Why Atoms Bond: Valence and Octet/Duet Rules
Atoms bond because the resulting arrangement has lower energy and is more stable than the separate atoms, and most main-group atoms tend to reach a stable outer shell of eight valence electrons (the octet rule), or two for hydrogen and helium (the duet rule). In brief: sodium loses one electron and chlorine gains one so that both have the electron arrangement of a noble gas, while two hydrogen atoms share a pair of electrons so that each has the two electrons of helium; in both cases, energy is released when the bond forms.
The study of chemical bonding explains why substances have the formulas and properties they have. Valence electrons, which are those in the outermost shell, are the only electrons that take part. This article explains why bonding lowers energy, how the octet and duet rules arise from the stability of noble gas configurations, describes the three main types of bond, shows how the number of valence electrons predicts the bonds an atom forms, works through examples and gives the history of the octet idea.
Why does bonding lower the energy?
Consider two hydrogen atoms that approach each other. At a large distance, they do not interact. As they come closer, each nucleus attracts the electron of the other atom, and the potential energy decreases. If the atoms get too close, the repulsion between the two positive nuclei and between the electrons becomes strong, and the energy rises sharply. The minimum of the energy curve is at a distance of 74 pm, which is the bond length of H2. At this point, the energy is 436 kJ/mol lower than that of two separate atoms. This is the bond energy, and it is the energy that has to be supplied to break the bond. In general, a bond forms when the attractions between nuclei and electrons in the product outweigh the repulsions, giving a lower total energy.
What are the octet and duet rules?
The noble gases (except helium) have eight electrons in the outer shell, and they are unreactive and very stable. Atoms of other main-group elements tend to gain, lose or share electrons until they have eight valence electrons, which is the octet rule. Hydrogen and the other very small atoms near helium tend to reach two electrons, the duet rule, since the first shell holds only two electrons. For example:
- Sodium (2, 8, 1) loses one electron and becomes Na+ (2, 8), like neon.
- Chlorine (2, 8, 7) gains one electron and becomes Cl− (2, 8, 8), like argon.
- Oxygen (2, 6) shares two electrons in water or gains two to form O2−, in each case reaching eight.
- Hydrogen (1) shares one electron to reach two, as in H2, or gains one in hydrides such as LiH.
What are the main types of bond?
| Type | Between | Electron behavior | Example |
|---|---|---|---|
| Ionic | Metal and nonmetal | Electrons transferred; ions attract | NaCl, MgO |
| Covalent | Nonmetal and nonmetal | Electron pairs shared | H2O, CO2, CH4 |
| Metallic | Metal atoms | Valence electrons delocalized across the lattice | Cu, Fe, Na |
These are idealized cases. Many bonds are intermediate, such as polar covalent bonds, in which sharing is unequal.
Valence electrons and typical bonding
| Group | Valence electrons | Typical ionic behavior | Typical number of covalent bonds |
|---|---|---|---|
| 1 | 1 | Lose 1, form 1+ | 1 (H) |
| 2 | 2 | Lose 2, form 2+ | 2 (Be, in some compounds) |
| 13 | 3 | Lose 3 (Al3+) | 3 (B) |
| 14 | 4 | Seldom ions | 4 (C, Si) |
| 15 | 5 | Gain 3 (N3−) | 3 (N, P) |
| 16 | 6 | Gain 2 (O2−) | 2 (O, S) |
| 17 | 7 | Gain 1 (Cl−) | 1 (F, Cl) |
| 18 | 8 (He 2) | None | 0 |
The number of covalent bonds a nonmetal forms is usually 8 minus the number of its valence electrons (for groups 14 to 17), or equal to the number of electrons it needs to complete its octet: carbon needs 4, nitrogen 3, oxygen 2 and chlorine 1. Hydrogen needs 1.
How can you predict the type of bond?
- A metal and a nonmetal usually form an ionic bond, because the metal’s ionization energy is low and the nonmetal’s electron affinity is high.
- Two nonmetals form covalent bonds, since neither atom easily gives up electrons.
- Two metals form a metallic bond.
- The difference in electronegativity gives a more quantitative guide: a difference of more than about 1.7 suggests ionic character, and less than about 0.4 suggests a nonpolar covalent bond.
Worked examples
- Magnesium and oxygen. Mg (2, 8, 2) loses 2 electrons to become Mg2+ (2, 8). O (2, 6) gains 2 to become O2− (2, 8). The ions are in a 1 : 1 ratio, so the compound is MgO.
- Calcium and chlorine. Ca loses 2 electrons, and each Cl gains 1. Two chlorine atoms are needed, so the formula is CaCl2.
- Nitrogen and hydrogen. N has 5 valence electrons and needs 3 more. Each H needs 1. Three hydrogen atoms share one pair each with nitrogen: NH3. Nitrogen has 3 shared pairs and 1 lone pair, a total of 8 electrons, and each hydrogen has 2.
- Counting electrons in methane. Carbon has 4 valence electrons and each of 4 hydrogen atoms has 1, so the molecule has 8 valence electrons. In CH4, carbon is surrounded by 4 shared pairs (8 electrons), and each hydrogen shares one pair (2 electrons).
- Energy released by H2 formation. Forming 1 mol of H2 from atoms releases 436 kJ. For 1.008 g of hydrogen atoms (1 mol H atoms, which forms 0.5 mol of H2), the energy released is 0.5 × 436 = 218 kJ.
- Why helium does not bond. Helium has 2 valence electrons, which fill its only shell, so it has no tendency to gain, lose or share electrons.
What are the limits of the rules?
The octet rule is a guide that works well for the elements of the second period, especially carbon, nitrogen, oxygen and fluorine. It has exceptions. Some molecules have fewer than eight electrons around the central atom (BF3), some have an odd number of electrons (NO) and some of the heavier elements have more than eight (SF6). Transition metals follow an 18-electron rule more often. These cases are described in a later article.
Who proposed the octet rule?
In 1916, Gilbert N. Lewis proposed that atoms bond by sharing electron pairs to complete a stable group of eight, with his “cubical atom” model, and introduced the dot diagrams now named after him. In the same year, Walther Kossel proposed that ionic bonds form by the transfer of electrons to reach noble gas configurations. In 1919 and 1920, Irving Langmuir extended the ideas and introduced the terms octet and covalent bond. Linus Pauling later put the theory on a quantum mechanical basis in the 1930s.
Which mistakes are common?
Mistake 1: Thinking that atoms bond “to be happy”
Atoms bond because the bonded state has lower energy. The octet is a consequence, not a goal.
Mistake 2: Saying that bonding takes energy
Breaking bonds requires energy. Forming bonds releases energy.
Mistake 3: Applying the octet rule to hydrogen
Hydrogen follows the duet rule, with two electrons.
Mistake 4: Treating the octet rule as a law
It is a useful guide with exceptions, especially for the heavier elements.