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{{short description|Compact notation for chemical compounds}}
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{{Sources exist|date=July 2024}}
{{Infobox
| title            = <chem>Al_2(SO_4)_3</chem>
| data2            = Chemical formula for [[aluminium sulfate]]
}}
{{Infobox
| title            = <chem>H-\overset{\displaystyle H \atop |}{\underset{| \atop \displaystyle H}{C}}-\overset{\displaystyle H \atop |}{\underset{| \atop \displaystyle H}{C}}-\overset{\displaystyle H \atop |}{\underset{| \atop \displaystyle H}{C}}-\overset{\displaystyle H \atop |}{\underset{| \atop \displaystyle H}{C}}-H</chem>
| data2            = [[Structural formula]] for [[butane]]
}}

A '''chemical formula''' is a way of  presenting information about the chemical proportions of [[atom]]s that constitute a particular [[chemical compound]] or [[molecule]], using [[chemical element]] symbols, numbers, and sometimes also other symbols, such as parentheses, dashes, brackets, commas and ''plus'' (+) and ''minus'' (−) signs. These are limited to a single typographic line of symbols, which may include [[Subscript and superscript|subscripts and superscripts]]. A chemical formula is not a [[chemical nomenclature|chemical name]] since it does not contain any words. Although a chemical formula may imply certain simple [[chemical structure]]s, it is not the same as a full chemical [[structural formula]]. Chemical formulae can fully specify the structure of only the simplest of molecules and [[chemical substance]]s, and are generally more limited in power than chemical names and structural formulae.

The simplest types of chemical formulae are called ''[[empirical formula]]e'', which use letters and numbers indicating the numerical ''proportions'' of atoms of each type. '''Molecular formulae''' indicate the simple numbers of each type of atom in a molecule, with no information on structure. For example, the empirical formula for [[glucose]] is {{chem2|CH2O}} (twice as many [[hydrogen]] atoms as [[carbon]] and [[oxygen]]), while its molecular formula is {{chem2|C6H12O6}} (12 hydrogen atoms, six carbon and oxygen atoms).

Sometimes a chemical formula is complicated by being written as a [[condensed formula]] (or condensed molecular formula, occasionally called a "semi-structural formula"), which conveys additional information about the particular ways in which the atoms are [[chemical bond|chemically bonded]] together, either in [[covalent bond]]s, [[ionic bond]]s, or various combinations of these types. This is possible if the relevant bonding is easy to show in one dimension. An example is the condensed molecular/chemical formula for [[ethanol]], which is {{chem2|CH3\sCH2\sOH}} or {{chem2|CH3CH2OH}}. However, even a condensed chemical formula is necessarily limited in its ability to show complex bonding relationships between atoms, especially atoms that have bonds to four or more different [[substituent]]s.

Since a chemical formula must be expressed as a single line of chemical [[element symbol]]s, it often cannot be as informative as a true structural formula, which is a graphical representation of the spatial relationship between atoms in chemical compounds (see for example the figure for butane structural and chemical formulae, at right). For reasons of structural complexity, a single condensed chemical formula (or semi-structural formula) may correspond to different molecules, known as [[isomer]]s. For example, glucose shares its [[molecular formula]] {{chem2|C6H12O6}} with a number of other [[sugar]]s, including [[fructose]], [[galactose]] and [[mannose]]. Linear equivalent chemical ''names'' exist that can and do specify uniquely any complex structural formula (see [[chemical nomenclature]]), but such names must use many terms (words), rather than the simple element symbols, numbers, and simple typographical symbols that define a chemical formula.

Chemical formulae may be used in [[chemical equation]]s to describe [[chemical reaction]]s and other chemical transformations, such as the dissolving of ionic compounds into solution. While, as noted, chemical formulae do not have the full power of structural formulae to show chemical relationships between atoms, they are sufficient to keep track of numbers of atoms and numbers of electrical charges in chemical reactions, thus [[Chemical equation#Balancing chemical equations|balancing chemical equations]] so that these equations can be used in chemical problems involving conservation of atoms, and conservation of electric charge.

