# Valence (chemistry)

For other uses, see Valence (disambiguation).
"Multivalent" redirects here. For other uses, see Polyvalence (disambiguation).

In chemistry, the valence (or valency) of an element is a measure of its combining power with other atoms when it forms chemical compounds or molecules. The concept of valence was developed in the last half of the 19th century and was successful in explaining the molecular structure of many organic compounds. [1] The quest for the underlying causes of valence lead to the modern theories of chemical bonding, including Lewis structures (1916), valence bond theory (1927), molecular orbitals (1928), valence shell electron pair repulsion theory (1958) and all the advanced methods of quantum chemistry.

The combining power or affinity of an atom of an element was determined by the number of hydrogen atoms that it combined with. In methane, carbon has a valence of 4; in ammonia, nitrogen has a valence of 3; in water, oxygen has a valence of two; and in hydrogen chloride, chlorine has a valence of 1. Chlorine, as it has a valence of one, can be substituted for hydrogen, so phosphorus has a valence of 5 in phosphorus pentachloride, PCl5. Valence diagrams of a compound represent the connectivity of the elements, lines between two elements, sometimes called bonds, represented a saturated valency for each element.[1] Examples are:-

 Compound H2 CH4 C3H8 C2H2 NH3 NaCN H2S H2SO4 Cl2O7 Diagram Valencies Hydrogen 1 Carbon 4 Hydrogen 1 Carbon 4 Hydrogen 1 Carbon 4 Hydrogen 1 Nitrogen 3 Hydrogen 1 Sodium 1 Carbon 4 Nitrogen 3 Sulfur 2 Hydrogen 1 Sulfur 6 Oxygen 2 Hydrogen 1 Chlorine 7 Oxygen 2

Valence only describes connectivity, it does not describe the geometry of molecular compounds, or what are now known to be ionic compounds or giant covalent structures. The line between atoms does not represent a pair of electrons as it does in Lewis diagrams.

## Modern definitions

Valence is defined by the IUPAC as:-

The maximum number of univalent atoms (originally hydrogen or chlorine atoms) that may combine with an atom of the element under consideration, or with a fragment, or for which an atom of this element can be substituted. .[2]

An alternative modern description is:-[3]

The number of hydrogen atoms that can combine with an element in a binary hydride or twice the number of oxygen atoms combining with an element in its oxide or oxides. This definition differs from the IUPAC definition as an element can be said to have more than one valence.

## History

The etymology of the word "valence" traces back to 1425, meaning "extract, preparation," from Latin valentia "strength, capacity," and the chemical meaning referring to the "combining power of an element" is recorded from 1884, from German Valenz.[4]

William Higgins' combinations of ultimate particles (1789)

In 1789, William Higgins published views on what he called combinations of "ultimate" particles, which foreshadowed the concept of valency bonds.[5] If, for example, according to Higgins, the force between the ultimate particle of oxygen and the ultimate particle of nitrogen were 6, then the strength of the force would be divided accordingly, and likewise for the other combinations of ultimate particles (see illustration).

The exact inception, however, of the theory of chemical valencies can be traced to an 1852 paper by Edward Frankland, in which he combined the older theories of free radicals and “type theory” with thoughts on chemical affinity to show that certain elements have the tendency to combine with other elements to form compounds containing 3, i.e. in the three atom groups (e.g., NO3, NH3, NI3, etc.) or 5, i.e. in the five atom groups (e.g., NO5, NH4O, PO5, etc.), equivalents of the attached elements. It is in this manner, according to Frankland, that their affinities are best satisfied. Following these examples and postulates, Frankland declares how obvious it is that:[6]

This “combining power” was afterwards called quantivalence or valency (and valence by American chemists).[5]

## Common valences

For elements in the main groups of the periodic table, the valence can vary between one and seven.

