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Let's get this over with.
Combining Capacity of Elements with Other Atoms
For those prone to confusion, yes, there's a whole disambiguation page for Valence. Don't get lost. And for the truly dense, this is not to be mistaken for coordination number, oxidation state, or the rather obvious valence electron. If you need to delve deeper into the concept of multiple valences, there's Polyvalency (chemistry) – a topic that, frankly, is more fascinating than this.
In the grim, unforgiving landscape of chemistry, the valence (or valency, if you prefer the British way of making things sound more complicated) of an atom is essentially a measure of its capacity to engage with other atoms. Think of it as its social aptitude, its willingness to form chemical compounds or molecules. It's generally understood as the number of chemical bonds that an atom of a particular chemical element typically decides to forge. We're talking about the straightforward ones: a double bond counts as two, a triple bond as three, a quadruple bond as four, a quintuple bond as five, and a sextuple bond as six. These are the rules of engagement, the basic interactions. In the grand scheme of things, hydrogen usually plays nice with a valence of 1, oxygen tends to form two bonds, nitrogen three, and carbon, the architect of so much complexity, four. But don't get it twisted; valence isn't some monolithic concept. It's distinct from the more nuanced ideas of coordination number, oxidation state, or the mere count of valence electrons an atom might possess.
Description
So, the valence, this "combining capacity," is determined by how many of those unassuming hydrogen atoms an element can latch onto. Take methane, for instance. Carbon here is showing off a valence of 4. Then there's ammonia, where nitrogen is content with a valence of 3. In water, oxygen settles for 2. And in hydrogen chloride, chlorine is a simple one, valence 1. This chlorine, with its singular bond-forming potential, can often step in to replace hydrogen in various compounds, a sort of chemical understudy. But elements aren't always so predictable. Phosphorus, in phosphine (PH 3 ), exhibits a valence of 3. Yet, in phosphorus pentachloride (PCl 5 ), it escalates to a valence of 5. This demonstrates that an element can, and often does, display more than one valence. The structural formula of a compound, a diagram of how atoms are connected, uses lines to represent these bonds. Each line is a bond, a connection. The tables below offer a glimpse into this dance of atoms, showing various compounds, their structural representations, and the valences of each participating element. It’s a visual representation of their willingness to connect, or perhaps, their desperation.
| Compound | H₂ Hydrogen | CH₄ Methane | C₃H₈ Propane | C₃H₆ Propylene | C₂H₂ Acetylene |
|---|---|---|---|---|---|
| Diagram | |||||
| Valencies | Hydrogen: 1 | Carbon: 4 Hydrogen: 1 |
Carbon: 4 Hydrogen: 1 |
Carbon: 4 Hydrogen: 1 |
Carbon: 4 Hydrogen: 1 |
| Compound | NH₃ Ammonia NaCN Sodium cyanide |
PSCl₃ Thiophosphoryl chloride | H₂S Hydrogen sulfide | H₂SO₄ Sulfuric acid | H₂S₂O₆ Dithionic acid | Cl₂O₇ Dichlorine heptoxide | XeO₄ Xenon tetroxide |
|---|---|---|---|---|---|---|---|
| Diagram | |||||||
| Valencies | Nitrogen: 3 Hydrogen: 1 |
Phosphorus: 5 Sulfur: 2 Chlorine: 1 |
Sulfur: 2 Hydrogen: 1 |
Sulfur: 6 Oxygen: 2 Hydrogen: 1 |
Sulfur: 6 Oxygen: 2 Hydrogen: 1 |
Chlorine: 7 Oxygen: 2 |
Xenon: 8 Oxygen: 2 |
Definition
The IUPAC, in its infinite wisdom, defines valence 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.
A more modern, perhaps more pragmatic, description suggests:
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 latter definition, mind you, allows for the possibility that an element might possess more than one valence. Because, of course, life isn't simple enough.
Historical Development
The very words "valence" and "valency" have a rather unassuming origin, dating back to 1425, meaning something as mundane as "extract" or "preparation." It wasn't until much later, around 1884, that the chemical meaning – the "combining power of an element" – emerged, likely from the German Valenz.
William Higgins' Combinations of Ultimate Particles (1789)
The true conceptualization of valence, the idea that atoms have a specific combining capacity, began to solidify in the latter half of the 19th century. This understanding was crucial in deciphering the intricate molecular structures of both inorganic and organic compounds. The relentless pursuit of what drives this "valence" eventually paved the way for our current, and still evolving, theories of chemical bonding. We’ve gone from the somewhat quaint cubical atom model of 1902, through the intuitive Lewis structures of 1916, the foundational valence bond theory of 1927, the more complex molecular orbitals approach of 1928, and the predictive valence shell electron pair repulsion theory of 1958, all leading to the sophisticated landscape of quantum chemistry we navigate today.
