Valency

Research: Science & Education

Valency Peter G. Nelson School of Chemistry, University of Hull, Hull HU6 7RX, UK In the 19th century, valency was one of the central concepts of chemistry (1). It was used to rationalize and predict the atomic composition of compounds, and to characterize and classify the compounds formed by an element. In the 20th century, however, the concept has suffered a demise, so much so that in many modern textbooks, it is scarcely even mentioned, authors preferring to use electronic theories to derive chemical formulas, and oxidation number (O.N.) and coordination number (C.N.) to classify compounds. However, this change has brought with it a number of problems. One problem is that some of the methods used to derive formulas are not completely satisfactory. For example, while Lewis’ theory correctly predicts the composition of many main-group compounds, it fails to do so for many transition-metal compounds. Moreover, it gives the wrong ground state for the O2 molecule, it fails to give equivalent bonds in species like NO2{ and benzene, and it implies that atoms like oxygen have lone pairs in molecules to a greater degree than they have (2). Again, hybridization theory fails for many transitionmetal compounds. It also implies that d-orbitals play a greater part in the bonding of hypervalent species than they do (3, 4). For example, while sp3 d2 hybridization of the sulfur atom in SF6 requires 33% of the valence electron density on the atom to be in 3dσ orbitals, SCF calculations give only 5% (3). Another problem is that, as currently defined, oxidation number is an artificial concept (5). It involves assigning charges to atoms that are known to be unrealistic, e.g., +5, +6, and +7 to the manganese atom in [MnO4 ]3{, [MnO4 ]2{, and [MnO4 ]{, respectively (calculations give +0.2, +0.7 and +1.0 [6]). In these examples the implied d-electron configurations (d2 , d 1, d0 ) are also unrealistic (the calculated number of 3d electrons is ca. 5 in all three species [6]). In some cases even the signs of the charges are conventional—for example, for H and Co in HCo(CO)4 . Finally, classifying compounds by oxidation number can separate closely related species, for example, NH 3, NH2 F, NHF 2, and NF3 (O.N. of N = {3, {1, +1, and +3), H2S, H2 S2, H2 S3, etc. (O.N. of S = {2, {1, {2/3, etc.), and Fe(CO) 5, Fe(CO)4 Cl2 , and Fe(CO)2(NO)2 (O.N. of Fe = 0, +2, and {2, all 18-electron species). My aim in this paper is to overcome these problems by refining the concept of valency and extending its scope. The resulting theory enables atomic composition to be predicted for a wide variety of compounds, without reference to the nature of the bonding. The theory also provides a better classification of compounds than oxidation number. Types of Valency Valency may be defined as the capacity of an atom (A) or radical (R) to combine with other atoms or radicals in a family of compounds. (A radical is a bound group of atoms occurring in a series of compounds; for example, CH 3, NH4, BF4.) The valency value determines, or partly determines, the number of atoms or radicals with which A or R will combine.

I shall distinguish three kinds of valency: primary or classical (v), coordinate (c) and nonclassical (v9). Primary or Classical Valency This rationalizes the composition of most compounds between nonmetals, many between metals and nonmetals, and some between metals.

Determination The primary valency of an atom or radical X can be determined by considering compounds of known structure and electrical conductivity formed between it and other atoms and radicals Y. The first step is to exclude compounds of the following types: metallic and semimetallic compounds, compounds containing X–X and/or Y–Y bonds, and compounds containing X bound in more than one way (as, e.g., Ga in GaCl2). Then if, in all the remaining compounds, X combines with at most one other species Y to form a unit of a compound [XY in (XY)n], X is exclusively univalent. This condition is satisfied by H, F, and alkali metal atoms, and by alkyl, aryl, and other radicals. The valencies of other species can be obtained from these. If X combines with v exclusively univalent atoms or radicals Y 1 to form a unit XY1v of a compound, the primary valency of X is v. Some atoms and radicals, while not forming simple compounds comprising XY1v units, form multiple compounds containing these units (see below), or compounds containing equivalent units, e.g., X2 Ov. For example, chlorine does not form ClF7, but it does form Cl2 O7, ClO 3F, and ClO2F 3. Such atoms have an effective valency of v. Note that valency transcends structure. For example, aluminum has a valency of three in [Al(mesityl)3]1 , [Al(CH3)3]2, and (AlF3 )∞ (C.N. = 3, 4, and 6, respectively). Note also that the values of v can be used, not only for compounds of the type from which they have been determined, but also for compounds in which there is catenation, or there are atoms or radicals bound in more than one way. Values For metal atoms, primary valencies are generally the same as oxidation numbers, except that they do not carry a sign (e.g., v = 1 for Au in CsAu). However, they differ for compounds in which there are metal–metal bonds (e.g., for Hg2F2 , O.N. = 1, v = 2). The primary valencies of nonmetal atoms are given in Table 1. Effective values are bracketed. The value of 5 for nitrogen is based on its formation of X 13 NO, X1 NO2 , and N2O 5. I have excluded compounds like CO that do not belong to a family. Note that the values are independent of the nature of the bonding in compounds. In particular such values as 5 for nitrogen or 6 for sulfur hold irrespective of how many pairs of electrons there are around the atom. This is discussed further below. Scope Primary valencies rationalize, or partially rationalize, the composition of compounds of the following types.