== Overview ==
A chemical formula identifies each constituent [[chemical element|element]] by its [[chemical symbol]] and indicates the proportionate number of atoms of each element. In empirical formulae, these proportions begin with a key element and then assign numbers of atoms of the other elements in the compound, by ratios to the key element. For molecular compounds, these ratio numbers can all be expressed as whole numbers. For example, the empirical formula of [[ethanol]] may be written {{chem2|C2H6O}} because the molecules of ethanol all contain two carbon atoms, six hydrogen atoms, and one oxygen atom. Some types of ionic compounds, however, cannot be written with entirely whole-number empirical formulae. An example is [[boron carbide]], whose formula of {{chem2|CB_{''n''} }} is a variable non-whole number ratio with n ranging from over 4 to more than 6.5.

When the chemical compound of the formula consists of simple [[molecule]]s, chemical formulae often employ ways to suggest the structure of the molecule. These types of formulae are variously known as ''molecular formulae'' and ''[[structural formula|condensed formulae]]''. A molecular formula enumerates the number of atoms to reflect those in the molecule, so that the molecular formula for [[glucose]] is {{chem2|C6H12O6}} rather than the glucose empirical formula, which is {{chem2|CH2O}}. However, except for very simple substances, molecular chemical formulae lack needed structural information, and are ambiguous.

For simple molecules, a condensed (or semi-structural) formula is a type of chemical formula that may fully imply a correct structural formula. For example, ethanol may be represented by the condensed chemical formula {{chem2|CH3CH2OH}}, and [[dimethyl ether]] by the condensed formula {{chem2|CH3OCH3}}. These two molecules have the same empirical and molecular formulae ({{chem2|C2H6O}}), but may be differentiated by the condensed formulae shown, which are sufficient to represent the full structure of these simple [[organic compound]]s.

Condensed chemical formulae may also be used to represent [[ionic compound]]s that do not exist as discrete molecules, but nonetheless do contain covalently bound clusters within them. These [[polyatomic ion]]s are groups of atoms that are covalently bound together and have an overall ionic charge, such as the [[sulfate]] {{chem2|[SO4]^{2-} }} ion. Each polyatomic ion in a compound is written individually in order to illustrate the separate groupings. For example, the compound [[dichlorine hexoxide]] has an empirical formula {{chem2|ClO3}}, and molecular formula {{chem2|Cl2O6}}, but in liquid or solid forms, this compound is more correctly shown by an ionic condensed formula {{chem2|[ClO2]+[ClO4]-}}, which illustrates that this compound consists of {{chem2|[ClO2]+}} ions and {{chem2|[ClO4]-}} ions. In such cases, the condensed formula only need be complex enough to show at least one of each ionic species.

Chemical formulae as described here are distinct from the far more complex chemical systematic names that are used in various systems of [[chemical nomenclature]]. For example, one systematic name for glucose is (2''R'',3''S'',4''R'',5''R'')-2,3,4,5,6-pentahydroxyhexanal. This name, interpreted by the rules behind it, fully specifies glucose's structural formula, but the name is not a chemical formula as usually understood, and uses terms and words not used in chemical formulae. Such names, unlike basic formulae, may be able to represent full structural formulae without graphs.

== Types ==

=== Empirical formula ===
{{anchor|1=Empirical formulae}}
{{main|Empirical formula}}
In [[chemistry]], the [[empirical formula]] of a chemical is a simple expression of the relative number of each type of atom or ratio of the elements in the compound. Empirical formulae are the standard for [[ionic compound]]s, such as {{chem2|CaCl2}}, and for macromolecules, such as {{chem2|SiO2}}. An empirical formula makes no reference to [[isomer]]ism, structure, or absolute number of atoms. The term ''empirical'' refers to the process of [[elemental analysis]], a technique of [[analytical chemistry]] used to determine the relative percent composition of a pure chemical substance by element.

