Valence (chemistry)

Last updated

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.

Contents

Description

The combining power, or affinity of an atom of a given element is determined by the number of hydrogen atoms that it combines with. In methane, carbon has a valence of 4; in ammonia, nitrogen has a valence of 3; in water, oxygen has a valence of 2; and in hydrogen chloride, chlorine has a valence of 1. Chlorine, as it has a valence of one, can be substituted for hydrogen. Phosphorus has a valence of 5 in phosphorus pentachloride, PCl5. Valence diagrams of a compound represent the connectivity of the elements, with lines drawn between two elements, sometimes called bonds, representing a saturated valency for each element. [1] The two tables below show some examples of different compounds, their valence diagrams, and the valences for each element of the compound.

Compound H2
Hydrogen
CH4
Methane
C3H8
Propane
C2H2
Acetylene
Diagram Wasserstoff.svg Methane-2D-flat-small.png Propane-2D-flat.png Ethyne-2D-flat.png
Valencies
  • Hydrogen: 1
  • Carbon: 4
  • Hydrogen: 1
  • Carbon: 4
  • Hydrogen: 1
  • Carbon: 4
  • Hydrogen: 1


Compound NH3
Ammonia
NaCN
Sodium cyanide
H2S
Hydrogen sulfide
H2SO4
Sulfuric acid
Cl2O7Dichlorine heptoxide
Diagram Ammoniak.png Sodium cyanide-2D.svg Hydrogen sulfide.svg Sulfuric acid chemical structure.png Dichlorine heptoxide.svg
Valencies
  • 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. A 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: [2]

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.

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.

A very similar modern definition given in a recent article defines the valence of a particular atom in a molecule as "the number of electrons that an atom uses in bonding", with two equivalent formulas for calculating valence: [4]

valence = number of electrons in valence shell of free atomnumber of non-bonding electrons on atom in molecule,

and

valence = number of bonds + formal charge.

Historical development

The etymology of the words valence (plural valences ) and valency (plural valencies ) traces back to 1425, meaning "extract, preparation", from Latin valentia "strength, capacity", from the earlier valor "worth, value", and the chemical meaning referring to the "combining power of an element" is recorded from 1884, from German Valenz. [5]

William Higgins' combinations of ultimate particles (1789) Higgins-particles.jpg
William Higgins' combinations of ultimate particles (1789)

The concept of valence was developed in the second half of the 19th century and helped successfully explain the molecular structure of inorganic and organic compounds. [1] The quest for the underlying causes of valence led to the modern theories of chemical bonding, including the cubical atom (1902), Lewis structures (1916), valence bond theory (1927), molecular orbitals (1928), valence shell electron pair repulsion theory (1958), and all of the advanced methods of quantum chemistry.

In 1789, William Higgins published views on what he called combinations of "ultimate" particles, which foreshadowed the concept of valency bonds. [6] 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 radical 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 3-atom groups (e.g., NO3, NH3, NI3, etc.) or 5, i.e., in the 5-atom groups (e.g., NO5, NH4O, PO5, etc.), equivalents of the attached elements. According to him, this is the manner in which their affinities are best satisfied, and by following these examples and postulates, he declares how obvious it is that [7]

A tendency or law prevails (here), and that, no matter what the characters of the uniting atoms may be, the combining power of the attracting element, if I may be allowed the term, is always satisfied by the same number of these atoms.

This “combining power” was afterwards called quantivalence or valency (and valence by American chemists). [6] In 1857 August Kekulé proposed fixed valences for many elements, such as 4 for carbon, and used them to propose structural formulas for many organic molecules, which are still accepted today.

Most 19th-century chemists defined the valence of an element as the number of its bonds without distinguishing different types of valence or of bond. However, in 1893 Alfred Werner described transition metal coordination complexes such as [Co(NH3)6]Cl3, in which he distinguished principal and subsidiary valences (German: 'Hauptvalenz' and 'Nebenvalenz'), corresponding to the modern concepts of oxidation state and coordination number respectively.

