william@lorien.newcastle.ac.uk (William Coyne) (10/28/90)
Thanks to those who replied to my earlier question on osmosis, but none explained what was going on at the atomic or molecular level. Perhaps the following will make my question clearer. Imagine a container with a semi-permiable membrane down the middle with a high salt concentration solution on one side and a low conc solution on the other. Initially both solutions are the same depth, then after the membrane is uncovered osmosis begins. Eventually the depths of the water on either side will stop changing and one side will be deeper than the other(see below) | * | |^^^^^^^* | |^^^^^^^^*^^^^^^^^| | * | | * | | *^^^^^^^^| | high * lo | |medium * medium | | * | | * | ------------------ ---------------- BEFORE AFTER What mechanism is allowing the salt to cause the water to build up on left hand side? Are the salt molecules forming weak bonds with the water molecules so reducing the number of molecules passing from the high to low concentration? Would the container need to be very large before gravity would prevent the water on left hand side rising noticeably. Replies by email should be sent to - JANET: W.P.Coyne@uk.ac.newcastle UUCP : ...!ukc!newcastle.ac.uk!W.P.Coyne ARPA : W.P.Coyne%newcastle.ac.uk@nss.cs.ucl.ac.uk .............................................................
ske@pkmab.se (Kristoffer Eriksson) (11/01/90)
In article <1990Oct28.115303.7221@newcastle.ac.uk> W.P.Coyne@newcastle.ac.uk writes: > | * | |^^^^^^^* | > |^^^^^^^^*^^^^^^^^| | * | > | * | | *^^^^^^^^| > | high * lo | |medium * medium | > | * | | * | > ------------------ ---------------- > BEFORE AFTER > >What mechanism is allowing the salt to cause the water to build >up on left hand side? The way I remember it, the key to this is that the salt ions can't pass through the membrane, only the water can. The solutions on both sides of the membrane tend to even out their respective concentrations, and the only way that can be done is by raising the amount of water on the side with the higher salt concentration, and vice versa, since the amount of salt can't be changed. 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. >Would the container need to be very large before gravity would >prevent the water on left hand side rising noticeably. If the water remaind and equal levels, gravity would also act equally on both sides, and would therefore not stop the sides from differentiating. I suppose that if one of the sides would rise considerably above the other side, it could be compressed enough by gravity to make the number of water molecules to a given surface area on both sides equal slightly before the concentrations become equal. (The water pressures would become equal without the solution concentrations being equal.) -- Kristoffer Eriksson, Peridot Konsult AB, Hagagatan 6, S-703 40 Oerebro, Sweden Phone: +46 19-13 03 60 ! e-mail: ske@pkmab.se Fax: +46 19-11 51 03 ! or ...!{uunet,mcsun}!sunic.sunet.se!kullmar!pkmab!ske
chooft@ruunsa.fys.ruu.nl (Rob Hooft) (11/01/90)
In <4396@pkmab.se> ske@pkmab.se (Kristoffer Eriksson) writes: >If the water remaind and equal levels, gravity would also act equally on >both sides, and would therefore not stop the sides from differentiating. >I suppose that if one of the sides would rise considerably above the >other side, it could be compressed enough by gravity to make the number >of water molecules to a given surface area on both sides equal slightly >before the concentrations become equal. (The water pressures would become >equal without the solution concentrations being equal.) This is the only way of stopping the process if we only add salt to one of the two compartments. The osmotic value is also named osmotic pressure, and if you calculate some values, say for a 0.1 M NaCl solution, (0.2 Moles/liter so, since number of moles.R.Temperature in K osmotic pressure = ----------------------------------- Volume in M3 = 200 mole/m3 * 8.31441 J/K/mole * 298 K = 500000 Pa = 5 Bar ) then you can realize that the water in that compartment would have to rise 50 meters to obtain equilibrium (if dilution is not taken into account). In fact this method is being used to measure molar masses of compounds. A rise of 1 cm in the compartment means 0.00004 mole/liter concentration. So the procedure is simple: weigh x grams, put it into the compartment of y ml, if it rises z cm it is p moles, such that the molar mass is x/p gram/mole. I hope this makes things somewhat more clear. -- Rob Hooft, Chemistry department University of Utrecht. hooft@hutruu54.bitnet hooft@chem.ruu.nl chooft@fys.ruu.nl
eddy@boulder.Colorado.EDU (Sean Eddy) (11/01/90)
>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. This is a highly useful property, of course; we can measure the molecular weights of things by finding the osmotic pressure of (and hence the number of particles in) a given weight of stuff. 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
sachs@cartan.berkeley.edu (Rainer Sachs) (11/02/90)
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.