For example, [[hexane]] has a molecular formula of {{chem2|C6H14}}, and (for one of its isomers, n-hexane) a structural formula {{chem2|CH3CH2CH2CH2CH2CH3}}, implying that it has a chain structure of 6 [[carbon]] atoms, and 14 [[hydrogen]] atoms. However, the empirical formula for hexane is {{chem2|C3H7}}. Likewise the empirical formula for [[hydrogen peroxide]], {{chem2|H2O2}}, is simply {{chem2|HO}}, expressing the 1:1 ratio of component elements. [[Formaldehyde]] and [[acetic acid]] have the same empirical formula, {{chem2|CH2O}}. This is also the molecular formula for formaldehyde, but acetic acid has double the number of atoms.

Like the other formula types detailed below, an empirical formula shows the number of elements in a molecule, and determines whether it is a [[binary compound]], [[ternary compound]], [[quaternary compound]], or has even more elements.

=== Molecular formula ===
[[File:Isobutane_numbered_2D.svg|class=skin-invert-image|thumb|right|180px|[[Isobutane]] structural formula<br />Molecular formula: {{chem2|C4H10}}<br />Condensed formula: {{chem2|(CH3)3CH}}]]

{{Image frame
|content=<chem>H-\overset{\displaystyle H \atop |}{\underset{| \atop \displaystyle H}{C}}-\overset{\displaystyle H \atop |}{\underset{| \atop \displaystyle H}{C}}-\overset{\displaystyle H \atop |}{\underset{| \atop \displaystyle H}{C}}-\overset{\displaystyle H \atop |}{\underset{| \atop \displaystyle H}{C}}-H</chem>
|align=right|width=180
|caption=[[n-Butane|''n''-Butane]] structural formula<br />Molecular formula: {{chem2|C4H10}}<br />Condensed formula: {{chem2|CH3CH2CH2CH3}}
}}

Molecular formulae simply indicate the numbers of each type of atom in a molecule of a molecular substance. They are the same as empirical formulae for molecules that only have one atom of a particular type, but otherwise may have larger numbers. An example of the difference is the empirical formula for glucose, which is {{chem2|CH2O}} (''ratio'' 1:2:1), while its molecular formula is {{chem2|C6H12O6}} (''number of atoms'' 6:12:6). For water, both formulae are {{chem2|H2O}}. A molecular formula provides more information about a molecule than its empirical formula, but is more difficult to establish.

=== Structural formula ===
{{Main|Structural formula}}
In addition to indicating the number of atoms of each elementa molecule, a structural formula indicates how the atoms are organized, and shows (or implies) the [[chemical bond]]s between the atoms. There are multiple types of structural formulas focused on different aspects of the molecular structure.

The two diagrams show two molecules which are [[structural isomer]]s of each other, since they both have the same molecular formula {{chem2|C4H10}}, but they have different structural formulas as shown.

=== Condensed formula ===
{{Main|Condensed formula}}
The [[connectivity (graph theory)|connectivity]] of a molecule often has a strong influence on its physical and chemical properties and behavior. Two molecules composed of the same numbers of the same types of atoms (i.e. a pair of [[isomer]]s) might have completely different chemical and/or physical properties if the atoms are connected differently or in different positions. In such cases, a [[structural formula]] is useful, as it illustrates which atoms are bonded to which other ones. From the connectivity, it is often possible to deduce the approximate [[molecular geometry|shape of the molecule]].

A condensed (or semi-structural) formula may represent the types and spatial arrangement of [[Chemical bond|bonds]] in a simple chemical substance, though it does not necessarily specify [[isomer]]s or complex structures. For example, [[ethane]] consists of two carbon atoms single-bonded to each other, with each carbon atom having three hydrogen atoms bonded to it. Its chemical formula can be rendered as {{chem2|CH3CH3}}. In [[ethylene]] there is a double bond between the carbon atoms (and thus each carbon only has two hydrogens), therefore the chemical formula may be written: {{chem2|CH2CH2}}, and the fact that there is a double bond between the carbons is implicit because carbon has a valence of four. However, a more explicit method is to write {{chem2|H2C\dCH2}} or less commonly {{chem2|H2C::CH2}}. The two lines (or two pairs of dots) indicate that a [[double bond]] connects the atoms on either side of them.