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Research: Science & Education Simple atomic compounds—compounds whose composition is completely determined by a single valency for each atom [e.g., H12O2 , Na1Cl1, C4H13I1 (superior numbers = valencies)]. The value of v may vary from one family of compounds to another, but within a family only one value is required. “Complex” compounds require some of the atoms in them to have more than one valency (see below).

Table 1. Primary Valencies of Nonmetal Atoms Hydrogen

Multiple compounds—compounds formed by the addition of simple compounds in proportions that are not determined by the primary valencies of the atoms or radicals in them (e.g., CH 4 · ~6H2 O, KCl · MgCl 2, NH3 · HCl, KF · BF3). For these the primary valencies determine the composition of the components. Some multiple compounds can be treated as simple radical ones [e.g., NH3 · HCl = (NH4)Cl, KF · BF3 = K(BF4 )].

Algebraic Method Let n(XY) be the number of valencies on X that are satisfied by an adjacent atom or radical Y and vice versa (the bond number). Then for all the valencies in a compound to be satisfied, eq 1 must hold for all X. The sum is over all the atoms or radicals adjacent to X.

ΣY n (XY) = v (X)

(1)

To illustrate the application of this equation consider a compound containing only X and Y, XxYy. If there is no catenation in the compound, and all the X’s are bound to the same number (ay) of Y’s and vice versa, eq 1 gives ayn (XY) = v (X) and axn (XY) = v (Y), whence x / y = v (Y) / v (X). Thus for the chloride of a bivalent element, X : Cl = 1 : 2. In general, eq 1 does not determine the arrangement of atoms in a compound. This is shown in Figure 1, where some of the possible arrangements for the chloride of a bivalent element are given (7), all satisfying eq 1. For certain types of compound, however, the number of possible arrangements is limited. Thus for organic compounds the number is restricted by the empirical condition n ≥ 1. The same restriction applies to most compounds between nonmetals. However, for most compounds between a metal and a nonmetal, n ≤ 1. Some exceptions to these rules are shown in Figure 2. Graphical Method Because the atomic composition of simple compounds is determined by valency irrespective of the arrangement of atoms in them, atomic composition can be predicted by taking n = integer. Valency can then be represented by short strokes (e.g., {X{, Cl{) and the satisfaction of valency by matching up strokes (e.g. Cl{ {X{ {Cl, Cl{ {X{ {X{ {Cl). The resulting compositions will be correct, whether or not the structures are.

466

1

Boron

Simple radical compounds—compounds whose composition is completely determined by single radical valencies [e.g., (CH3 )1I1 , (NH4)1Cl1 , K1(BF4 )1 ]. Radicals can be simple [i.e., their composition and valency are completely determined by single atomic valencies, e.g., (C4H13 )1 ] or complex [e.g., (BF4)1]. Valencies can be assigned to radicals without reference to their inner constitution.

Prediction of Atomic Composition The atomic composition of simple compounds can be predicted by applying the principle that in such compounds, the primary valencies of all the atoms or radicals are satisfied. This can be done algebraically or graphically. The latter is simpler, but less rigorous.

v

Element 3

Carbon

4

Silicon

4

Nitrogen

3

(5)

Phosphorus

3

5

Oxygen

2

Sulfur

2

4

6

Selenium

2

4

6

Fluorine

1

Chlorine

1

3

5

(7)

Bromine

1

3

5

(7)

Iodine

1

3

5

7

Krypton

2

Xenon

2

4

6

(8)