chooft@ruunsa.fys.ruu.nl (Rob Hooft) (11/02/90)
In <29046@boulder.Colorado.EDU> eddy@boulder.Colorado.EDU (Sean Eddy) writes: >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. . . . >What is the detailed rationale for osmotic pressure being >dependent upon only the number of solute molecules, not >their size, shape, and mass? Entropy is. And the ideal gas law p.V=n.R.T is derived from entropy too. If water flows from the pure-water to the mixture compartment the entropy of the system rises, because there are more possible realisations of the locations of the solute. This is exactly the same reason that some amount of gas will always take all the volume it can get. You need to input energy (compressing the gas, applying gravity) to stop the expansion process. From the analogy it can be derived that the ideal gas law also holds for osmosis, such that p=n.R.T/V is the osmotic pressure. some theory ----------- Equilibrium in the system means that the thermodynamic potential (mu) of the components that can diffuse must be equal in both compartments. In the compartment with the solute present, the potential is raised by pressure, and lowered by the presence of the solute, such that the equilibrium can be stated as follows: mu(pure water) +(derivative of mu to the pressure)*(osmotic pressure) -R*T*(molefraction solute) = mu(pure water) and so: (derivative of mu to the pressure)*(osmotic pressure) =R*T*(molefraction solute) the derivative of mu to the pressure is the volume of one mole of water in the solution. This can be replaced by the total volume of a "unit of solution" in case of dilute solutions: ("unit solution" Volume)*(osmotic pressure) =R*T*(molefraction solute) Multiply both sides by the number of moles present: (total volume)*(osmotic pressure) =R*T*(number of moles of solute) or: R*T*(number of moles of solute) osmotic pressure = --------------------------------- Total volume Hope this helps again. Reference in Dutch: Korte inleiding in de chemische Thermodynamica, J.M. Bijvoet, A.F. Peerdeman, A.Schuijff, E.H. Wiebenga. Utrecht, 1984. -- Rob Hooft, Chemistry department University of Utrecht. hooft@hutruu54.bitnet hooft@chem.ruu.nl chooft@fys.ruu.nl
richard@locus.com (Richard M. Mathews) (11/02/90)
eddy@boulder.Colorado.EDU (Sean Eddy) writes: >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.... >Osmosis is a colligative property. That is, osmotic pressure is >dependent on the *number* of particles in solution -- *not* >their size, mass, etc. I have a thought on an intuitive answer. Think of a large particle in the solution as a perfectly rigid, lumpy blob. Think of the membrane as a perfectly rigid, lumpy surface. In general when you bring 2 lumpy surfaces together they will touch at no more than 3 points. When the particle touches at just one point, that might be enough to start bouncing it away. If the gaps between the particle and the membrane are large enough for water molecules to fit (which isn't very big) then we find that each particle is only capable of blocking water in 1 to 3 spots. At most we have to account for a factor of 3 difference between a monatomic particle and a huge molecule rather than a factor based on the ratio of surface areas. If the assumption of perfect rigidity is wrong, the factor could be a bit larger; but in the time scale of a collision, I would expect rigidity to be a halfway decent approximation. Richard M. Mathews D efend Locus Computing Corporation E stonian-Latvian-Lithuanian richard@locus.com I ndependence lcc!richard@seas.ucla.edu ...!{uunet|ucla-se|turnkey}!lcc!richard
mroussel@alchemy.chem.utoronto.ca (Marc Roussel) (11/02/90)
In article <richard.657537509@fafnir.la.locus.com> richard@locus.com (Richard M. Mathews) writes: >eddy@boulder.Colorado.EDU (Sean Eddy) writes: > >>Osmosis is a colligative property. That is, osmotic pressure is >>dependent on the *number* of particles in solution -- *not* >>their size, mass, etc. > > Think of a large particle in >the solution as a perfectly rigid, lumpy blob. Think of the membrane >as a perfectly rigid, lumpy surface. In general when you bring 2 lumpy >surfaces together they will touch at no more than 3 points. When the >particle touches at just one point, that might be enough to start >bouncing it away. If the gaps between the particle and the membrane >are large enough for water molecules to fit (which isn't very big) then >we find that each particle is only capable of blocking water in 1 to 3 >spots. At most we have to account for a factor of 3 difference between >a monatomic particle and a huge molecule rather than a factor based on the >ratio of surface areas. If the assumption of perfect rigidity is wrong, >the factor could be a bit larger; but in the time scale of a collision, >I would expect rigidity to be a halfway decent approximation. In fact deviations from the ideal law of a factor of two or three are relatively easy to find with large polymers. This is the point I was attempting to make in a previous post: the truth isn't as simple as the textbooks make it out to be. Marc R. Roussel mroussel@alchemy.chem.utoronto.ca
