The combining power of a chemical element for other elements as measured by the number of bonds to other atoms that one atom of the given element forms upon chemical combination; also known as valency. Valence theory concerns all the physical and chemical properties of molecules that especially depend on molecular electronic structure.
Thus, in water, H2O or
the valence of each hydrogen atom is 1; the valence of oxygen, 2. In methane, CH4 or
the valence of hydrogen again is 1; of carbon 4. In sodium chloride, NaCl, and carbon tetrachloride, CCl4, the valence of chlorine is 1, and CH2 the valence of carbon is 2.
Much more is known about a water molecule than that it contains two hydrogen atoms and one oxygen atom. Each OH distance is 9.57 nanometers and the HOH bond angle is 104°27′. The oxygen and hydrogen ends of the molecule are negatively and positively charged, giving it a dipole moment 1.84 × 10−18 electrostatic unit (esu). The molecule absorbs infrared light strongly but is transparent to visible light. Scientists have provided quantitative understanding of these properties and many more in terms of the fundamental theory of quantum mechanics. See also: Bond angle and distance; Quantum chemistry
Combining power of an element
By the 1920s the most important facts about atoms had been established experimentally. A neutral atom of atomic number Z comprises a massive nucleus of charge +Ze and Z very light electrons, each of charge −e, where e = 4.80 × 10−10 esu; most of the space within the atom is empty. Atomic nuclei are immutable through ordinary chemical changes; when one molecule of hydrogen (H2) combines with one molecule of chlorine (Cl2) to give two molecules of hydrogen chloride (HCl), the four nuclei (two hydrogen nuclei, or protons, of charge +1e and two chlorine nuclei of charge +17e) are unchanged. It is redistribution of electrons between atoms which constitutes chemical combination. This is what valences of atoms control, and this is what a theory of valence must explain.
Atomic structure
Understanding of molecule formation requires an understanding of the electronic structure of atoms. According to N. Bohr, electrons in an atom move in orbits much like the orbits of planets about a sun, held to the nucleus by electrical attractions for it, prevented from falling into it by centrifugal forces. A special quantum effect is operative at the atomic level, however, which possesses no analogy in the motions of planets; not all orbits are possible for an electron, but only those for which the angular momentum of the electron as it moves about the nucleus is an integer multiple of , where h = 6.63 × 10−34 J is Planck's constant, and for which the energy is similarly quantized. Furthermore, not more than two electrons can move in one orbit at once. See also: Atomic structure and spectra; Electron configuration
When the consequences of these ideas are worked out, there actually emerges the periodic classification of the elements. To cover just part of the periodic table, occupation of orbits by electrons in the lighter atoms are shown in the table, where the symbol 2p stands for three distinct orbits of the same energy and shape but differently oriented in space. The lowest energy orbit is 1s, forming the K shell. Next in energy are 2s and 2p, making up the L shell. The 3s state is still higher, in the M shell. The chemically inert gases helium (He) and neon (Ne) are characterized by closed shells of 2, and 2 + 8 = 10 electrons, respectively. The next inert gas is argon (Ar), with a closed shell of 2 + 8 + 8 = 18 electrons, followed by krypton (Kr) with 2 + 8 + 18 + 8 = 36 electrons, and the others. See also: Inert gases; Periodic table
| Orbit | ||||||||
|---|---|---|---|---|---|---|---|---|
| K shell | L shell | M shell | ||||||
| Atom | Z | 1s | 2s | 2p | 3s | 3p | 3d | |
| Hydrogen | (H) | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| Helium | (He) | 2 | 2 | 0 | 0 | 0 | 0 | 0 |
| Lithium | (Li) | 3 | 2 | 1 | 0 | 0 | 0 | 0 |
| Beryllium | (Be) | 4 | 2 | 2 | 0 | 0 | 0 | 0 |
| Boron | (B) | 5 | 2 | 2 | 1 | 0 | 0 | 0 |
| Carbon | (C) | 6 | 2 | 2 | 2 | 0 | 0 | 0 |
| Nitrogen | (N) | 7 | 2 | 2 | 3 | 0 | 0 | 0 |
| Oxygen | (O) | 8 | 2 | 2 | 4 | 0 | 0 | 0 |
| Fluorine | (F) | 9 | 2 | 2 | 5 | 0 | 0 | 0 |
| Neon | (Ne) | 10 | 2 | 2 | 6 | 0 | 0 | 0 |
| Sodium | (Na) | 11 | 2 | 2 | 6 | 1 | 0 | 0 |
| Magnesium | (Mg) | 12 | 2 | 2 | 6 | 2 | 0 | 0 |