A [[triple bond]] may be expressed with three lines ({{chem2|HC\tCH}}) or three pairs of dots ({{chem2|HC:::CH}}), and if there may be ambiguity, a single line or pair of dots may be used to indicate a single bond.

Molecules with multiple [[functional group]]s that are the same may be expressed by enclosing the repeated group in [[parenthesis|round brackets]]. For example, [[isobutane]] may be written {{chem2|(CH3)3CH}}. This condensed structural formula implies a different connectivity from other molecules that can be formed using the same atoms in the same proportions ([[isomer]]s). The formula {{chem2|(CH3)3CH}} implies a central carbon atom connected to one hydrogen atom and three [[methyl group]]s ({{chem2|CH3}}). The same number of atoms of each element (10 hydrogens and 4 carbons, or {{chem2|C4H10}}) may be used to make a straight chain molecule, ''n''-[[butane]]: {{chem2|CH3CH2CH2CH3}}.

=== Chemical names in answer to limitations of chemical formulae ===<!-- what why here??? -->
{{main|Chemical nomenclature}}
The alkene called [[but-2-ene]] has two isomers, which the chemical formula {{chem2|CH3CH\dCHCH3}} does not identify. The relative position of the two methyl groups must be indicated by additional notation denoting whether the methyl groups are on the same side of the double bond (''cis'' or ''Z'') or on the opposite sides from each other (''trans'' or ''E'').<ref>{{Cite book|last=Burrows, Andrew.|title=Chemistry³ : introducing inorganic, organic and physical chemistry|isbn=978-0-19-969185-2|edition=Second|location=Oxford|oclc=818450212|date=2013-03-21 |publisher=Oxford University Press}}</ref>

As noted above, in order to represent the full structural formulae of many complex organic and inorganic compounds, [[chemical nomenclature]] may be needed which goes well beyond the available resources used above in simple condensed formulae. See [[IUPAC nomenclature of organic chemistry]] and [[IUPAC nomenclature of inorganic chemistry|IUPAC nomenclature of inorganic chemistry 2005]] for examples. In addition, linear naming systems such as [[International Chemical Identifier]] (InChI) allow a computer to construct a structural formula, and [[simplified molecular-input line-entry system]] (SMILES) allows a more human-readable ASCII input. However, all these nomenclature systems go beyond the standards of chemical formulae, and technically are chemical naming systems, not formula systems.<ref>{{Cite web |last=Miles |first=Linda |title=LibGuides: CHE 120 - Introduction to Organic Chemistry - Textbook: Chapter 1 - Organic Chemistry Review / Hydrocarbons |url=https://guides.hostos.cuny.edu/che120/chapter1 |access-date=2024-07-13 |website=guides.hostos.cuny.edu |language=en}}</ref> 

=== Polymers in condensed formulae ===

For [[polymer]]s in condensed chemical formulae, parentheses are placed around the repeating unit. For example, a [[hydrocarbon]] molecule that is described as {{chem2|CH3(CH2)50CH3}}, is a molecule with fifty repeating units. If the number of repeating units is unknown or variable, the letter ''n'' may be used to indicate this formula: {{chem2|CH3(CH2)_{''n''}CH3}}.

=== Ions in condensed formulae ===
For [[ion]]s, the charge on a particular atom may be denoted with a right-hand superscript. For example, {{chem2|Na+}}, or {{chem2|Cu(2+)}}. The total charge on a charged molecule or a [[polyatomic ion]] may also be shown in this way, such as for [[hydronium]], {{chem2|H3O+}}, or [[sulfate]], {{chem2|SO4(2-)}}. Here + and − are used in place of +1 and −1, respectively.

