Multiple Valences

FIELDS OF STUDY: Inorganic Chemistry; Organic Chemistry

ABSTRACT

Valence is central to the formation and study of various compounds. Multivalent atoms form a number of bonds to other atoms, depending on both the number of valence electrons they possess and the vacant orbitals in their valence shells.

The Behavior of Electrons

In chemistry, "valence" refers to the number of bonds that a given atom can form with other atoms, which is determined by the number of electrons that atom has in its outermost electron shell. Each electron shell contains between one and four subshells (a fifth subshell is theoretically possible but has yet to be observed), which in turn contain a specific number of orbitals. There are four known orbital shapes, designated s, p, d, and f. These shapes appear in subshells in set numbers, so that a subshell may contain one s orbital, three p orbitals, five d orbitals, or seven f orbitals, each occupied by a maximum of two electrons. For simplicity’s sake, the term "orbital" is often applied to the subshell as a whole, so that a subshell containing three p orbitals, each with two electrons, may also be referred to as a single p orbital containing six electrons.

Electrons fill the orbitals in order from the lowest energy level to the highest, usually progressing from one electron shell to the next only when a shell has all of the electrons it is allowed to have. Each shell is designated by its principal quantum number (n), so that the first electron shell is called the n = 1 shell, the second is the n = 2 shell, and so on. Subshells are labeled 1s, 2s, 2p, et cetera. Due to variations in the energy levels of the subshells, once the d orbitals first appear in the n = 3 shell, electrons stop filling the orbitals in a strictly numerical order, and the s orbital of the next shell is filled before the d orbitals of the current shell. The f orbitals, which first appear in the n = 4 shell, add an additional layer of complexity.

Electrons are typically distributed individually rather than in pairs, so that each orbital in a subshell contains a single unpaired electron before the first orbital gains its second electron. In the case of most atoms, when all of an atom’s electrons have filled the available electron shells, the outermost electron shell will contain fewer than the maximum number. This outermost electron shell is called the valence shell, and it is where all normal chemistry takes place, through the interactions of each atom’s valence-shell electrons and orbitals.

A central feature of valence-shell electron configuration is what is known as the octet rule. The elements in group 18 of the periodic table (the farthest-right column), known as the noble-gas elements, each have full s and p orbitals in their outermost electron shells, for a total of eight valence electrons. (The one exception to this is helium, which contains only a single s orbital and thus two electrons total.) This noble-gas configuration seems to be the most stable energy state an atom can have, and other atoms either give up or gain electrons to form cations or anions (positively or negatively charged ions), respectively, in order to achieve the same electron configuration as the nearest noble-gas element.

Whether an atom forms an anion or a cation depends on its number of valence electrons. For example, the potassium atom (atomic number 19) readily gives up its single valence electron to form a potassium cation (K⁺) with the same electron configuration as the noble-gas element argon (atomic number 18), while the chlorine atom (atomic number 17), which has seven valence electrons, readily takes an eighth electron into its valence shell to form a chloride anion (Cl⁻), which also has the same electron configuration as argon.

Valence and Oxidation State

Valence-shell electrons and orbitals determine the chemical behavior of atoms in a variety of ways. In many compounds, the valence of an atom corresponds exactly to the number of electrons it has either gained or lost. However, in others, the situation is not as clear. One way of keeping track of valence electrons in a compound is to assign an oxidation state to each atom. Essentially an accounting method for electrons, the oxidation state is just the number of electrons that an atom has gained or lost. This system treats all atoms as though they actually lose or gain electrons when forming a compound, regardless of whether the electrons are simply shared between atoms, as in covalent bonds, rather than transferred from one to another.

There are basic rules for assigning the oxidation state. Hydrogen is typically assigned the oxidation state of +1, and oxygen is typically −2, while an atom bonded to an identical atom is assigned an oxidation state of 0. Ions are always assigned the oxidation state that corresponds to their electrical charge, and the sum of all oxidation states within a single neutral molecule must be zero. For example, in the compound potassium dichromate (K₂Cr₂O₇), each potassium ion would be assigned an oxidation state of +1, for a total oxidation number of +2; each oxygen atom would have an oxidation state of −2, for a total oxidation number of −14; and, to balance the charges, each of the two chromium atoms must have an oxidation state of +6, for a total oxidation number of +12.

While valence and oxidation are related and often convey the same information—that is, the number of electrons "lost" or "gained" by an atom in a compound is usually equal to the number of its chemical bonds—the oxidation state is used more often than the valence number, as it tends to be less ambiguous. One advantage of oxidation state is that valence refers to the number of chemical bonds an atom can form and thus is always a positive number, while the oxidation number is positive or negative depending on whether electrons have been lost or gained (or donated or accepted in order to form a covalent bond).