For main-group elements, in 1904 Richard Abegg considered positive and negative valences (maximal and minimal oxidation states), and proposed Abegg's rule to the effect that their difference is often 8.

Electrons and valence

The Rutherford model of the nuclear atom (1911) showed that the exterior of an atom is occupied by electrons, which suggests that electrons are responsible for the interaction of atoms and the formation of chemical bonds. In 1916, Gilbert N. Lewis explained valence and chemical bonding in terms of a tendency of (main-group) atoms to achieve a stable octet of 8 valence-shell electrons. According to Lewis, covalent bonding leads to octets by the sharing of electrons, and ionic bonding leads to octets by the transfer of electrons from one atom to the other. The term covalence is attributed to Irving Langmuir, who stated in 1919 that "the number of pairs of electrons which any given atom shares with the adjacent atoms is called the covalence of that atom". [8] The prefix co- means "together", so that a co-valent bond means that the atoms share a valence. Subsequent to that, it is now more common to speak of covalent bonds rather than valence, which has fallen out of use in higher-level work from the advances in the theory of chemical bonding, but it is still widely used in elementary studies, where it provides a heuristic introduction to the subject.

In the 1930s, Linus Pauling proposed that there are also polar covalent bonds, which are intermediate between covalent and ionic, and that the degree of ionic character depends on the difference of electronegativity of the two bonded atoms.

Pauling also considered hypervalent molecules, in which main-group elements have apparent valences greater than the maximal of 4 allowed by the octet rule. For example, in the sulfur hexafluoride molecule (SF6), Pauling considered that the sulfur forms 6 true two-electron bonds using sp3d2 hybrid atomic orbitals, which combine one s, three p and two d orbitals. However more recently, quantum-mechanical calculations on this and similar molecules have shown that the role of d orbitals in the bonding is minimal, and that the SF6 molecule should be described as having 6 polar covalent (partly ionic) bonds made from only four orbitals on sulfur (one s and three p) in accordance with the octet rule, together with six orbitals on the fluorines. [9] Similar calculations on transition-metal molecules show that the role of p orbitals is minor, so that one s and five d orbitals on the metal are sufficient to describe the bonding. [10]

Common valences

For elements in the main groups of the periodic table, the valence can vary between 1 and 7.

GroupValence 1Valence 2Valence 3Valence 4Valence 5Valence 6Valence 7Typical valences
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 HClO2 ClO2 HClO3 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 Greek/Latin numeral prefixes (mono-/uni-, di-/bi-, tri-/ter-, and so on) are used to describe ions in the charge states 1, 2, 3, and so on, respectively. Polyvalence or multivalence refers to species that are not restricted to a specific number of valence bonds. Species with a single charge are univalent (monovalent). For example, the Cs+ cation is a univalent or monovalent cation, whereas the Ca2+ cation is a divalent cation, and the Fe3+ cation is a trivalent cation. Unlike Cs and Ca, Fe can also exist in other charge states, notably 2+ and 4+, and is thus known as a multivalent (polyvalent) ion. [11] Transition metals and metals to the right are typically multivalent but there is no simple pattern predicting their valency. [12]

Valence adjectives using the -valent suffix†
ValenceMore common adjective‡Less common synonymous adjective‡§
0-valent zerovalent nonvalent
1-valent monovalent univalent
2-valent divalent bivalent
3-valent trivalent tervalent
4-valent tetravalent quadrivalent
5-valent pentavalent quinquevalent / quinquivalent
6-valent hexavalent sexivalent
7-valent heptavalent septivalent
8-valent octavalent
9-valent nonavalent
10-valent decavalent
multiple / many / variable polyvalent multivalent
together covalent
not together noncovalent

† The same adjectives are also used in medicine to refer to vaccine valence, with the slight difference that in the latter sense, quadri- is more common than tetra-.

