Water potential

So right here I have a container of water that is open to the atmosphere. It's standard atmospheric pressure up here. Let's just assume that everything in our system—the air and the water, the container—everything is 21 degrees Celsius.

Now, our chamber is—or our container of water—is divided into two chambers: a left chamber and a right chamber, which is divided by a semi-permeable membrane. It's permeable only to the water, but not to the solute in the water. On the left-hand side, we have pure water, so it's just molecules of H2O. You could view that as distilled water. While on the right-hand side, we don't have pure water; we have some sodium chloride that has been dissolved in the water.

We want to get a little quantitative in this video, so let's say it is 0.25 moles per liter, or 0.25 molar sodium chloride right over here. Well, we know intuitively from our study of osmosis what is going to happen here. Since our membrane is only permeable to water, and the right side is hypertonic relative to the left—it has a higher concentration of solute—we will have the water going from left to right.

But what we're going to do in this video is get a little bit more quantitative and think about, well, what is the potential of the water to go from the left to the right? To do that, we're going to talk about something known as water potential, which is denoted by the Greek letter psi. Now, by convention, the water potential of the pure distilled water, when it is in an open container exposed to standard atmospheric pressure, is going to be—so psi over here—is going to be equal to zero bars.

As you can see here, the units for psi for water potential are the same as the units for pressure; here we're using bars, but you could use psi or atmospheres or something else. But what is going to be the water potential on the right-hand side? Well, generally speaking, you can break down your water potential into subcomponents.

The subcomponents that we typically talk about—but there are more—are the component due to the solute and the component due to pressure. This is often known as the solute potential and the pressure potential. Now, because this right chamber is open to the atmosphere and its standard atmospheric pressure, the pressure potential in this situation is going to be equal to zero. So, our total water potential on the right-hand side is going to be the same thing as our solute potential.

Now, to figure out our solute potential, we will turn to a formula, and I'll show you a formula sheet right over here that's given by the college board when folks take the AP Biology exam. But we'll see that this formula is actually quite intuitive and related to the ideal gas law that you first studied in chemistry.

It tells us that our solute potential is going to be equal to negative i—and I'll talk about what that is in a second—times our molar concentration c times our pressure constant r. Now, they're calling it the pressure constant in this context, but it's actually the same r that we see in the ideal gas law, times the temperature in kelvin, so times t.

So first, let's start with i. So let me write this down. This is going to be equal to—it's all going to be negative because all of these are going to be positive values—so i is known as the ionization constant. One way to think about it is for every molecule of solute, how many molecules does it disassociate into when you put it into the water?

So if I take a molecule of sodium chloride, we know that when we put it into water, it's going to disassociate into sodium ions and chloride ions, or into two ions for every one molecule of sodium chloride. So here, our ionization constant is going to be equal to two.

Now, what's our molar concentration? Well, we already know that our molar concentration is going to be 0.25 molar, or we could write it as 0.25 moles per liter. Then we're going to multiply that times our pressure constant, which is the same as the ideal gas constant, and that is going to be—they give it to us right over here—0.0831 liter bars per mole kelvin.

Then we are going to multiply that times the temperature in kelvin. Now, what's that going to be? What's going to be our temperature in Celsius plus 273? So you had 21 plus 273; you're gonna get 294 kelvin.

This is going to be approximately equal to—we're going to have this negative out front. If we look at our units, let's see: we have moles cancelling with moles, liters cancelling with liters, and then kelvin cancelling with kelvin. So our units are going to be in bars, which makes sense because, as we already talked about, that's the units that we're dealing with here.

So let me get a calculator out. See, we already have the negative, so it's going to be 2 times 0.25 times 0.0831 times 294. It is equal to—and I'll just round to one decimal place—so 12.2. But I have that negative there, so approximately negative 12.2 bars.

So our solute potential over here is negative 12.2 bars, or it's approximately equal to that—and that's going to be equal to our total water potential because the pressure potential is zero. So how do we interpret that? Well, one way to think about it is you could almost view it as, since it's negative relative to the left-hand side, that it would pull water in.

The water, if the membrane is only permeable to the water, is going to go from high potential to low potential, and that's exactly what we thought would happen intuitively.

Now, another thing that we could think about is, well, how would we keep the water from flowing? Well, then we could add some pressure potential right over here. Maybe we could put a piston over here, and we could apply some pressure above and beyond the standard atmospheric pressure.

Well, how much pressure would we have to apply here to kind of push down on that water so that we don't have a net inflow from the left to the right? Well, imagine if this was 12.2 bars that we were to apply up here. Well, then all of a sudden this pressure potential wouldn't be zero; it would be positive 12.2.

Then on the right, we would have negative 12.2 bars of solute potential plus positive 12.2 bars of pressure potential. That would add up to be a zero water potential, in which case, since the left and the right-hand side would have the same water potential, you would not have a net flow of water in either direction.

So, as you can see, this idea of water potential allows us to think a little bit more precisely and a little bit more quantitatively about these ideas of osmosis and tonicity.