For more complex ions, brackets [ ] are often used to enclose the ionic formula, as in {{chem2|[B12H12](2-)}}, which is found in compounds such as [[caesium dodecaborate]], {{chem2|Cs2[B12H12]}}. Parentheses ( ) can be nested inside brackets to indicate a repeating unit, as in [[Hexamminecobalt(III) chloride]], {{chem2|[Co(NH3)6](3+)Cl3-}}. Here, {{chem2|(NH3)6}} indicates that the ion contains six [[Metal ammine complex|ammine group]]s ({{chem2|NH3}}) bonded to [[cobalt]], and [ ] encloses the entire formula of the ion with charge +3. {{Elucidate|date=November 2012}}

This is strictly optional; a chemical formula is valid with or without ionization information, and Hexamminecobalt(III) chloride may be written as {{chem2|[Co(NH3)6](3+)Cl3-}} or {{chem2|[Co(NH3)6]Cl3}}. Brackets, like parentheses, behave in chemistry as they do in mathematics, grouping terms together{{snd}}they are not specifically employed only for ionization states. In the latter case here, the parentheses indicate 6 groups all of the same shape, bonded to another group of size 1 (the cobalt atom), and then the entire bundle, as a group, is bonded to 3 chlorine atoms. In the former case, it is clearer that the bond connecting the chlorines is [[ionic bonding|ionic]], rather than [[covalent bond|covalent]].

== Isotopes ==

Although [[isotope]]s are more relevant to [[nuclear chemistry]] or [[stable isotope]] chemistry than to conventional chemistry, different isotopes may be indicated with a prefixed [[superscript]] in a chemical formula. For example, the phosphate ion containing radioactive phosphorus-32 is {{chem2|[^{32}PO4]^{3-} }}. Also a study involving stable isotope ratios might include the molecule {{chem2|^{18}O^{16}O}}.

A left-hand subscript is sometimes used redundantly to indicate the [[atomic number]]. For example, {{chem2|_{8}O2}} for dioxygen, and {{ComplexNuclide|O|16|q=2}}  for the most abundant isotopic species of dioxygen. This is convenient when writing equations for [[nuclear reaction]]s, in order to show the balance of charge more clearly.

== Trapped atoms ==
[[File:Endohedral fullerene.png|thumb|180px|Traditional formula: {{chem2|MC60}}<br>The "@" notation: {{chem2|M@C60}}]]
{{main|Endohedral fullerene}}
The @ symbol ([[at sign]]) indicates an atom or molecule trapped inside a cage but not chemically bound to it. For example, a [[buckminsterfullerene]] ({{chem2|C60}}) with an atom (M) would simply be represented as {{chem2|MC60}} regardless of whether M was inside the fullerene without chemical bonding or outside, bound to one of the carbon atoms. Using the @ symbol, this would be denoted {{chem2|M@C60}} if M was inside the carbon network. A non-fullerene example is {{chem2|[As@Ni12As20](3-)}}, an ion in which one [[arsenic]] (As) atom is trapped in a cage formed by the other 32 atoms.

This notation was proposed in 1991<ref name=YanChai>{{cite journal |title=Fullerenes wlth Metals Inside |author1=Chai, Yan |author2=Guo, Ting |author3=Jin, Changming |author4=Haufler, Robert E. |author5=Chibante, L. P. Felipe |author6=Fure, Jan |author7=Wang, Lihong |author8=Alford, J. Michael |author9=Smalley, Richard E. |journal=Journal of Physical Chemistry |volume=95 |issue=20 |year=1991 |pages=7564–7568 |doi=10.1021/j100173a002}}</ref> with the discovery of [[fullerene]] cages ([[endohedral fullerene]]s), which can trap atoms such as [[Lanthanum|La]] to form, for example, {{chem2|La@C60}} or {{chem2|La@C82}}. The choice of the symbol has been explained by the authors as being concise, readily printed and transmitted electronically (the at sign is included in [[ASCII]], which most modern character encoding schemes are based on), and the visual aspects suggesting the structure of an endohedral fullerene.

== Non-stoichiometric chemical formulae ==

{{Main|Non-stoichiometric compound}}

Chemical formulae most often use [[integer]]s for each element. However, there is a class of compounds, called [[non-stoichiometric compound]]s, that cannot be represented by small integers. Such a formula might be written using [[decimal fraction]]s, as in {{chem2|Fe0.95O}}, or it might include a variable part represented by a letter, as in {{chem2|Fe_{1–''x''}O}}, where ''x'' is normally much less than 1.

