Concise Physical Chemistry

c12 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

194 SOLUTION CHEMISTRY

but the mole fraction of the solute tends towardn 2 /n 1 at small concentrations, so

π

V

n 1

=RT

n 2

n 1

orπV=n 2 RT, which has the form, but not the content or meaning, of the ideal gas

law. This is called the van’t Hoff equation for osmotic pressure (as distinct from the

van’t Hoff equation for equilibrium).

12.9 COLLIGATIVE PROPERTIES

If we calculate molality m from the formula weight of solute—for example,

NaCl—and use it in the equation for osmotic pressure, we shall be wrong. Os-

motic pressureπ, like
p,
Tb, and
Tf,isacolligativeproperty because it is a

property of thenumber of particlesin solution. Our error results from two factors:

First, the number of solute particles in solution may double or triple due to ionization;

and, second, thefreesolvent concentration may be reduced by solvation.

If NaCl is the nonvolatile solute in water for example, there will be an effective

molality approximately two times the anticipated value because NaCl exists as Na+

ions and Cl−ions in aqueous solution. The number of particles in solution is thevan’t

Hoff i factor,2 for NaCl solutions, 1 for sucrose, which does not ionize, 3 for ZnCl 2 ,

and so on. Van’t Hoffifactors are, however, integers only at infinite dilution.

In real solutions, van’t Hoffifactors show a systematic deviation from integral

values due to strong solvation (hydration) of the molecules or ions. When there is

a strong association between a solute molecule and solvent molecules, the solvent

molecules are effectively “taken away” from the solution. The amount of free solvent

is reduced and the relative amount of solute isgreaterthan we conventionally calculate

it to be. The measured change in colligative properties is augmented.

The freezing points of aqueous solutions of NH 3 , which is not ionized to any

appreciable extent, are shown in Fig. 12.7. The freezing point of water decreases

with ammonia concentration according to the van’t Hoff equation
Tf=− 1. 86 mto

aboutm∼= 4 .0 but then the freezing point becomes more negative than theory predicts,

as though the solution were more concentrated than it actually is. The effective

molality (Zavitsas, 2001) is reduced tom 1 −hm 2 , wherehis a parameter called

the solvation number, which gives the number of solvent molecules held so tightly

by solute as to be ineffective. In water solution,his called thehydration number.

The solvation numberhis not an integer because it is an average over many solute

molecules or ions. It is not difficult to determineh; it is just an empirical parameter

chosen to cause real colligative behavior to approach the van’t Hoff equation. In the

case of ammonia dissolved in water, the choiceh=1.8 leads to the function shown

by open circles in Fig. 12.7. These experimental freezing points differ from those

shown by solid circles only in that the molalities have been recalculated as moles of

solute per kilogram offreewater remaining after the solute has been hydrated.