Bond Number and Bond Strength In many compounds there is a good correlation between bond number and bond strength, as measured, for example, by bond length. This is particularly true of crystalline solids in which there is an alternation of polarity, as in most minerals (8). For these there is a sufficiently precise correlation with bond length that this can be used to determine bond numbers in a proposed crystal structure, to see whether they satisfy eq 1. This is a useful aid in the determination of complex structures (8). However, the value of n given by eq 1 is not always reflected in a bond’s strength. For example, the C–C bonds in benzene have n = 11 /2 but their strength corresponds to n9 ≈ 12 /3 (9). Again, the Na–Cl bonds in crystalline NaCl have n = 1/6, but by comparison with the bond in a gaseous NaCl molecule their strength corresponds to n9 ≈ 1/4.1 For covalent molecules Pauling called n “bond number” and n9 “bond order” (9). For ionic crystals, however, he called an equivalent quantity to n “electrostatic bond strength” (10). I shall use “bond number” for n irrespective of the type of bonding. Some authors call n “bond valence” (8). The distinction between n and n9 is important when discussing whether nitrogen is “really” quinquivalent in some of its compounds. For example, the N–O bond length in (CH3 )3NO (1.40 Å [11]) corresponds to n9 ≈ 1 (12), but this does not alter the fact that the composition of the compound corresponds to n (NO) = 2 and v (N) = 5. Indeed, for the same bond in F3NO (length 1.16 Å [13]) n9 ≈ 2 (12). Quantum-mechanical calculations reveal no fundamental difference between hypervalent compounds of first- and second-row elements (4). Valency and Ionic Charge The charge number (z) of an ion is related to the valency of the atom or radical from which it is derived by eq 2. z = ±v

(2)

This equation is based on Faraday’s laws. The sign is determined empirically (from the direction the ion moves in electrolysis, or from the sign of the counterion). Thus for the sodium ion, v = 1 and z = +1, and for the sulfate ion, v = 2 and z = {2. The values of z provide an alternative means of

Journal of Chemical Education • Vol. 74 No. 4 April 1997

Research: Science & Education

Figure 1. Atomic arrangements in some chlorides of bivalent elements.

predicting the composition of polar compounds, by balancing charges [e.g., (Na+)2 SO42{]. This method is very useful, but the resulting formulas must not be taken to give an accurate picture of the charge distribution, as this can change when ions come together. Equation 2 can be used to predict the charge number of an ion, though this is seldom necessary. Note, however, that the fact that it gives a value for a species does not necessarily mean that the species exists. For example, the equation gives z (O) = {2, z (N) = {3, and z (C) = {4, but whether oxides, nitrides, and carbides contain ions having these charge numbers is disputed (14). Equation 2 can be generalized by dividing valency into electrovalency (ve) and covalency (vc) as in eqs 3 and 4. v = |v e| + vc ve = z

(3) (4)

These equations apply not only to ions, for which they reduce to eq 2,2 but also, for simple ions, to atoms or radicals (X) within an ion, z representing the charge number of X. In the latter case, the covalencies are satisfied according to eq 5 (cf. eq 1), and the electrovalencies give the charge number of the ion as in eq 6.

ΣY n c(XY) = vc(X) ΣX ve(X) = z (ion)

(a)

(b)

(c) Figure 2. Formula for (a) ammonium chloride (CsCl structure), (b) diborane, (c) Mo2(OR)6.

(5) (6)

Equations 3–6 enable the composition and charge of a simple ion to be predicted. Like eq 1, however, they do not usually have a unique solution, unless further conditions are imposed. This is shown in Figure 3, where different formulas for the nitrite ion are given, all consistent with eqs 3–6. Formula (a) corresponds to taking ∑|ve| = minimum and ve = integer. In (b) only the first restriction applies; in (c) and (d), only the second. Any can be used to predict composition and overall charge, but not the distribution of charge. Predictions can be made graphically by representing covalencies by strokes and electrovalencies by their values (e.g., { O{ ), and matching strokes (e.g., R{ { O{ ). Equations 3–6 can also be applied to uncharged species, by setting z(ion) = 0. They give the same composition for these as eq 1, but with a range of charge distributions, as illustrated in Figure 4 for SF6. Quantum-mechanical calculations (3, 15) give a distribution close to formula (c), for which ve(S) = +3 and vc(S) = 3. The latter value and those obtained from calculations (4, 15) on other molecules suggest that for main-group atoms, vc cannot exceed 4. This corresponds to an octet. However, for the purposes of predicting composition, there is no advantage in using eqs 3–6 over eq 1. Coordinate Valency This valency relates to multiple compounds whose proportions are determined in whole or in part by subsidiary valencies for some of the atoms in them (complex or coordination compounds). Compounds of this kind were considered by Werner and rationalized by his coordination theory (16). The following is a modified version of this. Many multiple compounds contain atoms that are bound to a greater number of neighbors than corresponds to their primary valency. The more electropositive of these are called nuclear or central atoms; the more electronegative, ligating.

Figure 3. Formulas for the nitrite ion. Covalent bonds are represented by thick lines to distinguish them from bonds in formulas in which electrovalency and covalency are not differentiated, as in Figures 1 and 2.