Back in 1789, William Higgins, in his musings on the "combinations of ultimate particles," offered early hints of what we now recognize as valency bonds. He posited that the force between particles, say oxygen and nitrogen, would distribute itself, influencing their combinations. It was a nascent idea, a whisper of the forces at play.
However, the more formal genesis of chemical valency theory is often credited to Edward Frankland in 1852. He dared to blend the established radical theory with notions of chemical affinity, proposing that certain elements consistently combined in groups of three or five equivalents. He observed that their affinities seemed best satisfied this way. He famously declared:
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 later christened "quantivalence" or "valency" (and, in the US, simply "valence"). [5] Then, in 1857, August Kekulé boldly assigned fixed valences to many elements, including the now-iconic 4 for carbon. He used these assignments to construct structural formulas for organic molecules, many of which still stand today.
Lothar Meyer, in his 1864 treatise Die modernen Theorien der Chemie, presented an early iteration of the periodic table. This table, featuring 28 elements, was notable for classifying them into six families based on their valence. Before this, the organization of elements had been hampered by the prevalent use of equivalent weights instead of atomic weights. [7]
Most chemists of the 19th century operated with a simpler definition of valence: the number of bonds an element formed, without much distinction between bond types. That is, until 1893, when Alfred Werner, grappling with transition metal coordination complexes like [Co(NH₃)₆]Cl₃, began to differentiate between "principal valences" and "subsidiary valences" (German: 'Hauptvalenz' and 'Nebenvalenz'). These concepts foreshadowed our modern understanding of oxidation state and coordination number, respectively.
Later, in 1904, Richard Abegg explored the idea of positive and negative valences for main-group elements, linking them to maximum and minimum oxidation states. He proposed Abegg's rule, noting that the difference between these valences often summed to eight.
An alternative perspective on valence, still championed by some today, emerged in the 1920s. This definition, particularly useful for covalent molecules, defines an atom's valence by the number of electrons it has used in bonding: [8] [9] [10] [11]
valence = number of electrons in valence shell of free atom − number of non-bonding electrons on atom in molecule
Or, put more simply:
valence = number of bonds + formal charge.
Under this convention, the nitrogen in an ammonium ion [NH₄]⁺, despite bonding to four hydrogen atoms, is considered pentavalent because all five of nitrogen's valence electrons are engaged in bonding. [8]
Electrons and Valence
The Rutherford model of the atom, established in 1911, revealed that the atom's exterior is populated by electrons. This naturally led to the conclusion that electrons must be the key players in atomic interactions and the formation of chemical bonds. By 1916, Gilbert N. Lewis offered an explanation for valence and bonding, rooted in the tendency of (main-group) atoms to achieve a stable configuration of eight valence-shell electrons – the famous octet rule. Lewis proposed that covalent bonding achieved this stability through electron sharing, while ionic bonding did so via electron transfer. The term "covalence" itself is attributed to Irving Langmuir, who in 1919 stated that "the number of pairs of electrons which any given atom shares with the adjacent atoms is called the covalence of that atom." [12] The prefix "co-" signifies "together," implying that a covalent bond is a partnership of shared valence. Over time, as our understanding of chemical bonding deepened, the term "covalent bond" became more prevalent than "valence" in advanced discussions, though "valence" persists as a valuable introductory concept, a heuristic stepping stone into the subject.
In the 1930s, Linus Pauling introduced the concept of polar covalent bonds, bridging the gap between purely covalent and ionic bonds. He explained that the degree of ionic character depended on the difference in electronegativity between the bonded atoms.
Pauling also delved into the realm of hypervalent molecules, where main-group elements seemed to exceed the octet rule's limit of four bonds. For instance, in sulfur hexafluoride (SF₆), Pauling suggested that sulfur formed six true two-electron bonds by employing hybrid atomic orbitals, specifically sp³d². However, more recent quantum-mechanical calculations have cast doubt on the significant role of d orbitals in such bonding. These calculations suggest that SF₆ is better described as having six polar covalent (partially ionic) bonds, formed using only four orbitals on sulfur (one s and three p), in line with the octet rule, and engaging the six orbitals of the fluorine atoms. [13] Similar analyses of transition-metal compounds indicate a reduced role for p orbitals, suggesting that one s and five d orbitals on the metal are sufficient for describing the bonding. [14]
Common Valences
For elements situated in the main groups of the periodic table, valence values can range from 1 to 8.