Oxidation States of Transition Metals

An element with multiple valences is one that can take on more than one oxidation state in order to form different numbers of bonds within a compound. While any element can potentially have multiple valences, according to the number of electrons present in the valence shell, this is rarely observed in elements that are either one or two valence electrons away from a noble-gas configuration; such atoms almost exclusively form compounds in which they have only one or two bonds, respectively. The assigning of different oxidation states to nonmetal atoms, such as carbon and nitrogen, in their various compounds is more a formality than it is an indication of multiple valences.

Rather, the property of multiple valences is the province of the transition metals, including the lanthanides and the actinides (often called "inner transition metals"). These are elements that have incomplete d or f orbitals, which seems to be the determining factor in whether an element can exhibit multiple valence behavior. Because the d and f orbitals of each electron shell are filled in a slightly different order from the s and p orbitals, a transition metal can have an incomplete inner electron shell; in first-row transition metals, for example, the n = 4 shell is the outermost electron shell, but the 4s orbital is filled before the 3d orbitals, meaning the 3d orbitals may be incomplete when the 4s orbital is not. The electrons in this incomplete inner shell can also act as valence electrons when needed, giving the atom the ability to lose more electrons than the number of electrons in its outermost shell would suggest. Transition metals, like ordinary metals, form cations rather than anions, as they lose electrons much more easily than they could gain them.

Because transition metals may have different valences in different compounds, the best way to determine the valence of such an element in a particular compound is to use the oxidation-state accounting method described in the potassium dichromate (K₂Cr₂O₇) example above. Of the three elements in the compound—potassium, chromium, and oxygen—only chromium is a transition metal; the other two have relatively consistent oxidation states. Thus, the oxidation state of the transition metal can be determined by balancing the known oxidation states of the other elements. In this compound, the oxidation state of chromium is +6; accordingly, each chromium atom is only bonded to four oxygen atoms, but two of those chromium-oxygen bonds are double bonds, making six bonds total and giving a valence of 6.

In chemical notation, if an element has multiple valences, the oxidation number of the element in a particular compound is displayed either as a superscript or in parentheses, written in roman numerals to distinguish it from the charge number. For example, the +6 oxidation state of the chromium atoms in potassium dichromate could be represented as Cr^VI or Cr(VI). This oxidation state can also be conveyed in the name of the compound by putting the roman numerals in parentheses immediately after the name of the element, so that an alternative name for this compound would be potassium dichromate(VI).

Typically, however, this notation is only used if the same name could be applied to two or more compounds formed with the same element in different oxidation states. Thus, because the name "iron chloride" could refer to either the compound FeCl₂, in which the iron has an oxidation state of +2, or the compound FeCl₃, in which it has an oxidation state of +3, the two compounds are differentiated by the names iron(II) chloride and iron(III) chloride, respectively. In addition, atoms of the same element in different oxidation states can be present in the same compound, as in iron(II,III) sulfide (Fe₃S₄), where the −2 oxidation states of the four sulfur atoms (for a total of −8) are balanced by one iron(II) atom (+2) and two iron(III) atoms (+6). The formula of such a compound is often given in the format FeS∙Fe₂S₃.

VSEPR Theory

Valence-shell electron-pair repulsion theory, or VSEPR theory for short, is related directly to the quantum-mechanical description of atomic orbitals in the modern theory of atomic structure. The electrons in the valence shell of an atom all carry the same electrical charge and therefore exert a force of repulsion on each other, the magnitude of which is proportional to their proximity to each other. Atoms in compounds have contributed electrons to form bonds to other atoms. Each atom typically contributes one electron per bond. The carbon atom, for example, has four electrons in its valence shell and so can contribute an electron to the formation of four bonds.

Because atoms are spherical, the forces of repulsion are minimized when these bonds are radially distributed about the nucleus. The four electrons in the carbon atom are distributed so that two are in the 2s orbital and the third and fourth are in two of the three 2p orbitals. The s orbital is spherical and the p orbitals are at right angles to each other, making the spatial distribution of the charge on their electrons asymmetrical. By combining the s and p orbitals into four "hybrid" atomic orbitals oriented toward the apexes of a tetrahedron, the repulsive force between the electron pairs in the four bonds is minimized. The same principle applies to all other compounds. VSEPR theory essentially states that the chemical bonds within compounds are oriented in ways that minimize the repulsive forces between their electron pairs, including any lone (nonbonding) pairs of electrons.

PRINCIPAL TERMS

• electron shell: a region surrounding the nucleus of an atom that contains one or more orbitals capable of holding a specific maximum number of electrons.
• orbital: a specific region of space about the nucleus of an atom in which electrons of a given energy level are most likely to be found.
• oxidation state: a number that indicates the degree to which an atom or ion in a chemical compound has been oxidized or reduced.
• transition metals: the elements of the periodic table that have valence electrons in their d orbitals.
• VSEPR theory: the valence-shell electron-pair repulsion theory, which states that electron pairs in the valence shell of an atom will arrange themselves so that the electrostatic repulsion between them is minimized.

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