Physical Chemistry , 1st ed.

Although 0.010 molal is not a very concentrated solution, the predicted

osmotic pressure effects are substantial.

Osmotic pressure considerations have some important applications. One is

in biology. A cell membrane is a semipermeable membrane. Therefore, osmotic

pressures on either side of the membrane must be very close to equal, or the

effects of osmotic pressure may cause cells to either collapse or expand due to

transfer of H 2 O from regions of low concentrations to high concentrations.

Either expansion or collapse can kill the cell. Figure 7.30 shows photographs

of red blood cells in solutions of higher, equal, and lower osmotic pressures.

Osmotic pressure effects also explain why people stranded in lifeboats on the

ocean cannot safely drink the seawater. Its osmotic pressure is too high, and

drinking it will cause one’s cells to literally dehydrate, rather than hydrate.

Osmotic pressure is also a factor in delivering water from the roots of trees

to the leaves in their tops, which might be dozens or even hundreds of feet

from the ground. It is also important in keeping nonwoody plants sturdy and

upright, and uncooked vegetables crisp and crunchy.

Osmotic pressure can be used to determine the average molecular weights

of macromolecules and polymers. As Example 7.15 showed, significant os-

motic pressure effects do not require a large concentration. Relatively dilute

solutions can show measurable osmotic effects, which allow one to calculate

the molality of the solution and, stepwise, the molecular weight of the solute.

Of course, if the high-molecular-weight polymer is even slightly impure, the

number of presumably lower-molecular-weight impurities will dramatically

affect the final determination. Again, this is because osmotic pressure is a

colligative property, which depends only on the number of molecules, not their

identities, in the solution.

Example 7.16

An aqueous poly(vinyl alcohol) solution that is made by dissolving 0.0100 g of

polymer in 1.00 L of water has an osmotic pressure of 0.0030 bar. What is the

average molecular weight of the polymer? Assume 298 K, and also assume that

the volume of the solvent does not change appreciably when the solute is added.

Solution

Using the van’t Hoff equation, we set up the following expression:

(0.0030 bar)Vxsolute0.08314 

m

L

o

b

l

a

K

r

298 K

We still need Vand xsolute. But since the mole fraction of the solute is so

small, we can approximate that

xso

V

lute

V

n

so

so

lu

lu

ti

t

o

e

n

molarity of solution

(Notice that we are no longer using the molar volume,V.) We can therefore

determine the molarity of the solution by rearranging the equation to

molarity nso

V

lute

Working out the numbers and the units, we find that

molarity 0.000123 

m

L

ol



0.0030 bar



(0.08314 mLoblaKr) 298 K

200 CHAPTER 7 Equilibria in Multiple-Component Systems

Figure 7.30 Demonstration of the effects of

osmotic pressure on red blood cells. If the os-

motic pressures inside and outside the cell are

equal, the cells look normal. However, if the os-

motic pressure outside the cell is too low, the cells

swell; if it is too high, the cells shrivel. Neither sit-

uation is good for the body.

© David Phillips/Science Source/Photo Researchers, Inc.