Covalent and ionic bonds account for the majority of bonds between atoms in molecules and crystals. There are two other interactions that play a lesser role in interactions between atoms and molecules: van der Waals interactions and hydrogen bonds. These are much weaker but nevertheless play an important role in chemical interactions, particularly where water and organic substances are involved.
Van der Waals interactions arise from asymmetric distribution of charge in molecules and crystals. There are three sources for van der Waals interactions: dipole–dipole attraction, induction, and London dispersion forces. As we noted above, many molecules, including water, have permanent dipole moments. When two polar molecules encounter each other, they will behave much as two bar magnets: they will tend to orient themselves so that the positive part of one molecule is closest to the negative part of another (Figure 1.7a). This results in a net attractive force between the two molecules. When the distance between molecules is large compared with the distance between charges within molecules, the energy of attraction can be shown to be:
(1.3)
where U∞ is the interaction energy, μ is the dipole moment, T is temperature (absolute, or thermodynamic temperature, which we will introduce in the next chapter), k is a constant (Boltzmann's constant, which we shall also meet in the next chapter), and r is distance. We do not want to get lost in equations at this point; however, we can infer several important things about dipole–dipole interactions just from a quick glance at it. First, the interaction energy depends inversely on the sixth power of distance. Many important forces, such as electromagnetic and gravitational forces, depend on the inverse square of distance. Thus, we may infer that dipole−dipole forces become weaker with distance very rapidly. Indeed, they are likely to be negligible unless the molecules are very close. Second, the interaction energy depends on the fourth power of the dipole moment, so that small differences in dipole moment will result in large differences in interaction energy. For example, the dipole moment of water (1.84 Debyes) is less than twice that of HCl (1.03 Debyes), yet the dipole interaction energy between two water molecules (716 J/mol) is nearly 10 times as great as that between two HCl molecules (72.24 J/mol) at the same temperature and distance (298 K and 50 pm). Finally, we see that dipole interaction energy will decrease with temperature.
Figure 1.7 Van der Waals interactions arise because of the polar nature of some molecules. Illustrated here are (a) dipole−dipole interactions, which occur when two dipolar molecules orient themselves so oppositely charged sides are closest, and (b) the induction effect, which arises when the electron orbits of one molecule are perturbed by the electromagnetic field of another molecule.
Dipole molecules may also polarize electrons in a neighboring molecule and distort their orbits in such a way that their interaction with the dipole of the first molecule is attractive. This is known as the induction effect (Figure 1.7b). The induction energy also depends on the inverse sixth power of intermolecular distance, but only on the square of the dipole moment of the molecules involved. In addition, another parameter, the polarizability of a molecule, is also needed to describe this effect. In general, the attraction arising from induction is less important than from dipole–dipole interaction. However, because it depends only on the square of dipole moment, the induction attraction can be larger than the dipole–dipole attraction for some weakly dipolar molecules.
Finally, van der Waals forces can also occur as a consequence of fluctuations of charge distribution on molecules that occur on time scales of 10–16 seconds. These are known as London dispersion forces. They arise when the instantaneous dipole of one molecule induces a dipole in a neighboring molecule. As was the case in induction, the molecules will orient themselves so that the net forces between them are attractive.
The total energy of all three types of van der Waals interactions between water molecules is about 380 J/mol, assuming an intermolecular distance of 5 pm and a temperature of 298 K (25°C). Though some interaction energies can be much stronger (e.g., CCl4, 2.8 kJ/mol) or weaker (1 J/mol for He), an energy of a few hundred joules per mole is typical of many substances. By comparison, the hydrogen–oxygen bond energy for each H–O bond in the water molecule is 46.5 kJ/mol. Thus, van der Waals interactions are quite weak compared with typical intramolecular bond energies.
The hydrogen bond is similar to van der Waals interactions in that it arises from nonsymmetric distribution of charge in molecules. However, it differs from van der Waals interactions in a number of ways. First, it occurs exclusively between hydrogen and strongly electronegative atoms, namely oxygen, nitrogen, and fluorine. Second, it can be several orders of magnitude stronger than van der Waals interactions, though still weak by comparison with covalent and ionic bonds. In the water molecule, binding between oxygen and hydrogen results in hybridization of s and p orbitals to yield two bonding orbitals between the O and two H atoms, and two nonbinding sp3 orbitals on the oxygen. The latter are prominent on the opposite side of the O from the hydrogens. The hydrogen in one water molecule, carrying a net positive charge, is attracted by the nonbinding sp3 electrons of the oxygen of another water molecule, forming a hydrogen bond with it (Figure 1.8).
Hydrogen bonds typically have energies in the range of 20–40 kJ/mol. These are much higher than expected for electrostatic interactions alone, and indeed approach values similar to intramolecular bond energies. Thus, there is the suspicion that some degree of covalency is also involved in the hydrogen bond. That is to say, the nonbinding electrons of oxygen are to some degree shared with the hydrogen in another molecule. Hydrogen bonds are perhaps most important in water, where they account for some of the extremely usual properties of this compound, such as its high heat of vaporization, but they can also be important in organic molecules and are present in HF and ammonia as well.
1.5.5 Molecules, crystals, and minerals
1.5.5.1 Molecules
Molecules, which result from the chemical bonds between atoms discussed above, are a familiar concept. By some definitions, they are electrically neutral; charged species consisting of two or more atoms are known as radicals. The properties of molecules are generally quite different from those of their constituent atoms. Carbon dioxide is a good example: the equilibrium form of pure carbon at the room temperature and pressure is a solid, graphite, while that of oxygen is a diatomic gas. The properties of molecules depend on the bond lengths, which depend on the strength of the chemical bond, as well as the geometric arrangement of the atoms. For example, the polar nature of the water molecule, from which many of its unusual properties arise (and which will discuss in Chapter 3), including the formation of hydrogen bonds, is a consequence of the tendency of valence electron pairs surrounding an atom tend to repel each other which results in an arrangement in which the two hydrogens are separated by an angle of 104.45° (Figure 1.8a) and a partial positive charge on the hydrogens and a partial negative one on the other side of the molecule In contrast, the arrangement of atoms in CO2 is
