🚀 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. [...]
>
>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 :) )

     Actually, as usual, the truth is far more complicated than typical
textbook presentations.  The osmotic pressure is only linear in
concentration at low concentrations.  Especially for larger molecules,
deviations from the linear law are easy to observe.  The deviations can
be expressed as a virial equation.  I suspect that careful measurements
would show that the second virial coefficient increases with size of the
molecule, although I'm not aware of any work done on this.  (For a
start, you can look at W.J. Moore's Basic Physical Chemistry.)
     We have to remember also that there are many statistical effects in
play here.  Surely a DNA molecule has to obscure more of the surface
than a simple sugar, but the molecules that do congregate at the
membrane won't necessarily be plastered against the thing.  Thus two
smaller molecules may (on average) obscure more of the surface than one
big one.  To figure out how much of the membrane a given polymer
molecule covers, you have to work out the detailed statistical mechanics
of these things.  It's not a trivial task and frankly not one that I
have much expertise in.  My gut feeling however is that to lowest
order, you'll find that the coverage only depends on the number of
molecules as long as the polymer in question isn't exceedingly hydrophobic.
If you're really interested in asking someone who actually knows something
about this, try sending email to Professor Whittington
(swhittin@alchemy.chem.utoronto.ca).

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca