242 Chapter 7. Entropic forces at work[[Student version, January 17, 2003]]
awater molecule. Get a few dozen friends to assume the same pose. Now instruct everyone to
grab someone’s ankle with each hand (this works better in zero gravity). Now you’re an ice crystal
(Figure 7.12b).
X-ray crystallography reveals that ice really does have the structure shown in Figure 7.12. Each
oxygen is surrounded by four hydrogen atoms. Two are at the distance 0.097nmappropriate for a
covalent bond, while the other two are at a distance 0. 177 nm.The latter distance is too long to be
acovalent bond, but much shorter than the distance 0. 26 nmwe’d expect from adding the radii of
atomic oxygen and hydrogen. Instead, it reflects the fact that the hydrogen has been stripped of
its electron cloud; its size is essentially zero. (One often sees the “length of the H-bond” in water
quoted as 0. 27 nm.This number actually refers to the distance between the oxygen atoms, that is,
thesumof the lengths of the heavy and dashed lines in Figure 7.12a.)
The energy of attraction of two water molecules, oriented to optimize their H-bonding, is inter-
mediate between a true (covalent) chemical bond and the generic attraction of any two molecules;
this is why it gets the separate name “H-bond.” More precisely, when two isolated water molecules
(in vapor) stick together, the energy change is about− 9 kBTr.For comparison, the generic
(van der Waals) attraction between any two small neutral molecules is typically only 0.6–1.6kBTr.
True chemical bond energies range from 90–350kBTr.
The hydrogen bond network of liquid water The network of H-bonds shown in Figure 7.12
cannot withstand thermal agitation when the temperature exceeds 273K:Ice melts. Even liquid
water, however, remains partially ordered by H-bonds. It adopts a compromise between the ener-
getic drive to form a lattice and the entropic drive to disorder. Thus instead of a single tetrahedral
network, we can think of water as a collection of many small fragments of such networks. Ther-
mal motion constantly agitates the fragments, moving, breaking, and reconnecting them, but the
neighborhood of each water molecule still looks approximately like the figure. In fact, at room tem-
perature each water molecule maintains most of its H-bonds (on average about 3.5 of the original
4atanygiven time). Because each water molecule still has most of its H-bonds, and these are
stronger than the generic attractions between small molecules, we expect that liquid water will be
harder to break apart into individual molecules (water vapor) than other liquids of small, but not
H-bonding, molecules. And indeed, the boiling point of water is 189Khigher than that of the small
hydrocarbon molecule ethane. Methanol, another small molecule capable of makingoneH-bond
from its OH group, boils at an intermediate temperature, 36Klower than water (with two H-bonds
permolecule). In short:
Hydrogen bonds increase thecohesive forcesbetween the molecules of water
relative to those between other small molecules.(7.32)
Hydrogen bonds as interactions within and between macromolecules in solution Hy-
drogen bonds will also occur between molecules containing hydrogen covalently bonded toany
electronegative atom (specifically oxygen, nitrogen, or fluorine). Thus not only water, but also
alcohol and many of the molecules described in Chapter 2 can interact via H-bonding. We cannot
directly apply the estimates just given for H-bond strength to the water environment, however.
Suppose that two parts of a macromolecule are initially in direct contact, forming an H-bond (for
example, the two halves of a DNA basepair, Figure 2.13 on page 42). When we separate the two
parts, their H-bond is lost. But each of the two will immediately form H-bonds with surrounding
water molecules, partially compensating for the loss! In fact, thenet free energy cost to break