tom@stl.stc.co.uk (Tom Thomson) (11/06/90)
In article <29046@boulder.Colorado.EDU> eddy@boulder.Colorado.EDU (Sean Eddy) writes: >Osmosis is a colligative property. That is, osmotic pressure is >dependent on the *number* of particles in solution -- *not* >their size, mass, etc. The interesting thing is how much space they take up, not how big they are: it's not as if they were closely and rigidly packed so that the space they take depends on their size. Even with BIG molecules in solution, the average radius is SMALL compared with the mean free path. Tom
richard@locus.com (Richard M. Mathews) (11/06/90)
tom@stl.stc.co.uk (Tom Thomson) writes: >In article <29046@boulder.Colorado.EDU> eddy@boulder.Colorado.EDU (Sean Eddy) writes: >>Osmosis is a colligative property. That is, osmotic pressure is >>dependent on the *number* of particles in solution -- *not* >>their size, mass, etc. >The interesting thing is how much space they take up, not how big >they are: it's not as if they were closely and rigidly packed so >that the space they take depends on their size. Even with BIG >molecules in solution, the average radius is SMALL compared with >the mean free path. What you say is generally true of a gas. A liquid is not a gas. In a solid you will probably agree that the molecules are more or less "closely and rigidly packed." Since liquid water is more dense than ice, we can conclude that water molecules are pretty closely packed as a liquid. The space occupied by small molecules and radicals in solution cannot be anywhere near the space occupied by a DNA molecule. density of water == 1 g/cc == 1/18 mole/cc == 1/3 * 1e24 molecules/cc Since 1 cc == 1e24 cubic Angstroms, density of water == 1 molecule / 3 cubic Angstroms. Richard M. Mathews D efend Locus Computing Corporation E stonian-Latvian-Lithuanian richard@locus.com I ndependence lcc!richard@seas.ucla.edu ...!{uunet|ucla-se|turnkey}!lcc!richard
mroussel@alchemy.chem.utoronto.ca (Marc Roussel) (11/07/90)
In article <richard.657852606@fafnir.la.locus.com> richard@locus.com (Richard M. Mathews) writes: >tom@stl.stc.co.uk (Tom Thomson) writes: >>The interesting thing is how much space they take up, not how big >>they are: it's not as if they were closely and rigidly packed so >>that the space they take depends on their size. Even with BIG >>molecules in solution, the average radius is SMALL compared with >>the mean free path. >The space occupied by small molecules and radicals in solution >cannot be anywhere near the space occupied by a DNA molecule. This is certainly true. You are both focussing on the wrong aspect of the problem however. It is not the size of the molecules that matters, but their area of contact with the membrane. Consider a simple ion in solution. It can cover an area of the membrane roughly proportional to the square of its radius. Now consider a big ugly polymer. In order to even guesstimate how much of the membrane it can cover, we need to know its conformation in solution. Suppose it is hydrophobic and "balls up". Even if it is a big molecule, the point of contact will be (to the lowest order approximation) a single atom. It therefore doesn't obscure any more of the surface than the simple ion. Suppose now that the thing loves water and stretches out into a long string. To figure out how much of the surface it covers, you have to work out in detail the statistics of such chains in water. (This is related to the problem of computing boundary visits in self-avoiding random walks of finite length.) By far the likeliest thing for reasonably short chains however is that if one end touches the membrane, no other point will (again, contact area goes roughly as the square of one atomic radius). For longer chains, we have a significant probability that the membrane will be touched in more than one place by a single molecule. This explains why significant deviations from the ideal p~c law are observed with polymers at moderate concentrations. Marc R. Roussel mroussel@alchemy.chem.utoronto.ca
bhoughto@cmdnfs.intel.com (Blair P. Houghton) (11/07/90)
In article <1990Nov6.235518.8507@alchemy.chem.utoronto.ca> mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes: > This is certainly true. You are both focussing on the wrong aspect of >the problem however. It is not the size of the molecules that matters, >but their area of contact with the membrane. If the contact plugs a hole then it plugs traffic in both directions. All it does is reduce the effective area of the membrane. This has no effect on the osmotic pressure. The real question is whether diffusion itself (never mind the osmotic case with semi-permeable membranes) is affected by the relative size of the constituents of the system in a manner not expressible by a set of diffusion constants. --Blair "This has no effect on the usenetic pressure..."
