A cloud begins forming (a) as water molecules gather 

 around dust (orange) and sulfuric acid (green) impuri- 

 ties in the air. Attracted by intermolecular forces, more 

 molecules join the cluster (b). Eventually the cluster 

 reaches a critical size — about 50 molecules — of less 

 than 1 nanometer (c). Until this stage, the collection of 

 molecules is highly unstable and may break up. Getting 

 over the energy barrier of the critical cluster constitutes 

 a phase transformation from gas to liquid. The growth 

 process takes off (d) eventually resulting in condensation 

 nuclei, made up of particles that differ in size by a factor 

 of ten or even a thousand. A cloud droplet (e) ultimately 

 emerges, made of 10' 5 molecules; it may eventually grow 

 into a raindrop (f) of 10 20 molecules. 



centers of negative electronic charge, which cluster at the 

 opposite two corners of the tetrahedron. 



When the two water molecules are brought together, 

 opposite charges attract. One of the sites of positive 

 charge — a hydrogen atom — in one molecule becomes 

 attracted to one of the negatively charged sites associ- 

 ated with the oxygen atom in the second molecule. This 

 attractive interaction is known as a hydrogen bond. In 

 liquid water, each molecule often forms four hydrogen 

 bonds. Two of them link the two hydrogen atoms with 

 the oxygen atoms of two other water molecules [see 

 illustration on page 33]. The other two hydrogen bonds 

 link the oxygen atom with hydrogen atoms of two more 

 water molecules. Those bonds give rise to a stable net- 

 work of tetrahedral water molecules. In the liquid the 

 network extends only locally, and the hydrogen bonds 

 continually break and re-form. But in ice, the network 

 of tetrahedrons extends over a long range and becomes 

 a relatively unchanging lattice. 



Within a network of tetrahedrons, the number of ways 

 incident energy can create rotations, twists, vibrations, 

 and suchlike significantly rises. Each new mode of motion 

 provides an additional degree of freedom, and so the heat 

 capacity of the network far exceeds the heat capacity of 

 a single constituent molecule. Note, though, that many 



other molecules, including other triatomic molecules 

 such as carbon disulfide (CS2), also form linked networks 

 whose heat capacity far exceeds the heat capacity of one 

 of their constituent molecules. 



In fact, although it is not widely appreciated, the heat 

 capacity of water, even within a linked network having 

 many degrees of freedom, is not unusually large — pro- 

 vided the heat capacities are stated in units of energy per 

 molecule or per mole, which is 6.02 X 10 23 molecules of 

 the substance. On that basis, the heat capacity of water 

 is about the same as that of other triatomic molecules. 

 In the appropriate units, for instance, the heat capacity 

 of water is 75.3, whereas the heat capacity of carbon 

 disulfide is 75.7. 



Only when heat capacity is measured in the amount of 

 energy per unit mass does the heat capacity of water look 

 anomalously large. The reason is that the molecular mass 

 of water is small compared with that of other triatomic 

 molecules. Expressed in those units, the heat capacity of 

 H2O is more than four times that of CS2. 



The study of the various configurations ot the hydrogen 

 bond has made it possible for molecular scientists to explain 

 a number of other anomalies of water. For example, in ice, 

 the hydrogen bonds tend to be slightly longer than they 

 are in the liquid phase, resulting in a larger volume and 



November 2007 natural HISTORY 



35 



