

Chemistry: Osmosis



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  • Type: Video Tutorial
  • Length: 13:10
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  • Size: 141 MB
  • Posted: 07/14/2009

This lesson is part of the following series:

Chemistry: Full Course (303 lessons, $198.00)
Chemistry: Physical Properties of Solutions (14 lessons, $22.77)
Chemistry: Colligative Properties (5 lessons, $9.90)





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2918 - Osmosis
We've seen how, by taking a solute and dissolving it in a solvent, we change fundamental physical properties of that solvent. We change the boiling point, the freezing point, the vapor pressure... And our explanation for all of this had to do with the fact that when we dissolved the solute in the liquid, we increased the entropy of the system. By doing that, we're in a sense, favoring the liquid state over its gas or solid states, and as a result again, we got these changes in the physical properties.
There is one other colligative property that I want to discuss. And that is osmosis. And, like the other colligative properties, it is referred to as a colligative property because it is independent of the chemical nature of the solute. The way osmosis works - so in order to explain osmosis to you - let me start out with a thought experiment.
Imagine we took a tank and imagine that the tank, we partitioned with a membrane and the membrane was such that it had small holes in it that would allow solvent to pass freely through those holes, but would not allow the transfer of solute particles. Now the solute particles are just simply too big. We could imagine our cartoon; that would show that idea. If this is the membrane, if we're on the molecular level here, suppose the little brown dots are solvent, that they truly can pass through these holes, but the solute particles, the red dots, they are not able to get through that membrane. So remember, solute cannot pass through the membrane, solvent can move easily in and out.
Well, returning back to our thought experiment then. If we then set up the experiment such that on the right side, the right half, we introduced a solute. Then we might expect the solvent particles to transfer across the membrane such that we increase the volume of the solution, decreasing the volume of the pure solvent. That would cause a change in pressure, if we could measure again as a thought experiment, the pressure buildup as more and more volume transferred across that membrane to the right side, and we could measure what that pressure would be. Eventually the system would come to an equilibrium where the physical pressure of pushing the solvent molecules back across the membrane due to a pressure buildup equaled this driving force of the solvent molecules wanting to be over on the solution side of the barrier.
Now, we could talk about that pressure that we measured as an osmotic pressure and, in fact, that pressure would be proportional to the concentration of our solute at that equilibrium point. So, M here is just "molar" or moles per liter, our final solution concentration; R is the gas constant as it turns out in liter atmospheres per moldecrete Kelvin and temperature is in Kelvins. And so that would describe then, this pressure. Now the important point about this is simply that the pressure depends on concentration. If we know what the pressure is, we can determine concentration of - let's suppose it's an unknown molecular weight solute, for instance. Now, this is not a convenient way to actually do this experiment. A much more convenient way in practice to do this is the following.
I'm going to show you an experiment that we set up yesterday, and in this particular case, what we did was we started out with just solute inside this tube - there was no solvent initially, or a very minimal amount of solvent at least - and we've got at the bottom of this tube here a semi permeable membrane which, remember, again, allows the transfer of solvent in to the tube, but does not allow for the solute to transfer out. We set that up yesterday, went home, came back, and now, look what's happened. The solvent molecules have moved inside the membrane, pushed up the volume until we reached a particular height. Now, I could come back a week from now and this wouldn't change anymore. This has leveled off at its final equilibrium value. Well, what are the forces at work here that are in balance. We have on the one hand, osmotic pressure, this notion that the solvent wants to be on the side of the membrane where the solute is. On the other hand, we have the mass of water pushing down, being pushed down by gravity, acceleration due to gravity, forcing the solvent molecules back out of the membrane. So, although again we have an equilibrium, it is dynamic in that there are solvent molecules always moving in and out of the membrane, but there is no net change in the height now, because we have this balance again between force due to gravity or pressure, if you will, due to gravity, and the osmotic pressure. Well, we can describe that in terms of the osmotic pressure being equal to the density of the liquid times acceleration due to gravity, that's g, times the height of the column. That's describing again what the pressure is pushing down on this column.
And so, it is convenient to go in the lab, set up this experiment, measure the height and by knowing acceleration due to gravity, which is just a constant, and the density of that liquid, we can relate that to osmotic pressure and from that point, relate it to concentration. That's the key link again. Relating concentration of something that is unknown to something we can easily measure.
