert (Peter Wolynes).
>Stay tuned.
>

OK, I did (ask Peter).

We have that (in TeX)

\int_0^{\Pi} V_A dP = -RT \log (P_A / P_A^*)

where \Pi is the osmotic pressure, P_A^* is the vapor pressure of 
pure solvent, and P_A the vapor pressure of solution, and V_A is the
partial molar volume of solvent.

OF course for ideal solutions V_A = V_A*, and P_A / P_A^* = X_A,
the mole fraction. 

This whole business assumes ideal solutions.  In fact, it is hard to
find membranes that will work well for many non-ideal ones. 
Biopolymers are reasonable ideal, at least at low concentrations.
The sum of the volume of the unmixed things is the volume of
the solution, and the heat of mixing is small. 

The free energy change of the solvent, which is what osmosis works on, 
of course, is then a purely entropic effect. The partial molar entropy
of dilution of the solvent is  - R \log (X_A). Being entropy only,
the numbers just come out as a function of the numbers of different
ways to distribute the molecules (of all kinds) in various orders.
Note very importantly that since olny very dilute polymer solutions
are ideal, a polymer never gets near another polymer - they are surronded
by solvent molecules. 


Doug McDonald