== General forms for organic compounds ==
A chemical formula used for a series of compounds that differ from each other by a constant unit is called a ''general formula''. It generates a [[homologous series]] of chemical formulae. For example, [[alcohols]] may be represented by the formula {{chem2|C_{''n''}H_{2''n'' + 1}OH}} (''n'' ≥  1), giving the homologs [[methanol]], [[ethanol]], [[propanol]] for 1 ≤ ''n'' ≤ 3.

== Hill system ==
The '''Hill system''' (or Hill notation) is a system of writing empirical chemical formulae, molecular chemical formulae and components of a condensed formula such that the number of [[carbon]] [[atom]]s in a [[molecule]] is indicated first, the number of [[hydrogen]] atoms next, and then the number of all other [[chemical element]]s subsequently, in [[alphabetical order]] of the [[chemical symbols]]. When the formula contains no carbon,  all the elements, including hydrogen, are listed alphabetically.

By sorting formulae according to the number of atoms of each element present in the formula according to these rules, with differences in earlier elements or numbers being treated as more significant than differences in any later element or number&mdash;like sorting text strings into [[lexicographical order]]&mdash;it is possible to [[collation|collate]] chemical formulae into what is known as Hill system order.

The Hill system was first published by [[Edwin A. Hill]] of the [[United States Patent and Trademark Office]] in 1900.<ref>{{cite journal | author = Edwin A. Hill | title = On a system of indexing chemical literature; Adopted by the Classification Division of the U.S. Patent Office | journal = [[J. Am. Chem. Soc.]] | year = 1900 | volume = 22 | issue = 8 | pages = 478–494 | doi = 10.1021/ja02046a005| bibcode = 1900JAChS..22..478H | hdl = 2027/uiug.30112063986233 | url = https://zenodo.org/record/1428916 }}</ref> It is the most commonly used system in chemical databases and printed indexes to sort lists of compounds.<ref name="wiggins">Wiggins, Gary. (1991). ''Chemical Information Sources.'' New York: McGraw Hill. p. 120.</ref>

A list of formulae in Hill system order is arranged alphabetically, as above, with single-letter elements coming before two-letter symbols when the symbols begin with the same letter (so "B" comes before "Be", which comes before "Br").<ref name="wiggins"/>

The following example formulae are written using the Hill system, and listed in Hill order:

* BrClH<sub>2</sub>Si
* BrI
* CCl<sub>4</sub>
* CH<sub>3</sub>I
* C<sub>2</sub>H<sub>5</sub>Br
* H<sub>2</sub>O<sub>4</sub>S

== See also ==
{{Portal|Chemistry}}
<!---♦♦♦ Please keep the list in alphabetical order ♦♦♦--->
* [[Formula unit]]
* [[Glossary of chemical formulae]]
* [[Nuclear notation]]
* [[Periodic table]]
* [[Skeletal formula]]
* [[Simplified molecular-input line-entry system]]

== Notes ==
{{notelist}}

== References ==
{{Wikidata property|P274}}
{{reflist}}
* {{cite book |last1 = Petrucci |first1 = Ralph H. |last2 = Harwood |first2 = William S. |last3 = Herring |first3 = F. Geoffrey |date=2002 |title = General chemistry: principles and modern applications |chapter-url = https://archive.org/details/generalchemistry00hill |chapter-url-access = registration |edition=8th |location=Upper Saddle River, N.J |publisher=Prentice Hall |isbn = 978-0-13-014329-7 |lccn=2001032331 |oclc=46872308 |chapter=3 }}

== External links ==
* {{Commons category-inline}}
* [http://library.uml.edu/personal/Marion_Muskiewicz/hillorder.htm Hill notation example], from the University of Massachusetts Lowell libraries, including how to sort into Hill system order
* [http://www.chemcalc.org Molecular formula calculation applying Hill notation]. The library calculating Hill notation is [https://www.npmjs.com/package/chemcalc available on npm].

{{Molecular visualization}}
{{Molecules detected in outer space}}
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