| Group | Valence 1 | Valence 2 | Valence 3 | Valence 4 | Valence 5 | Valence 6 | Valence 7 | Valence 8 | Typical valences |
|---|---|---|---|---|---|---|---|---|---|
| 1 (I) | NaCl NaCl, KCl KCl | 1 | |||||||
| 2 (II) | MgCl₂ MgCl₂, CaCl₂ CaCl₂ | 2 | |||||||
| 13 (III) | InBr InBr, TlI TlI | BCl₃ BCl₃, AlCl₃ AlCl₃, Al₂O₃ Al₂O₃ | 3 | ||||||
| 14 (IV) | CO CO, PbCl₂ PbCl₂ | CO₂ CO₂, CH₄ CH₄, SiCl₄ SiCl₄ | 2 and 4 | ||||||
| 15 (V) | NO NO | NH₃ NH₃, PH₃ PH₃, As₂O₃ As₂O₃ | NO₂ NO₂, N₂O₅ N₂O₅, PCl₅ PCl₅ | 3 and 5 | |||||
| 16 (VI) | H₂O H₂O, H₂S H₂S, SCl₂ SCl₂ | SO₂ SO₂, SF₄ SF₄ | SO₃ SO₃, SF₆ SF₆, H₂SO₄ H₂SO₄ | 2, 4 and 6 | |||||
| 17 (VII) | HCl HCl, ICl ICl | HClO₂ HClO₂, ClF₃ ClF₃ | ClO₂ ClO₂, IF₅ IF₅, HClO₃ HClO₃ | IF₇ IF₇, Cl₂O₇ Cl₂O₇, HClO₄ HClO₄ | 1, 3, 5 and 7 | ||||
| 18 (VIII) | KrF₂ KrF₂ | XeF₄ XeF₄ | XeO₃ XeO₃ | XeO₄ XeO₄ | 0, 2, 4, 6 and 8 |
Many elements exhibit a common valence dictated by their position in the periodic table, a phenomenon now largely explained by the octet rule.
The familiar Greek/Latin numeral prefixes (mono-/uni-, di-/bi-, tri-/ter-, and so on) are employed to denote ions with charges of 1, 2, 3, and so forth. The term "polyvalence" or "multivalence" applies to species that aren't confined to a single valence bond count. A species with a single charge is deemed univalent (or monovalent). For instance, the cation Cs⁺ is univalent, while Ca²⁺ is divalent, and Fe³⁺ is trivalent. Unlike Cs and Ca, iron (Fe) can exist in multiple charge states (notably 2+ and 4+), making it a multivalent (or polyvalent) ion. [15] Transition metals and elements towards the right of the periodic table are typically multivalent, though predicting their precise valency can be a rather haphazard affair. [16]
| Valence | More 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 | — |
| 11-valent | undecavalent | — |
| 12-valent | dodecavalent | — |
| Multiple / Many / Variable | polyvalent, multivalent | |
| Together covalent | — | |
| Not together noncovalent | — |
† These same adjectives are also used in medicine for vaccine valence, with "quadri-" being more common than "tetra-". ‡ Based on Google search data (accessed 2017). § Other forms exist but are not conventionally established.
Valence versus Oxidation State
Given the inherent ambiguity of the term "valence," [17] other notations are generally favored today. Beyond the lambda notation used in [IUPAC nomenclature of inorganic chemistry], [18] the oxidation state provides a much clearer picture of an atom's electronic condition within a molecule.
The oxidation state of an atom in a molecule quantifies the number of valence electrons it has either gained or lost. [19] Unlike valency, the oxidation state can be positive (for electropositive atoms) or negative (for electronegative atoms).
Elements in a high oxidation state (greater than +4) often correlate with elements in a high valence state (hypervalent elements), where the valence exceeds 4. For example, in perchlorates (ClO⁻₄), chlorine forms 7 valence bonds, making it heptavalent (valence 7), and its oxidation state is +7. Similarly, in ruthenium tetroxide (RuO₄), ruthenium forms 8 valence bonds, rendering it octavalent (valence 8), with an oxidation state of +8.
However, there are instances where valence and oxidation state diverge for a given atom. Consider disulfur decafluoride (S₂F₁₀). Each sulfur atom is bonded to five fluorine atoms and one other sulfur atom, giving it 6 valence bonds, hence it is hexavalent (valence 6). Yet, its oxidation state is +5. In the dioxygen molecule (O₂), each oxygen atom participates in 2 valence bonds, making it divalent (valence 2), but its oxidation state is 0. And in acetylene (H−C≡C−H), each carbon atom forms 4 valence bonds (one single bond with hydrogen and a triple bond with the other carbon). Each carbon is tetravalent (valence 4), but its oxidation state is −1.