Group Valence 1 Valence 2 Valence 3 Valence 4 Valence 5 Valence 6 Valence 7 Typical valencies
1 (I) NaCl 1
2 (II) MgCl2 2
13 (III) BCl3, AlCl3
Al2O3
3
14 (IV) CO CH4 4
15 (V) NO NH3
PH3
As2O3
NO2 N2O5
PCl5
3 and 5
16 (VI) H2O
H2S
SO2 SO3 2 and 6
17 (VII) HCl ClO2 Cl2O7 1 and 7

Many elements have a common valence related to their position in the periodic table, and nowadays this is rationalised by the octet rule. The prefixes uni/mono, di/bi, tri/ter, quadri/tetra, penta/quinque were both used by different writers. Polyvalence or multivalence refers to species that are not restricted to a distinct number of valence bonds. (Species with only one valence are univalent (monovalent)). For example, the Cs+ cation is a univalent or monovalent cation, whereas the Ca2+ cation is a divalent or polyvalent or multivalent cation and the Fe3+ cation is a trivalent or polyvalent or multivalent cation. As a result, examples of polyvalent cations include the Ca2+ cation and the Fe3+ cation.[citation needed]

## Valence versus oxidation state

Because of the ambiguity of the term valence,[7] nowadays other notations are used in practice. Beside the system of oxidation numbers as used in Stock nomenclature for coordination compounds,[8] and the lambda notation, as used in the IUPAC nomenclature of inorganic chemistry,[9] "oxidation state" is a more clear indication of the electronic state of atoms in a molecule.

The "oxidation state" of an atom in a molecule gives the number of valence electrons it has gained or lost.[10] In contrast to the valency number, the oxidation state can be positive (for an electropositive atom) or negative (for an electronegative atom).

Elements in a high oxidation state can have a valence higher than four. For example, in perchlorates, chlorine has seven valence bonds and ruthenium, in the +8 oxidation state in ruthenium tetroxide, has eight valence bonds.

### Examples

(valencies according to the number of valence bonds definition and conform oxidation states)

COMPOUND FORMULA VALENCE OXIDATION STATE
Hydrogen chloride HCl H=1   Cl=1 H=+1   Cl=−1
Perchloric acid * HClO4 H=1   Cl=7   O=2 H=+1   Cl=+7   O=−2
Sodium hydride NaH Na=1   H=1 Na=+1   H=−1
Ferrous oxide ** FeO Fe=2   O=2 Fe=+2   O=−2
Ferric oxide ** Fe2O3 Fe=3   O=2 Fe=+3   O=−2

* The univalent perchlorate ion (ClO4) has valence 1.
** Iron oxide appears in a crystal structure, so no typical molecule can be identified.
In ferrous oxide, Fe has oxidation number II, in ferric oxide, oxidation number III.

Examples where valences and oxidation states differ due to bonds between identical atoms:

COMPOUND FORMULA VALENCE OXIDATION STATE
Chlorine Cl2 Cl=1 Cl=0
Hydrogen peroxide H2O2 H=1   O=2 H=+1   O=−1
Acetylene C2H2 C=4   H=1 C=−1   H=+1
Mercury(I) chloride Hg2Cl2 Hg=2   Cl=1 Hg=+1   Cl=−1

Valences may also be different from absolute values of oxidation states due to different polarity of bonds. For example, in dichloromethane, CH2Cl2, carbon has valence 4 but oxidation state 0.

## "Maximum number of bonds" definition

Frankland took the view that the valence (he used the term "atomicity") of an element was a single value that corresponded to the maximum value observed. The number of unused valencies on atoms of what are now called the p-block elements is generally even, and Frankland suggested that the unused valencies saturated one another. For example, nitrogen has a maximum valence of 5, in forming ammonia two valencies are left unattached; sulfur has a maximum valence of 6, in forming hydrogen sulphide four valencies are left unattached.[11][12]

The International Union of Pure and Applied Chemistry (IUPAC) has made several attempts to arrive at an unambiguous definition of valence. The current version, adopted in 1994,:[13]

The maximum number of univalent atoms (originally hydrogen or chlorine atoms) that may combine with an atom of the element under consideration, or with a fragment, or for which an atom of this element can be substituted.[2]

Hydrogen and chlorine were originally used as examples of univalent atoms, because of their nature to form only one single bond. Hydrogen has only one valence electron and can form only one bond with an atom that has an incomplete outer shell. Chlorine has seven valence electrons and can form only one bond with an atom that donates a valence electron to complete chlorine's outer shell. However, chlorine can also have oxidation states from +1 to +7 and can form more than one bond by donating valence electrons.