‡ As demonstrated by hit counts in Google web search and Google Books search corpora (accessed 2017).

§ A few other forms can be found in large English-language corpora (for example, *quintavalent, *quintivalent, *decivalent), but they are not the conventionally established forms in English and thus are not entered in major dictionaries.

Valence versus oxidation state

Because of the ambiguity of the term valence, [13] other notations are currently preferred. Beside the system of oxidation numbers as used in Stock nomenclature for coordination compounds, [14] and the lambda notation, as used in the IUPAC nomenclature of inorganic chemistry, [15] 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. [16] 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; ruthenium, in the +8 oxidation state in ruthenium tetroxide, has eight valence bonds.

Examples

Variation of valence vs oxidation state for bonds between two different elements
CompoundFormulaValenceOxidation state
Hydrogen chloride HClH = 1   Cl = 1H = +1   Cl = −1
Perchloric acid *HClO4H = 1   Cl = 7   O = 2H = +1   Cl = +7   O = −2
Sodium hydride NaHNa = 1   H = 1Na = +1   H = −1
Ferrous oxide **FeOFe = 2   O = 2Fe = +2   O = −2
Ferric oxide **Fe2O3Fe = 3   O = 2Fe = +3   O = −2

* The univalent perchlorate ion (ClO
4
) 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.

Variation of valence vs oxidation state for bonds between two atoms of the same element
CompoundFormulaValenceOxidation state
Chlorine Cl2Cl = 1Cl = 0
Hydrogen peroxide H2O2H = 1   O = 2H = +1   O = −1
Acetylene C2H2C = 4   H = 1C = −1   H = +1
Mercury(I) chloride Hg2Cl2Hg = 2   Cl = 1Hg = +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. [17] [18]

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: [19]

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.

Hydrogen has only one valence electron, but it can form bonds with more than one atom. In the bifluoride ion ([HF
2
]
), for example, it forms a three-center four-electron bond with two fluoride atoms:

[ F–H F ↔ F H–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
57
La
Asterisks one.svg72
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
89
Ac
Asterisks 2 (vertical).svg104
Rf
105
Db
106
Sg
107
Bh
108
Hs
109
Mt
110
Ds
111
Rg
112
Cn
113
Nh
114
Fl
115
Mc
116
Lv
117
Ts
118
Og
 
Asterisks one.svg58
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
Asterisks 2 (vertical).svg90
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

See also

Related Research Articles

Chemistry scientific discipline

Chemistry is the scientific discipline involved with elements and compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a reaction with other substances.

Chemical bond Lasting attraction between atoms that enables the formation of chemical compounds

A chemical bond is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds. The bond may result from the electrostatic force of attraction between oppositely charged ions as in ionic bonds or through the sharing of electrons as in covalent bonds. The strength of chemical bonds varies considerably; there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force and hydrogen bonding.

Covalent bond Chemical bond that involves the sharing of electron pairs between atoms

A covalent bond, also called a molecular bond, is a chemical bond that involves the sharing of electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full outer shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonds are much more common than ionic bonds.

Electronegativity, symbol χ, is a concept that describes the tendency of an atom to attract a shared pair of electrons towards itself. An atom's electronegativity is affected by both its atomic number and the distance at which its valence electrons reside from the charged nucleus. The higher the associated electronegativity number, the more an atom or a substituent group attracts electrons towards itself.

Electron counting is a formalism used for classifying compounds and for explaining or predicting electronic structure and bonding. Many rules in chemistry rely on electron-counting:

Ionic bonding Chemical bonding involving attraction between ions

Ionic bonding is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, and is the primary interaction occurring in ionic compounds. It is one of the main types of bonding along with covalent bonding and metallic bonding. Ions are atoms with an electrostatic charge. Atoms that gain electrons make negatively charged ions. Atoms that lose electrons make positively charged ions. This transfer of electrons is known as electrovalence in contrast to covalence. In the simplest case, the cation is a metal atom and the anion is a nonmetal atom, but these ions can be of a more complex nature, e.g. molecular ions like NH+
4
or SO2−
4
. In simpler words, an ionic bond results from the transfer of electrons from a metal to a non-metal in order to obtain a full valence shell for both atoms.