richard@locus.com (Richard M. Mathews) (11/10/90)
bhoughto@cmdnfs.intel.com (Blair P. Houghton) writes: >In article <1990Nov6.235518.8507@alchemy.chem.utoronto.ca> mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes: >> This is certainly true. You are both focussing on the wrong aspect of >>the problem however. It is not the size of the molecules that matters, >>but their area of contact with the membrane. >If the contact plugs a hole then it plugs traffic in both directions. I'm not sure I agree. This would be true if the molecule plugs the hole for some length of time, but not if a point on the molecule just bounces off of the membrane. Say that when a water molecule hits the membrane, it has a certain probability of passing through. If it approaches from the opposite side as the other molecule and gets there just before the other molecule bounces, it will be able to pass through the membrane before striking the other molecule. Similarly, if it gets there just after the bounce, it will be able get through. Water molecules on the same side of the membrane as the other molecule, on the other hand, will be excuded from that neighborhood of the membrane for a short time. Put another way, the pressure of the water on one side will be able to push the plug out of the way, but the water on the same side as the plug will be blocked. Richard M. Mathews D efend Locus Computing Corporation E stonian-Latvian-Lithuanian richard@locus.com I ndependence lcc!richard@seas.ucla.edu ...!{uunet|ucla-se|turnkey}!lcc!richard
bhoughto@cmdnfs.intel.com (Blair P. Houghton) (11/11/90)
In article <richard.658194844@fafnir.la.locus.com> richard@locus.com (Richard M. Mathews) writes: >bhoughto@cmdnfs.intel.com (Blair P. Houghton) writes: >>If the contact plugs a hole then it plugs traffic in both directions. > >I'm not sure I agree. This would be true if the molecule plugs the >hole for some length of time, but not if a point on the molecule just >bounces off of the membrane. > >Say that when a water molecule hits the membrane, it has a certain >probability of passing through. If it approaches from the opposite >side as the other molecule and gets there just before the other molecule >bounces, it will be able to pass through the membrane before striking >the other molecule. Similarly, if it gets there just after the bounce, >it will be able get through. Water molecules on the same side of the >membrane as the other molecule, on the other hand, will be excuded from >that neighborhood of the membrane for a short time. Put another way, >the pressure of the water on one side will be able to push the plug >out of the way, but the water on the same side as the plug will be >blocked. Someone made a perpetual motion machine based on that principle; they put a particle in a box like so: +--------------------+ | / / . / | | | | | | |\==================\| | | | | | | / / / | +--------------------+ The '/' are one-way valves made by doors loaded with extremely-light-k springs that are also perfectly eleastic. Brownian motion of the particle would eventually carry it from one partition to the next. If hit that partition in the passable direction (here clockwise) it might get through (with some tiny probability) or it might not; but, it definitely would not if it were moving in the impassable direction (here anticlockwise). Close the system so no energy enters or leaves. Then the particle must, with some tiny probability, pass around the box in a clockwise direction. Note that the impossibility of perfect elasticity and near-quantum energetics of the springs have no bearing on the reasons this can't work. It has more to do with the fact that the particle is equally likely to cause the doors to open backwards as it is to get through them forwards. I'd prefer that someone who remembers who invented this look up this thing and tell us what the actual analysis was. --Blair "Mu?"
mroussel@alchemy.chem.utoronto.ca (Marc Roussel) (11/12/90)
In article <923@inews.intel.com> bhoughto@cmdnfs.intel.com (Blair P. Houghton) writes: >In article <richard.658194844@fafnir.la.locus.com> richard@locus.com (Richard >M. Mathews) writes: >>bhoughto@cmdnfs.intel.com (Blair P. Houghton) writes: >>>If the contact plugs a hole then it plugs traffic in both directions. >> >>I'm not sure I agree. This would be true if the molecule plugs the >>hole for some length of time, but not if a point on the molecule just >>bounces off of the membrane. >> >>[...] > >Someone made a perpetual motion machine based on that >principle; they put a particle in a box like so: > > +--------------------+ > | / / . / | > | | | | | > |\==================\| > | | | | | > | / / / | > +--------------------+ > >The '/' are one-way valves made by doors loaded with >extremely-light-k springs that are also perfectly >elastic. I'm pretty sure that Feynmann analyzes this machine in his Lectures. The point, if I remember correctly, is that in order for the particle to have enough momentum to get past the spring-loaded doors, the springs have to be so weak that there's an appreciable probability that a thermal fluctuation will open them and thus that the particle goes back the way it came after bouncing off the back wall. (I'll verify this and post something if anyone doubts my memory... Just email and I'll do look it up.) This whole discussion is making me reevaluate my understanding of osmosis. I better go do some reading before I open my mouth again. Sincerely, Marc R. Roussel mroussel@alchemy.chem.utoronto.ca