# Lewis Structures

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In 1902, while trying to find a way to explain the Periodic Table to his students, the chemist Gilbert Newton Lewis discovered that the chemistry of the main-group elements could be explained using a model in which electrons arranged around atoms are conceived as occupying the faces of concentric cubes. This model was based on four assumptions.

1. The number of electrons in the outermost cube of an atom is equal to the number of electrons lost when the atom forms positive ions;
2. each neutral atom has one more electron in its outermost cube than the atom that precedes it in the Periodic Table;
3. it takes eight electrons—an octet—to complete a cube;
4. once an atom has an octet of electrons in its outermost cube, the cube becomes part of the cote of electrons about which the next cube is built.

Lewis determined the formulas of simple ionic compounds (such as NaCI) by theorizing that atoms gain electrons if the outermost cube is more than half full, and lose electrons if the cube is less that half-full (until the cube is either full or empty). Sodium, for example, loses the one electron in its outermost cube at the same time that chlorine gains the electron it needs to fill its outermost cube.

As understanding of the structure of the atom developed, it became apparent why the magic number of electrons for each of the main-group elements was eight. The outermost atomic orbitals for these elements are the s and p orbitals in a given shell, and it takes eight electrons in its outermost shell: [He] 2 s 2 2 p 3 . It therefore has to gain three electrons to fill this shell.

The electrons in an outermost shell are known as valence electrons. The number of bonds an element can form is called valence (from the Latin valens, "to be strong"). An atom's valence electrons are those electrons that can be gained or lost in a chemical reaction. Because the electrons that occupy filled d or f subshells are seldom disturbed in a chemical reaction, we can also define an atom's valence electrons as the electrons that are not present in an atom of the preceding rare gas (ignoring filled d or f subshells). Gallium, for example, has the following electron configuration: [Ar] 4 s 2 3 d 10 4 p 1 . The 4 s and 4 p electrons can be lost in a chemical reaction, but the electrons in the filled 3 d subshell cannot. Gallium therefore has three valence electrons.

By 1916 Lewis realized that there was another way that atoms can combine to achieve an octet of valence electrons: They can share electrons and form a covalent bond . Two fluorine atoms, for example, by sharing a pair of electrons can form a stable F 2 molecule in which each atom has an octet of valence electrons. A pair of oxygen atoms, by sharing two pairs of electrons, can form an O 2 molecule in which each atom has a total of eight valence electrons.

Whenever Lewis applied his model to covalent compounds, he noted that the atoms seemed to share pairs of electrons. He also noted that most compounds contained even numbers of electrons, which suggested that electrons exist in pairs. He therefore replaced his cubic model of the atom, in which eight electrons were oriented toward the surfaces of a cube, with a model based on pairs of electrons. In this notation, each atom is surrounded by up to four pairs of dots, corresponding to the eight possible valence electrons. This symbolism is still in use today. The only significant modification is the use of lines to indicate covalent bonds formed by the sharing of a pair of electrons. The Lewis structures for F 2 and O 2 are written as follows:

The prefix "co-" is used to indicate that two or more entities are joined or have equal standing (as in, for example, coexist, cooperate, and coordinate ). It is therefore appropriate that the term "covalent bond" is used to describe molecular bonds that result from the sharing of one or more pairs of electrons.

The Lewis structure of a compound can be arrived at by trial and error. We start by notating symbols that contain the correct number of valence electrons for the atoms in the molecule. We then pair electrons to indicate covalent bonds until we come up with a Lewis structure in which each atom (with the exception of hydrogen atoms) has an octet of valence electrons. The trial-and-error method for writing Lewis structures can be time-consuming, however. For all but the simplest molecules, the step-by-step process is faster.

Step 1: Determine the total number of valence electrons.

Step 2: Write the skeleton structure of the molecule.

Step 3: Assign two valence electrons to each covalent bond in the skeleton structure.

Step 4: Try to complete the octets of the atoms by distributing the remaining valence electrons as nonbonding electrons.

The first step involves calculating the number of valence electrons in the molecule or ion. For a neutral molecule it is the sum of the valence electrons of each atom. If the molecule carries an electric charge, we add one electron for each negative charge or subtract one electron for each positive charge.