| Aluminum | (Al) | 13 | 2 | 2 | 6 | 2 | 1 | 0 |
Rule of eight
Many of the simple facts of valence follow from the postulate that atoms combine in such a way as to seek closed-shell or inert-gas structures (rule of eight) by the transfer of electrons between them or the sharing of a pair of electrons between them. Many molecular structures may be obtained by inspection by using these rules. The electrons in the K shell are not involved in the bonding for atoms after He, nor are the electrons in the K and L shells for atoms following Ne.
Hydrogen has a valence of 1, because one more electron will give a hydrogen atom an inert-gas structure. Carbon can form four bonds, because four more electrons give it the neon electronic structure.
Bond types
The bond between two atoms is covalent if one electron in the bonding electron pair comes from each atom, as in H:H or the CH bonds in CH4. It is coordinate covalent if both electrons come from one atom, as the boron-nitrogen bond in the compound F3B
NH3. If there is complete transfer of electrons from one atom to another, the bond is electrovalent or ionic, as in sodium fluoride (NaF). Bonds intermediate in type are possible; the bond in hydrogen fluoride (HF) is between covalent and ionic. An ionic bond X+Y− will be more stable the less the ionization potential of X and the greater the affinity of Y for electrons, that is, when X is a metallic element from the lower left corner of the periodic table and Y is a nonmetallic element from the upper right corner. Bond type can be inferred from both chemical and physical evidence. See also: Chemical bonding; Electronegativity
Bonds involving one or three electrons are known, but they are rare; H2+ and HeH are examples. Multiple bonds between atoms are common and important; examples are the carbon-carbon bond and the carbon-oxygen bonds in ethylene and carbon dioxide. For discussion of a bond of special importance in biology See also: Hydrogen bond .
Valence electrons are the electrons of an atom that can participate in chemical bonding, for example, for H and He the 1s electrons, for Li through Ne the 2s and 2p electrons, and for Na the 3s electrons.
Oxidation-reduction
As generally used, the word valence is ambiguous. Before a value can be assigned to the valence of an atom in a molecule, the electronic structure of the molecule must be known exactly, and this structure must be describable simply in terms of simple bonds. In practice, neither of these conditions is ever precisely fulfilled. A term not so ambiguous is oxidation number or valence number. Oxidation numbers are useful for the balancing of oxidation-reduction equations, but they are not related simply to ordinary valences. Thus the valence of carbon in CH4, CHCl3, and CCl4 is 4; oxidation numbers of carbon in these three substances are −4, +2, and +4. See also: Oxidation-reduction
Quantum theory of valence
The above simple theory of valence is inadequate in at least three ways. First, it fails to account for many experimental facts, such as why the six CC bonds in the molecule benzene, C6H6, are physically and chemically equivalent, what the electronic structures of the boron hydrides are, why the HH bond is much stronger than the CC bond, why CO2 is a linear molecule but H2O nonlinear, and what principles govern the rates of chemical combination. Second, the explanations that are offered are not physically satisfying. The stability conferred upon a molecule by the sharing of a pair of electrons by two atoms is established, but what is the real origin of this stability? And third, the theory is not detailed or quantitative enough to allow correlation and prediction of the many different properties of molecules. Dozens of properties of molecules can be measured, many to a high degree of accuracy. The ultimate theory should account for all of these quantitatively. See also: Molecular structure and spectra