Although hydrogen has only one valence electron, it can form bonds with more than one atom in hypervalent bonds. In the bifluoride ion ([HF
2
]
), for example, it forms a three-center four-electron bond with two fluoride atoms: $[\ F \frac{\quad}{\quad} H\ {}^-\!F \quad \longleftrightarrow \quad F^- \ {}\!H \frac{\quad}{\quad} F\ ]$

Another example is the Three-center two-electron bond in diborane (B2H6).

## Maximum valences of the elements

Maximum valences for the elements are based on the data from list of oxidation states of the elements.

Maximum valences of the elements
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Group →
↓ Period
1 1
H
2
He
2 3
Li
4
Be
5
B
6
C
7
N
8
O
9
F
10
Ne
3 11
Na
12
Mg
13
Al
14
Si
15
P
16
S
17
Cl
18
Ar
4 19
K
20
Ca
21
Sc
22
Ti
23
V
24
Cr
25
Mn
26
Fe
27
Co
28
Ni
29
Cu
30
Zn
31
Ga
32
Ge
33
As
34
Se
35
Br
36
Kr
5 37
Rb
38
Sr
39
Y
40
Zr
41
Nb
42
Mo
43
Tc
44
Ru
45
Rh
46
Pd
47
Ag
48
Cd
49
In
50
Sn
51
Sb
52
Te
53
I
54
Xe
6 55
Cs
56
Ba
72
Hf
73
Ta
74
W
75
Re
76
Os
77
Ir
78
Pt
79
Au
80
Hg
81
Tl
82
Pb
83
Bi
84
Po
85
At
86
Rn
7 87
Fr
88
Ra
104
Rf
105
Db
106
Sg
107
Bh
108
Hs
109
Mt
110
Ds
111
Rg
112
Cn
113
Uut
114
Fl
115
Uup
116
Lv
117
Uus
118
Uuo

57
La
58
Ce
59
Pr
60
Nd
61
Pm
62
Sm
63
Eu
64
Gd
65
Tb
66
Dy
67
Ho
68
Er
69
Tm
70
Yb
71
Lu
89
Ac
90
Th
91
Pa
92
U
93
Np
94
Pu
95
Am
96
Cm
97
Bk
98
Cf
99
Es
100
Fm
101
Md
102
No
103
Lr
Maximum valences are based on the List of oxidation states of the elements
 0 1 2 3 4 5 6 7 8 Unknown Background color shows maximum valence of the chemical element
 black=Solid green=Liquid red=Gas grey=Unknown Color of the atomic number shows state of matter (at 0 °C and 1 atm)
 Primordial From decay Synthetic Border shows natural occurrence of the element

## Covalence

The term covalence is attributed to Irving Langmuir.[14] He stated that "the number of pairs of electrons which any given atom shares with the adjacent atoms is called the covalence of that atom." The prefix co- means "together", so that a co-valent bond means that the atoms share valence. Subsequent to this, it is now more common to speak of covalent bonds rather than "valence", which has fallen out of use in higher level work with the advances in the theory of chemical bonding, but is still widely used in elementary studies where it provides a heuristic introduction to the subject.

## References

1. ^ a b Partington, James Riddick (1921). A text-book of inorganic chemistry for university students (1st ed.). Retrieved April 13, 2014.
2. ^ a b IUPAC Gold Book definition: valence
3. ^ Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. ISBN 0080379419.
4. ^ Valence - Online Etymology Dictionary.
5. ^ a b Partington, J.R. (1989). A Short History of Chemistry. Dover Publications, Inc. ISBN 0-486-65977-1.
6. ^ Frankland, E. (1852). Phil. Trans., vol. cxlii, 417.
7. ^ The Free Dictionary: valence
8. ^ IUPAC, Gold Book definition: oxidation number
9. ^ IUPAC, Gold Book definition: lambda
10. ^ IUPAC Gold Book definition: oxidation state
11. ^ Frankland, E. (1870). Lecture notes for chemical students(Google eBook) (2d ed.). J. Van Voorst. p. 21. Retrieved April 30, 2014.
12. ^ Frankland, E.; Japp, F.R (1885). Inorganic chemistry (1st ed.). pp. 75–85. Retrieved April 8, 2014.
13. ^ Pure Appl. Chem. 66: 1175 (1994).
14. ^ Langmuir, Irving (1919-06-01). "The Arrangement of Electrons in Atoms and Molecules". Journal of the American Chemical Society 41 (6): 868–934. doi:10.1021/ja02227a002.