Consider the chlorate (ClO 3 ) ion. A chlorine atom (Group VIIa) has seven valence electrons, and each oxygen atom (Group VIa) has six valence electrons. Because the chlorate ion has a charge of −1, it contains one more electron than a neutral ClO 3 molecule. Thus, the ClO 3 ion has a total of twenty-six valence electrons.

ClO 3 : 7 + 3(6) + 1 = 26

The second step in this process involves deciding which atoms in the molecule are connected by covalent bonds. This can be the most difficult step in the process. As a rule, the least electronegative element is at the center of the molecule. It is also useful to note that the formula of the compound often provides a hint to the skeleton structure. The formula for the chlorate ion, for example, suggests the following skeleton structure.

The third step assumes that the skeleton structure of the molecule is based on covalent bonds. The valence electrons are therefore divided into two categories: bonding electrons and nonbonding electrons. Because it takes two electrons to form a covalent bond, we can calculate the number of nonbonding electrons in the molecule by subtracting two electrons for each bond in the skeleton structure from the total number of valence electrons.

There are three covalent bonds in the skeleton structure of the chlorate ion. As a result, six of the twenty-six valence electrons must be used as bonding electrons. This leaves twenty nonbonding electrons in the valence shell.

The fourth step in the process by which Lewis structures are generated involves using the nonbonding valence electrons to complete the octets of the atoms in the molecule. Each oxygen atom in the ClO 3 ion already has two electrons, the electrons in each Cl–O bond. Each oxygen atom therefore needs six nonbonding electrons to complete the octet. Thus, it takes eighteen nonbonding electrons to satisfy the octets of the three oxygen atoms. This leaves one pair of nonbonding electrons, which can be used to fill the octet of the central atom.

Occasionally, we encounter a molecule that does not seem to have enough valence electrons. When this happens, we have to remember why atoms share electrons in the first place. If we cannot achieve a satisfactory Lewis structure by having two atoms share a single pair of electrons, it may be possible to achieve this goal by having them share two or even three pairs of electrons. Consider formaldehyde (H 2 CO), for example, which contains twelve valence electrons.

H 2 CO: 2(1) + 4 + 6 = 12

The formula of this molecule suggests the following skeleton structure.

There are three covalent bonds in this skeleton structure, which means that six valence electrons must be used as bonding electrons. This leaves six nonbonding electrons. It is impossible, however, to complete the octets of the atoms in this molecule with only six nonbonding electrons. When the nonbonding electrons are used to complete the octet of the oxygen atom, the carbon atom has a total of only six valence electrons.

We therefore assume that the carbon and oxygen atoms share two pairs of electrons. There are now four bonds in the skeleton structure, which leaves only four nonbonding electrons. This is enough, however, to satisfy the octets of the carbon and oxygen atoms.

Every once in a while, we encounter a molecule for which it is impossible to write a satisfactory Lewis structure. Consider boron trifluoride (BF 3 ), for example, which contains twenty-four valence electrons.

BF 3 : 3 + 3(7) = 24

There are three covalent bonds in what is the most reasonable skeleton structure for the molecule. Because it takes six electrons to form the skeleton structure, there are eighteen nonbonding valence electrons. Each fluorine atom needs six nonbonding electrons to complete its octet. Thus, all nonbonding electrons are consumed by the three fluorine atoms. As a result, we run out of electrons, and the boron atom still has only six valence electrons.

For reasons that are not discussed here, the elements that form strong double or triple bonds are C, N, O, P, and S. Because neither boron nor fluorine falls in this group, we have to stop short with what appears to be an unsatisfactory Lewis structure.

It is also possible to encounter a molecule that seems to have too many valence electrons. When that happens, we expand the valence shell of the central atom. Consider the Lewis structure for sulfur tetrafluoride SF 4 , for example, which contains thirty-four valence electrons.

SF 4 : 6 + 4(7) = 34

There are four covalent bonds in the skeleton structure for SF 4 . Because this structure uses eight valence electrons to form the covalent bonds that hold the molecule together, there are twenty-six nonbonding valence electrons.

Each fluorine atom needs six nonbonding electrons to complete its octet. Because there are four of these atoms, we need twenty-four nonbonding electrons for this purpose. But there are twenty-six nonbonding electrons in this molecule. We have already completed the octets for all five atoms, and we still have one pair of valence electrons. We therefore expand the valence shell of the sulfur atom to hold more than eight electrons.