charges are of opposite sign and positive (repulsive) if of the same sign. The
force is inversely proportional to the square of the distance between the
centers of the chargesðrÞ; this implies that the attractive or repulsive energy
is inversely proportional to the distance, and it can therefore act over a
relatively long range. It is not direction specific, and it is additive. The latter
implies that, if we consider the electrostatic interaction between two
molecules or particles carrying more than one charged group, we must sum
the interactions between any group on the one molecule with all those on the
other molecule.
The Coulomb force also is inversely proportional to the dielectric
constant, and since the latter varies widely among materials (e.g., solvents),
so do the bond energies. For water, the relative dielectric constante&80 at
208 C. This implies that in water the energies involved are smaller by a factor
80 than most tabulated values, which apply to vacuumðe¼ 1 Þ. In water, the
force may be significant up to a range of about 20 nm. In airðe& 1 Þor oil
ðe& 3 Þ, the force can act over a longer range. It should be taken into
account, however, that the presence of electric charges is generally due to
dissociation of ionogenic molecules or groups, and in media of lowesuch
dissociation may not or hardly occur. This is because the ion–ion bonds
themselves are so very strong at low dielectric constant.
Note that eis the relative dielectric constant, i.e., relative to the
absolute dielectric constant (also called dielectric permittivity) of a vacuum,
e 0 , which equals 8: 854? 10 ^12 C?V^1 ?m^1.
Charge-Dipole. Several uncharged molecules bear permanent
dipoles, i.e., the geometric centers of the positive charge(s) and the
negative charge(s) do not coincide. Such molecules therefore have a dipole
moment and they are calledpolar. The dipole moment is the product of
charge (expressed in coulombs) and distance between charges; it is mostly
given in Debye units (D), where 1D¼ 3 : 34? 10 ^30 C?m. Water is the prime
example of a small polar moleculeðdipole moment¼ 1 :85 DÞ; see Figure
3.2a. This polarity is the origin of the high dielectric constant of water and it
also leads to fairly strong bonds between ions and water molecules. Charge-
dipole interactions are always attractive, since the dipole is free to orient in
such a way that the positive ‘‘end’’ of the molecule is close to a cation, etc.
Ions in water, for instance, are accompanied by a few water molecules. Like
ion–ion bonds, charge-dipole interactions are inversely proportional to the
dielectric constant of the medium.
van der Waals Forces. These are ubiquitous: they act between all
molecules and are always attractive (see Section 12.2.1 for an apparent
exception). They may be due to three somewhat different interactions: