Osmotic pressure depends on the number, and not the kind, of solute particles in
solution; it is therefore a colligative property.The osmotic pressure of a given aqueous solution can be measured with an apparatus
such as that depicted in Figure 14-16a. The solution of interest is placed inside an inverted
glass (thistle) tube that has a membrane firmly fastened across the bottom. This part of
the thistle tube and its membrane are then immersed in a container of pure water. As time
passes, the height of the solution in the neck rises until the pressure it exerts just coun-
terbalances the osmotic pressure.
Alternatively, we can view osmotic pressure as the external pressure exactly sufficient
to prevent osmosis. The pressure required (Figure 14-17) is equal to the osmotic pres-
sure of the solution.
Like molecules of an ideal gas, solute particles are widely separated in very dilute solu-
tions and do not interact significantly with one another. For very dilute solutions, osmotic
pressure, , is found to follow the equationnR
VT
In this equation nis the number of moles of solute in volume, V, (in liters) of the solu-
tion. The other quantities have the same meaning as in the ideal gas law. The term n/V
is a concentration term. In terms of molarity, M,MRTOsmotic pressure increases with increasing temperature because Taffects the number of
solvent–membrane collisions per unit time. It also increases with increasing molarity
because Maffects the difference in the numbers of solvent molecules hitting the membrane
from the two sides, and because a higher Mleads to a stronger drive to equalize the
concentration difference by dilution and to increase disorder in the solution. For dilute
aqueous solutions,the molarity is approximately equal to the molality (because the density
of the solution is nearly 1 kg/L), so
mRT (dilute aqueous solutions)
Osmotic pressures represent very significant forces. For example, a 1.00 molal solution
of a nonelectrolyte in water at 0°C produces an equilibrium osmotic pressure of approx-
imately 22.4 atmospheres (330 psi).EXAMPLE 14-13 Osmotic Pressure Calculation
What osmotic pressure would the 1.25 msucrose solution in Example 14-2 exhibit at 25°C?
The density of this solution is 1.34 g/mL.
Plan
We note that the approximation Mmis not very good for this solution, because the density
of this solution is quite different from 1 g/mL or kg/L. Thus, we must first find the molarity
of sucrose, and then use the relationship MRT.
Solution
Recall from Example 14-2 that there is 50.0 g of sucrose (0.146 mol) in 117 g of H 2 O which
gives 167 g of solution. The volume of this solution isvol solution167 g
11
.3m
4L
g125 mL, or 0.125 L
The greater the number of solute
particles, the greater the height to
which the column rises, and the
greater the osmotic pressure.
572 CHAPTER 14: Solutions
For a solution of an electrolyte,
meffectiveRT.
Figure 14-17 The pressure that is
just sufficient to prevent solvent flow
from the pure solvent side through
the semipermeable membrane to the
solution side is a measure of the
osmotic pressure of the solution.
Solution SolventEqual
levelsPressure =
Membrane