272 Chapter 8. Chemical forces and self-assembly[[Student version, January 17, 2003]]
negative spots, as does water itself: They are polar molecules. Polar molecules can participate at
least partially in the hydrogen-bonding network of water, so there is little hydrophobic penalty when
weintroduce such intruders into pure water. Moreover, the energy cost of breaking the attraction
of their plus ends to their neighbors’ minus ends (thedipole interaction)isoffset by the gain
of forming similar conjunctions with water molecules. Since again an entropic gain always favors
mixing, we expect polar molecules to be highly soluble in water.^4 Indeed based on this reasoning,
anysmall molecule with the highly polarhydroxyl,or–OH, group found in alcohol should be soluble
in water, and indeed it’s generally so. Another example is the amino, or –NH 2 group, for example
the one on methylamine. On the other hand, nonpolar molecules, like hydrocarbons, exact such a
high hydrophobic penalty that they are poorly soluble in water.
In this book we won’t develop the quantum-mechanical tools to predict a priori whether a
molecule will dissociate into polar components. This isn’t such a serious limitation, however. Our
attitude to all these observations will be simply that there is nothing surprising about the ionic
dissociation of a group in water; it’s just another simple chemical reaction, to be treated by the
usual methods developed in this chapter.
8.3.2 The strengths of acids and bases reflect their dissociation equilib-
rium constants
Section 7.4.1 discussed the diffuse charge layer that forms near a macromolecule’s surface when it
dissociates (breaks apart) into a large macroion and many small counterions. The analysis of that
section assumed that a constant number of charges per area,σq/e,always dissociated, but this is
not always a very good assumption. Let’s discuss the problem of dissociation in general, starting
with small molecules.
Water is a small molecule. Its dissociation reaction is
H 2 OH++OH−. (8.23)
Section 8.3.1 argued that reactions of this type need not be prohibitively costly, but still the
dissociation of water does cost more free energy than that of NaCl. Accordingly the equilibrium
constant for Reaction 8.23, while not negligible, is rather small. In fact, pure water hascH+ =
cOH−=10−^7 M.(These numbers can be obtained by measuring the electrical conductivity of pure
water; see Section 4.6.4 on page 127.) Since the concentration of H 2 Oisessentially fixed, the Mass
Action rule says that water maintains a fixed value of the “ion product,” defined as
Kw≡[H+][OH−]=(10−^7 )^2. ion product of water (8.24)Suppose we now disturb this equilibrium, for example by adding some hydrochloric acid. HCl
dissociates much more readily than H 2 O, so the disturbance increases the concentration of H+from
the tiny value for pure water. But Reaction 8.23 is still available, so its Mass Action constraint must
still hold in the new equilibrium, regardless of what has been added to the system. Accordingly,
the concentration of hydroxyl OH−ions must go down to preserve Equation 8.24.
Let’s instead add some sodium hydroxide (lye). NaOH also dissociates readily, so the disturbance
increases the concentration of OH−.Accordingly, [H+]must go down: The added OH−ions gobble
up the tiny number of H+ions, making it even tinier.
(^4) Westill don’t expect sugar tovaporizereadily, the way a small nonpolar molecule like acetone does. Vaporization
would break attractive dipole interactionswithoutreplacing them by anything else.