Ligating atoms have two valencies, primary and coordinate. The primary valency satisfies the primary valencies of other atoms or radicals. The coordinate valency

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Research: Science & Education determines the number of central atoms to which a ligating atom binds. This is usually one. Central atoms (A) have two valencies, primary and coordinate. The primary valency functions in the usual way. The coordinate valency determines the number of atoms immediately bound to A. It can be satisfied by atoms or radicals using their primary valency or by ligating atoms using their coordinate valency. In the above I have used the term “coordinate valency” to allow “coordination number” to be used as a general structural term, to describe the number of neighbors to an atom in any kind of compound, including ionic and metallic ones (compare ref 5). Note that, while the coordinate valency of a ligating atom corresponds to Werner’s “auxiliary” or “secondary” valency, the relationship between these for a central atom is: secondary valency = coordinate valency – primary valency. The application of this theory to the compound KF·BF 3 is shown in Figure 5a. The boron atom has a coordinate valency of 4 and the fluoride ion of one. To avoid the introduction of new symbolism, I have represented the coordinate bond as on the electronic theory (17). The equivalence of the B–F bonds can be expressed as in Figure 5b. The theory is most useful for central atoms that have fixed coordinate valencies. Some compounds can be formulated as simple or complex, as illustrated in Figures 6 and 7. The choice between the two formulations depends on the nature of the bonding. For example, if the coordinate links in Figure 6b contribute to the bonding, the metal halide is complex; but if they only indicate the coordination number, as is the case if the bonding is ionic, the compound is simple. Similarly, if the positive charge on a NX4 + ion (Fig. 7) resides mainly on X, the ion is complex, but if it resides on N, the ion is simple. Note, however, that, for the purposes of predicting composition, it is not necessary to choose between formulations in cases like these, as they both give the same result. Nonclassical Valency This relates to transition-metal carbonyls and similar compounds (nonclassical compounds). These are characterized by having a transition-metal atom bound to atoms that are incipiently unsaturated—for example, the carbon atom in CO, the phosphorus atom in PF3, and the carbon atoms in C2H4 . The unsaturation of these is shown by their ability to take up halogen atoms (X) to form X2 CO, X2 PF3 , and C2 H4X 2. Compounds of this type can be treated as coordination compounds. However, this is not entirely satisfactory, as it requires transition-metal atoms to have a primary valency of zero in some compounds [e.g., Fe(CO)5], and different primary and coordinate valencies in related species [e.g., Fe(CO)5 and Fe(CO)4Cl2]. An alternative procedure is to assign to transitionmetal atoms and ions a nonclassical valency (v9), one unit of which can be satisfied by a classical valency and two units by a coordinate valency. Nonclassical ligands can be regarded as being bound either by coordinate links (e.g., M← CO) or by ordinary bonds (e.g., M=C=O), the choice being immaterial. In either case the number of nonclassical valencies satisfied by a ligating atom (x) is equal to the number of halogen atoms or their equivalent with which it will combine. Some ligands have more than one valency; for example, NO [x(N) = 1 or 3, as in FNO and F3NO] and NR [x(N) = 2 or 4, as in H2 NR and O2NR]. The application of these principles to some iron compounds is shown in Figure 8. I have represented nonclassi-

468

Figure 4. Some solutions to eqs 3–6 for SF6. All the fluorine atoms carry the charge indicated. Covalent bonds are represented by thick lines as in Figure 3.

(b)

(a) Figure 5. Formulas for the compound KBF4.

(b)

(a)

Figure 6. Representation of a metal dihalide (a) as a simple compound, (b) as a complex.

(a)

(b)

Figure 7. Representation of a quaternary ammonium salt (a) as a compound of quinquivalent nitrogen, (b) as a coordination compound of X+.

Journal of Chemical Education • Vol. 74 No. 4 April 1997

Research: Science & Education

Table 2. Nonclassical Valencies for Iron

z

v’

Examplesa

{2

10

[Fe(CO)4]2{

{1

10

[HFe(CO)4]{

0

10

Fe(CO)5, H2Fe(CO)4

+1

12

[HFe(CO)5]+

+2

14

[Fe(CNR)6]2+

a

H taken as a radical.

n ox(X) = Σ n (XY>) – Σ n (XY

Figure 8. Formulas for some nonclassical iron compounds (staggered form of ferrocene shown).

cal bonds by M–L if x = 1, M← L if x = 2, and M← — L if x = 3 (L = ligating atom). The iron atom has v9 = 10. The theory unites the iron compounds mentioned at the beginning of this paper. The principal nonclassical valency of a transition-metal atom is given by eq 7, where N is the group number v9 = 18 – N

(7)

(e.g., for Ni, N = 10, v9 = 8). This equation corresponds to the 18-electron rule. Some atoms have a valency of 16 – N in some compounds, corresponding formally to their having 16 valence electrons (18). Values for anions are the same as for atoms, while those for cations differ by twice the charge number (Table 2).3

Equivalent Fragments Fragments of molecules that have the same valency and can replace each other in some compounds are equivalent; for example, (OC) 5 Mn{ is equivalent to H3C{, (OC)4 Fe< to H2C