Now, let's go to just a little bit better picture of this so you can get a little bit better idea of what that membrane looks like. And, again, you can imagine, this is very typical of how you might set up an experiment like this. This is called a thistle tube and we could wrap a membrane around the bottom part of the thistle tube and just dip it into a beaker of pure solvent. That pure solvent can transfer across that membrane and it starts to push this liquid up. So, we might start it here, let's say, or we could start it down here; it makes no difference where we start it. It makes no difference at all. All that's important is what the final height is once we reach our equilibrium. So this is pushed up to some final height and the height that we want to measure is not from here. It's from the liquid down here, at equilibrium, compared to here. How much above the rest of the liquid have we pushed that column of water? That times density times acceleration due to gravity is going to give us the pressure pushing out across the membrane, which is going to be balanced by the pressure, the osmotic pressure, pushing in on the membrane.
Now, we'll do a calculation to show you how this works. Because the only tricky part about this is the units can be a little confusing. But before we do that, let's just compare osmosis, or osmotic pressure, with other colligative properties. Let's suppose that we had again the problem of wanting to determine the molecular weight of an unknown material and we only had a little bit of that material, what would be the most sensitive colligative property to use to connect mass to concentration, in terms of moles and that, therefore, would give us, again, a molecular mass for the material. Okay, so as an example, let's suppose that we had a protein, a very large molecule, molecular weight or molecular mass of 23,000 g/mole. And so, we'll take two grams of this stuff, which is a lot of protein to biologists or biochemists, that's a huge amount of material for them to get their hands on. So, we're being very generous by saying that we have this much material. But understand this - that the molecular weight of the protein is so big that two grams really isn't very much at all. This is not - again, the molecular weight is so large here, that two grams corresponds to a very tiny fraction of one mole for this protein. We're going to take that two grams and we'll go ahead and dissolve it in a 100 milliliters of water and ask, what are the changes to boiling point, freezing point, vapor pressure, as a result of adding the solute to the solvent. Well, the vapor pressure lowering is a whopping 4.8 times 10 atmospheres. That's a number you're going to be very hard pressed to even measure. That's such a small difference as far as the pressure is concerned. The boiling point elevation turns out to be .0004 of a degree Celsius or of a Kelvin. Very, very small change there. Again, you're going to be lucky if you can find a thermometer that you can read to that degree of accuracy. The freezing point elevation is not much better. It is about .001 of a Kelvin difference. So, again, these are all very, very small differences that are actually, for all practical purposes, not measurable differences.
Compare that to osmosis. In the case of osmosis, we end up with a 220 millimeter rise, so .2 of a meter rise a very significant difference in the height. So, even for very, very low molar concentrations of material, we can measure significant differences in osmotic pressure. So, let's go ahead and look at an example of what you might be asked to do. Let's suppose we're talking about a maple tree. This is one of the many places where osmosis shows up in nature. In a maple tree, let's suppose that we have an average concentration of sucrose of 3 percent. So, we'll say that that's about a .1 molar solution of nutrients, let's say, that are in the veins of this tree and so forth. The rising of the sap in this tree is due primarily to osmosis. So you can imagine the membrane as being the roots of the tree and water being pulled out of the ground and sucked up into this tree; again, simply by this notion that the water solvent will want to get where there's a lot of solute dissolved. Again, the nutrients of the tree, the sugar in this case, primarily. How high will the sap actually rise, given this temperature. Let's go ahead and assume that the density of the liquid is one gram per milliliter, the same as that of water.
So, using the osmotic pressure formula that we saw just a moment ago, the osmotic pressure, which again is abbreviated as normally, is moles per liter concentration times the gas constant times temperature in Kelvins. So, our concentration times our gas constant in liter atmospheres per mole Kelvin times the temperature. That gives us an osmotic pressure of 2.4 atmospheres. Now, we want to relate that to height. After all, we're trying to figure out high the sap is going to get in this tree. So, 2.4 atmospheres. I'm going to now have to convert this to a set of units that are compatible with meters or millimeters or some measurement of height as well as meters per second squared, which is the units for gravity. So to do this, I have to convert this into Pascal. So, I'm going to multiple 2.4 atmospheres by the conversion factor 1.01 x 10 Pascals per atmosphere. That gives me 2.44 x 10 Pascals, and remember, that that is equal to density times gravity (acceleration due to gravity) times the height of the column. And that, in this case, is what we don't know. So, 2.4 x 10 is equal to - now I'm going to put in a couple of conversions here. This is the density - 1 gram per cubic centimeter. I'm going to convert grams to kilograms. I'm going to convert cubic centimeters to cubic meters. And finally, multiple this by acceleration due to gravity rather, in meters per second squared -that's just a constant again for gravity - and height is our only unknown. So taking all this into the denominator, we end up with a height of just about 25 meters. So, that's an enormous distance of water that we can push up into this tree, all due, again, to osmotic pressure.
So, just summarizing then - we have osmosis or osmotic pressure, vapor pressure lowering freezing point depression and boiling point elevation, all the direct result of the notion that a solute dissolved in a solvent, we end up with an increase in the stability of that system due to the entropy gain. And as a result, again, we see these changes in physical properties.
Physical Properties of Solutions
Colligative Properties
Osmosis Page [1 of 3]

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