The quantum theory of valence does not possess these faults. It is based on the precise laws of physics for the atomic domain that were formulated in the 1920s by E. Schrödinger and others, the discipline known as quantum mechanics. The primitive quantum ideas of M. Planck and N. Bohr require modification to take care of the experimental fact that electrons and other particles at times act like waves. Like waves, they interfere when they are on top of one another in a manner that can be precisely calculated. According to nineteenth-century physics, an electron moving about a proton would collapse onto it. In the Bohr theory this collapse is prevented by a special quantum hypothesis; in the new mechanics it is prevented by elementary energy considerations. It would be favored by the attractive potential energy of the particle pair, but it turns out to be catastrophic for their kinetic energy. Instead of collapse a compromise is reached; the electron, or wave, is smudged out over a region surrounding the nucleus which defines the atomic size. See also: Quantum mechanics; Uncertainty principle
The pattern of the periodic table comes out as before. The orbits of Bohr are replaced by other entities, orbitals, which represent not the paths of the electrons but the amplitudes of the electron waves at different points in space. Furthermore, electrons are treated as if they were spinning, but only in two possible ways. The rule that generates the periodic table then is that in an atom no two electrons can occupy the same atomic orbital with the same spin. See also: Exclusion principle
In a chemical bond, again there is interplay of kinetic and potential energies. An electron pair will tend to be shared by two atoms instead of being located on one of them if that situation is energetically favorable. The region between nuclei is more favorable for the potential energy of electron-nuclear attraction than other regions the same distance from just one nucleus. Moving in this region is not as favorable for the kinetic energy as moving on individual atoms, but the potential energy predominates when a bond is formed. The normal covalent bond may be described as two electrons occupying one molecular orbital, rather than two distinct atomic orbitals, with opposite spins because the exclusion principle is still operative. See also: Molecular orbital theory
When a detailed examination is made of these effects with the modified theory, the stabilities of actual molecules and other of their properties are quantitatively accounted for. In particular, if two atoms approach which have low-energy atomic orbitals which overlap each other in space, and if two electrons are available, the conditions are favorable for forming, with evolution of heat, a chemical bond. It follows that the valence of an atom is given by the number of unpaired electrons it possesses, an old basic rule of valence.
The greater the overlap between two atomic orbitals, the stronger the bond that can be formed with them (criterion of maximum overlapping). This condition may be regarded as determining the shapes of molecules. Two or more orbitals of comparable energy, as 2s and 2p orbitals, can be combined (hybridized) to give orbitals concentrated along certain directions in space, and these are the orbitals that participate in directed bond formation. In the carbon atom, for instance, the four electrons in the 2s and 2p subshells are potential valence electrons. The two 2s electrons are paired, however, so that to make four bonds possible one of these must be promoted to a vacant 2p orbital. Four bonds then are possible, in different directions. Four equivalent bonds can be formed, tetrahedrally directed, as in CH4. Three bonds in a plane and one other less strong one can be formed, as in H2C
CH2. In this manner L. Pauling and others have accounted for a multitude of phenomena in stereochemistry. See also: Stereochemistry
The peculiar bonding in benzene and other aromatic molecules has been explained, together with its consequences for chemical reactivity. The principles governing reaction rates have been formulated and applied. See also: Benzene; Delocalization; Resonance (molecular structure)
Research in valence theory has led to general and complete understanding of most aspects of molecular electronic structure, and has contributed toward acceptance of the language of modern physics as a proper language for chemistry. Considerable research in this field continues, however, because substances with new types of bonds are being synthesized constantly, and new physical methods for studying molecules are constantly revealing more intimate details of molecular structure which demand explanation. See also: Chelation; Chemical dynamics; Conjugation and hyperconjugation; Coordination chemistry; Ligand field theory; Organic chemistry; Organometallic compound; Structural chemistry