Noble gas Any of the group of chemical elements previously known as inert gases

The noble gases make up a class of chemical elements with similar properties; under standard conditions, they are all odourless, colourless, monatomic gases with very low chemical reactivity. The six naturally occurring noble gases are helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and the radioactive radon (Rn). Oganesson (Og) is variously predicted to be a noble gas as well or to break the trend due to relativistic effects; its chemistry has not yet been investigated.

In chemistry, the term transition metal has three possible definitions:

Sulfate Anion

The sulfate or sulphate ion is a polyatomic anion with the empirical formula SO2−
4
. Sulfate is the spelling recommended by IUPAC, but sulphate is used in British English. Salts, acid derivatives, and peroxides of sulfate are widely used in industry. Sulfates occur widely in everyday life. Sulfates are salts of sulfuric acid and many are prepared from that acid.

Octet rule Chemical rule of thumblets

The octet rule is a chemical rule of thumb that reflects the observation that main group elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rule is especially applicable to carbon, nitrogen, oxygen, and the halogens, but also to metals such as sodium or magnesium.

In chemistry, resonance is a way of describing bonding in certain molecules or ions by the combination of several contributing structures into a resonance hybrid in valence bond theory. It has particular value for describing delocalized electrons within certain molecules or polyatomic ions where the bonding cannot be expressed by one single Lewis structure.

Lewis structures, also known as Lewis dot diagrams, Lewis dot formulas,Lewis dot structures, electron dot structures, or Lewis electron dot structures (LEDS), are diagrams that show the bonding between atoms of a molecule and the lone pairs of electrons that may exist in the molecule. A Lewis structure can be drawn for any covalently bonded molecule, as well as coordination compounds. The Lewis structure was named after Gilbert N. Lewis, who introduced it in his 1916 article The Atom and the Molecule. Lewis structures extend the concept of the electron dot diagram by adding lines between atoms to represent shared pairs in a chemical bond.

Valence electron outer shell electron that is associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed

In chemistry and physics, a valence electron is an outer shell electron that is associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed; in a single covalent bond, both atoms in the bond contribute one valence electron in order to form a shared pair.

The inert pair effect is the tendency of the two electrons in the outermost atomic s-orbital to remain unshared in compounds of post-transition metals. The term inert pair effect is often used in relation to the increasing stability of oxidation states that are two less than the group valency for the heavier elements of groups 13, 14, 15 and 16. The term "inert pair" was first proposed by Nevil Sidgwick in 1927. The name suggests that the outermost s electrons are more tightly bound to the nucleus in these atoms, and therefore more difficult to ionize or share.

A hypervalent molecule (the phenomenon is sometimes colloquially known as expanded octet) is a molecule that contains one or more main group elements apparently bearing more than eight electrons in their valence shells. Phosphorus pentachloride (PCl5), sulfur hexafluoride (SF6), chlorine trifluoride (ClF3), the chlorite (ClO2) ion, and the triiodide (I3) ion are examples of hypervalent molecules.

In chemistry, orbital hybridisation is the concept of mixing atomic orbitals into new hybrid orbitals suitable for the pairing of electrons to form chemical bonds in valence bond theory. Hybrid orbitals are very useful in the explanation of molecular geometry and atomic bonding properties and are symmetrically disposed in space. Although sometimes taught together with the valence shell electron-pair repulsion (VSEPR) theory, valence bond and hybridisation are in fact not related to the VSEPR model.

