🚀 go-pugleaf

In article <29046@boulder.Colorado.EDU> eddy@boulder.Colorado.EDU (Sean Eddy) writes:
>>Why does the concentrations tend to even out? There will always be a lot
>>of water molecules that are passing through the membrane in both directions,
>>since nothing is stopping them from doing so. However, on the side with
>>higher salt concentration, there will be fewer water molecules (and more
>>salt ions) adjacent to a given membrane surface area, and therefore a
>>slightly lower flow of water from that side to the other than in the other
>>direction.
>
>Indeed, that's the explanation I was taught, and in turn taught to
>undergrads here at Boulder. It was intellectually satisfying to
>me until a couple of weeks ago, when my complacency was thrashed by
>a fellow grad student. We started arguing, and reading, and arguing
>some more, and pretty soon the debate was spreading through the
>department... but we're just a bunch o' biologists, so I'll
>relate the problem to you guys. 
>
>Osmosis is a colligative property. That is, osmotic pressure is
>dependent on the *number* of particles in solution -- *not*
>their size, mass, etc. ...
>
>But trying to figure out how osmotic pressure isn't affected
>by the size of the solute is the problem. Let me make it
>clearer: the osmotic pressure of a DNA solution, avg. MW
>say 10^8, length of the molecules damn near in the visible range, is
>the *same* osmotic pressure as, say, a sugar solution
>of the same concentration. I *cannot* rationalize this
>in my brain using the "more solute, proportionally less
>access to membrane for solvent" model. Big molecules would
>obscure more of the membrane. (Furthermore, cut those DNA
>molecules in half... now they have twice the osmotic pressure.
>Yeah, right :) )
>
>See my problem? P-chem texts have been unhelpful and generally
>quite circular in their logic on this point, it's seemed ("it
>just *is*").
>
>What is the detailed rationale for osmotic pressure being
>dependent upon only the number of solute molecules, not
>their size, shape, and mass?
>
>- Sean Eddy
>- Dept. of Molecular, Cellular, Developmental Biology
>- U. of Colorado at Boulder
>- eddy@boulder.colorado.edu

Intuitively speaking,
any small molecule has its own "turf", its own volume, which it 
"defends" not by occupying all of it but by bouncing off any
molecule that tries to enter, thereby tending to knock the
intruder out of the region.  Within limits this is independent of
physical size. Here is a (highly imperfect) analogy.  Suppose you
are being kept out of one corner of your room by an angry wasp.
A wasp half as small might be exactly as effective in keeping you
out of the same sized region.  In this analogy the wasp is a
solute moecule and you are a water molecule.
Of course solute molecules large compared to
their allocated volume (which is determined by pV=kT) behave
somewhat differently.

The independence of mass is related to the fact that at a given
temperature molecules with a small mass move faster;  the bigger
speed partially (not entirely) compensates for their small mass
in one hit on an intruder when they are "trying" to drive him out.
In addition, since they move faster they hit the intruder more
often and it turns out the combined effect is independent of
mass.

Some of your friends won't like these arguments; but if one
really studies the solutions of the Botlzmann equation with a
sensible collision kernel that's what the formalism comes down
to; the result can also be derived by equilibrium (statistical
mechanical) arguments (rather than by these kinetic-theoretical 
arguments using the Boltzmann equation), but reading between the lines I
gather these standard derivations don't satisfy you.

Hope that helps.