Examples
Variation of valence vs oxidation state for bonds between two different elements
| Compound | Formula | Valence | Oxidation state | Diagram |
|---|---|---|---|---|
| Hydrogen chloride | HCl | H = 1, Cl = 1 | H = +1, Cl = −1 | H−Cl |
| Perchloric acid * | HClO₄ | H = 1, Cl = 7, O = 2 | H = +1, Cl = +7, O = −2 | |
| Methane | CH₄ | C = 4, H = 1 | C = −4, H = +1 | |
| Dichloromethane ** | CH₂Cl₂ | C = 4, H = 1, Cl = 1 | C = 0, H = +1, Cl = −1 | |
| Ferrous oxide *** | FeO | Fe = 2, O = 2 | Fe = +2, O = −2 | Fe=O |
| Ferric oxide *** | Fe₂O₃ | Fe = 3, O = 2 | Fe = +3, O = −2 | O=Fe−O−Fe=O |
| Sodium hydride | NaH | Na = 1, H = 1 | Na = +1, H = −1 | Na−H |
* The perchlorate ion (ClO⁻₄) is monovalent, meaning it has a valence of 1. ** Valences can differ from the absolute values of oxidation states due to varying bond polarity. For instance, in dichloromethane (CH₂Cl₂), carbon has a valence of 4 but an oxidation state of 0. *** Iron oxides exist in a crystal structure, so a typical molecule isn't easily identified. In ferrous oxide, Fe has an oxidation state of +2; in ferric oxide, it's +3.
Variation of valence vs oxidation state for bonds between two atoms of the same element
| Compound | Formula | Valence | Oxidation state | Diagram |
|---|---|---|---|---|
| Hydrogen | H₂ | H = 1 | H = 0 | H−H |
| Chlorine | Cl₂ | Cl = 1 | Cl = 0 | Cl−Cl |
| Hydrogen peroxide | H₂O₂ | H = 1, O = 2 | H = +1, O = −1 | |
| Hydrazine | N₂H₄ | H = 1, N = 3 | H = +1, N = −2 | |
| Disulfur decafluoride | S₂F₁₀ | S = 6, F = 1 | S = +5, F = −1 | |
| Dithionic acid | H₂S₂O₆ | S = 6, O = 2, H = 1 | S = +5, O = −2, H = +1 | |
| Hexachloroethane | C₂Cl₆ | C = 4, Cl = 1 | C = +3, Cl = −1 | |
| Ethylene | C₂H₄ | C = 4, H = 1 | C = −2, H = +1 | |
| Acetylene | C₂H₂ | C = 4, H = 1 | C = −1, H = +1 | H−C≡C−H |
| Mercury(I) chloride | Hg₂Cl₂ | Hg = 2, Cl = 1 | Hg = +1, Cl = −1 | Cl−Hg−Hg−Cl |
"Maximum Number of Bonds" Definition
Edward Frankland viewed valence (which he termed "atomicity") as a singular, maximum value observed for an element. He proposed that any "unused valencies" on atoms, particularly in the p-block elements, would tend to saturate each other. For instance, nitrogen, with a maximum valence of 5, leaves two valencies unattached in ammonia. Sulfur, with a maximum valence of 6, leaves four unattached in hydrogen sulfide. [20] [21]
The International Union of Pure and Applied Chemistry (IUPAC) has, over time, attempted to refine the definition of valence for clarity. The current iteration, adopted in 1994, states:
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 initially chosen as examples of univalent atoms due to their propensity to form only a single bond. Hydrogen, with just one valence electron, can form a bond with an atom needing to complete its outer shell. Chlorine, possessing seven valence electrons, can form a single bond by accepting an electron to complete its shell. However, chlorine's capacity extends beyond this; it can exhibit oxidation states from +1 to +7 and form multiple bonds by donating valence electrons.
Even hydrogen, with its single valence electron, can engage in bonding with more than one atom. Consider the bifluoride ion ([HF₂]⁻), where it forms a three-center four-electron bond with two fluoride atoms:
[F−H F⁻ ↔ F⁻ H−F]
Another example of complex bonding is the three-center two-electron bond observed in diborane (B₂H₆).
Maximum Valences of the Elements
The maximum valences presented here are derived from the data found in the List of oxidation states of the elements. The color coding at the bottom of the table visually represents these maximum valences.
| Group → | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Period 1 ↓ | 1 H | 2 He | ||||||||||||||||
| Period 2 | 3 Li | 4 Be | 5 B | 6 C | 7 N | 8 O | 9 F | 10 Ne | ||||||||||
| Period 3 | 11 Na | 12 Mg | 13 Al | 14 Si | 15 P | 16 S | 17 Cl | 18 Ar | ||||||||||
| Period 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 |
| Period 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 |
| Period 6 | 55 Cs | 56 Ba | 71 Lu | 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 |
| Period 7 | 87 Fr | 88 Ra | 103 Lr | 104 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 |
| Lanthanides | 57 La to 70 Yb | |||||||||||||||||
| Actinides | 89 Ac to 102 No |
Color code: 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Unknown Background color indicates the maximum valence of the chemical element. Primordial From decay Synthetic Border shows natural occurrence of the element.