Formal charge Model for charges on atoms in molecules

In chemistry, a formal charge (FC) is the charge assigned to an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms, regardless of relative electronegativity. When determining the best Lewis structure for a molecule, the structure is chosen such that the formal charge on each of the atoms is as close to zero as possible.

The 3-center 4-electron (3c–4e) bond is a model used to explain bonding in certain hypervalent molecules such as tetratomic and hexatomic interhalogen compounds, sulfur tetrafluoride, the xenon fluorides, and the bifluoride ion. It is also known as the Pimentel–Rundle three-center model after the work published by George C. Pimentel in 1951, which built on concepts developed earlier by Robert E. Rundle for electron-deficient bonding. An extended version of this model is used to describe the whole class of hypervalent molecules such as phosphorus pentafluoride and sulfur hexafluoride as well as multi-center π-bonding such as ozone and sulfur trioxide.

This glossary of chemistry terms is a list of terms and definitions relevant to chemistry, including chemical laws, diagrams and formulae, laboratory tools, glassware, and equipment. Chemistry is a physical science concerned with the composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions; it features an extensive vocabulary and a significant amount of jargon.

Chemical compound Substance composed of multiple elements

A chemical compound is a chemical substance composed of many identical molecules composed of atoms from more than one element held together by chemical bonds. Two atoms of the same element bonded in a molecule do not form a chemical compound, since this would require two different elements.

References

  1. 1 2 Partington, James Riddick (1921). A text-book of inorganic chemistry for university students (1st ed.). OL   7221486M.
  2. 1 2 IUPAC Gold Book definition: valence
  3. Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. ISBN   978-0-08-037941-8.
  4. Parkin, Gerard (May 2006). "Valence, Oxidation Number, and Formal Charge: Three Related but Fundamentally Different Concepts". Journal of Chemical Education. 83 (5): 791. doi:10.1021/ed083p791. ISSN   0021-9584.
  5. Harper, Douglas. "valence". Online Etymology Dictionary .
  6. 1 2 Partington, J.R. (1989). A Short History of Chemistry . Dover Publications, Inc. ISBN   0-486-65977-1.
  7. Frankland, E. (1852). "On a New Series of Organic Bodies Containing Metals". Philosophical Transactions of the Royal Society of London. 142: 417–444. doi:10.1098/rstl.1852.0020.
  8. Langmuir, Irving (1919). "The Arrangement of Electrons in Atoms and Molecules". Journal of the American Chemical Society. 41 (6): 868–934. doi:10.1021/ja02227a002.
  9. Magnusson, Eric (1990). "Hypercoordinate molecules of second-row elements: d functions or d orbitals?". J. Am. Chem. Soc. 112 (22): 7940–7951. doi:10.1021/ja00178a014.
  10. Frenking, Gernot; Shaik, Sason, eds. (May 2014). "Chapter 7: Chemical bonding in Transition Metal Compounds". The Chemical Bond: Chemical Bonding Across the Periodic Table. Wiley -VCH. ISBN   978-3-527-33315-8.
  11. Merriam-Webster, Merriam-Webster's Unabridged Dictionary, Merriam-Webster.
  12. "Lesson 7: Ions and Their Names". Clackamas Community College. Retrieved 5 February 2019.
  13. The Free Dictionary: valence
  14. IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006) " Oxidation number ". doi : 10.1351/goldbook.O04363
  15. IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006) " Lambda ". doi : 10.1351/goldbook.L03418
  16. IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006) " Oxidation state ". doi : 10.1351/goldbook.O04365
  17. Frankland, E. (1870). Lecture notes for chemical students(Google eBook) (2d ed.). J. Van Voorst. p. 21.
  18. Frankland, E.; Japp, F.R (1885). Inorganic chemistry (1st ed.). pp. 75–85. OL   6994182M.
  19. Muller, P. (1994). "Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)". Pure and Applied Chemistry. 66 (5): 1077–1184. doi:10.1351/pac199466051077.