## Molarity Molality and Diffusion of Water

Examine the situation illustrated in Figure 3-1. We take 1 liter of pure water and dissolve some sugar in it. The dissolved sugar molecules take up some space that was formerly occupied by water molecules, and thus the volume of the solution increases. Recall that the concentration of a substance is defined as the number of molecules of that substance per unit volume of solution. In Figure 3-1, this means that the concentration of water in the sugar-water solution is lower than it was in the pure water before the sugar was dissolved. This is because the total volume increased after the sugar was added, but the total

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Figure 3-1 When sugar molecules (filled circles) are dissolved in a liter of water, the resulting solution occupies a volume greater than a liter. This is because the sugar molecules have taken up some space formerly occupied by water molecules (open circles). Therefore, the concentration of water (number of molecules of water per unit volume) is lower in the sugar-water solution.

number of water molecules present is the same before and after dissolving the sugar in the water.

To compare the concentrations of water in solutions containing different concentrations of dissolved substances, we will use the concept of osmolarity. A solution containing 1 mole of dissolved particles per liter of solution (a 1 molar, or 1 M, solution) is said to have an osmolarity of 1 osmolar (1 Osm), and a 1 millimolar (1 mM) solution has an osmolarity of 1 milliosmolar (1 mOsm). The higher the osmolarity of a solution, the lower the concentration of water. For practical purposes in biological solutions, it doesn't matter what the dissolved particle is; that is, the concentration of water is effectively the same in a solution of0.1 Osm glucose, 0.1 Osm sucrose, or 0.1 Osm urea. To be strictly correct in discussing the concentration of water in various solutions, we would have to speak of the molality, rather than the molarity, of the solutions. Whereas molarity is defined as moles of solute per liter of solution, molality is defined as moles of solute per kilogram of solvent. This definition means that molality takes into account the fact that solutes having a higher molecular weight displace more water per mole of solute than do solutes with a lower molecular weight. That is, a liter of solution containing 1 mole of a large molecule, like a protein, would contain less water (and hence fewer grams of water) than a liter of solution containing 1 mole of a small molecule, like urea. Thus, the molality of the protein solution would be higher than the molality of the urea solution, even though both solutions have the same mol-arity (1 M). For our purposes, however, it will be adequate to treat molarity and osmolarity as equivalent to molality and osmolality.

It is important in determining the osmolarity of a solution to take into account how many dissolved particles result from each molecule of the dissolved substance. Glucose, sucrose, and urea molecules don't dissociate when they dissolve, and thus a 0.1 M glucose solution is a 0.1 Osm solution. A solution of sodium chloride, however, contains two dissolved particles a sodium and a chloride ion from each molecule of salt that goes into solution. Thus, a 0.1 M NaCl solution is a 0.2 Osm solution. To be strictly correct, we would have to take into account interactions among the ions in a solution, so that the effective osmolarity might be less than we would expect from assuming that all dissolved particles behave independently. But for dilute solutions like those we usually encounter in cell biology, such interactions are weak and can be safely ignored. Thus, for practical purposes we will assume that all dissolved particles act independently in determining the total osmolarity of a solution. Under this assumption, then, solutions containing 300 mM glucose, 150 mM NaCl, 100 mM NaCl + 100 mM glucose, or 75 mM NaCl + 75 mM KCl would all have the same total osmolarity 300 mOsm.

When solutions of different osmolarity are placed in contact through a barrier that allows water to move across, water will diffuse across the barrier down its concentration gradient (that is, from the lower osmolar solution to the higher). This movement of water down its concentration gradient is called osmosis. Consider the example shown in Figure 3-2a, which shows a container

Figure 3-2 The effect of properties of the barrier separating two different glucose solutions on final volumes of the solutions. The starting conditions are shown in [a]. (b) If the barrier allows both glucose and water to cross, the volumes of the two solutions do not change when equilibrium is reached. (c) If the barrier allows only water to cross, osmolarities of the two solutions are the same at equilibrium, but the final volumes differ.

Figure 3-2 The effect of properties of the barrier separating two different glucose solutions on final volumes of the solutions. The starting conditions are shown in [a]. (b) If the barrier allows both glucose and water to cross, the volumes of the two solutions do not change when equilibrium is reached. (c) If the barrier allows only water to cross, osmolarities of the two solutions are the same at equilibrium, but the final volumes differ.

divided into two equal compartments that are filled with glucose solutions. Imagine that the barrier dividing the container is made of an elastic material, so that it can stretch freely. If the barrier allows both water and glucose to cross, then water will move from side 1 to side 2, down its concentration gradient, and glucose will move from side 2 to side 1. The movement of water and glucose will continue until their concentrations on the two sides of the barrier are equal. Thus, side 1 gains glucose and loses water, and side 2 loses glucose and gains water until the glucose concentration on both sides is 150 mM. There will be no net change in the volume of solution on either side of the barrier, as shown in Figure 3-2b.

If the barrier in Figure 3-2a allows water but not glucose to cross, however, the outcome will be quite different from that shown in Figure 3-2b. Once again, water will move down its concentration gradient from side 1 to side 2. In this case, though, the loss of water will not be compensated by a gain of glucose. As water continues to leave side 1 and accumulates on side 2, the volume of side 2 will increase and the volume of side 1 will decrease. The accumulating water will exert a pressure on the elastic barrier, causing it to expand to the left to accommodate the volume changes (as shown in Figure 3-2c). The resulting volume changes will increase the osmolarity of side 1 and decrease the osmol-arity of side 2, and this process will continue until the osmolarities of the two sides are equal 150 mOsm. In order to prevent the changes in volume, we would have to exert a pressure against the elastic barrier from side 1 to keep it from stretching. This pressure would be equal to the pressure moving water down its concentration gradient and would provide a measure of the osmotic pressure across the barrier.

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