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A chemical equation is the symbolic representation of a
chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and t ...

chemical reaction
in the form of symbols and formulae, wherein the
reactant 200px, Reactants, such as sulfur (''pictured''), are the starting materials that are used in chemical reactions. A reagent is a substance or compound added to a system to cause a chemical reaction A chemical reaction is a process that leads ...
entities are given on the left-hand side and the product entities on the right-hand side with a plus sign between the entities in both the reactants and the products and an arrow that points towards the products, and shows the direction of the reaction. The coefficients next to the symbols and formulae of entities are the absolute values of the stoichiometric numbers. The first chemical equation was diagrammed by Jean Beguin in 1615.


Formation of chemical reaction

A chemical equation consists of the
chemical formula A chemical formula is a way of presenting information about the chemical proportions of s that constitute a particular or molecule, using symbols, numbers, and sometimes also other symbols, such as parentheses, dashes, brackets, commas and ...
s of the reactants (the starting substances) and the chemical formula of the products (substances formed in the chemical reaction). The two are separated by an
arrow symbol An arrow is a graphical symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, Object (philosophy), object, or wikt:relationship, relationship. Symbols allow people to go beyond what i ...
(→, usually read as "yields") and each individual substance's chemical formula is separated from others by a
plus sign The plus and minus signs, and , are mathematical symbols used to represent the notions of sign (mathematics), positive and sign (mathematics), negative, respectively. In addition, represents the operation of addition, which results in a Sum (mat ...

plus sign
. As an example, the equation for the reaction of
hydrochloric acid Hydrochloric acid +(aq) Cl−(aq) or H3O+ Cl− also known as muriatic acid, is an aqueous solution of hydrogen chloride ( ). It is a colorless solution with a distinctive pungency, pungent smell. It is classified as a acid strength, stron ...

hydrochloric acid
with
sodium Sodium is a with the  Na (from Latin ''natrium'') and  11. It is a soft, silvery-white, highly reactive . Sodium is an , being in of the periodic table. Its only stable is 23Na. The free metal does not occur in nature, and must be ...

sodium
can be denoted: :2 + 2 → 2 + This equation would be read as "two HCl plus two Na yields two NaCl and H two." But, for equations involving complex chemicals, rather than reading the letter and its subscript, the chemical formulas are read using
IUPAC nomenclature The International Union of Pure and Applied Chemistry The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations that represents chemists in individual countries. It is a mem ...
. Using IUPAC nomenclature, this equation would be read as "hydrochloric acid plus sodium yields
sodium chloride Sodium chloride , commonly known as salt (although sea salt also contains other chemical salt (chemistry), salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With Molar mass, molar ...
and
hydrogen Hydrogen is the chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all have the same ...

hydrogen
gas." This equation indicates that sodium and HCl react to form NaCl and H2. It also indicates that two sodium molecules are required for every two hydrochloric acid molecules and the reaction will form two sodium chloride molecules and one
diatomic Diatomic molecules are molecule A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecule is an electrically neutral group of two or more atoms held together by chemical b ...
molecule of hydrogen gas molecule for every two hydrochloric acid and two sodium molecules that react. The
stoichiometric coefficients Stoichiometry is the calculation of reactant 200px, Reactants, such as sulfur (''pictured''), are the starting materials that are used in chemical reactions. A reagent is a substance or compound added to a system to cause a chemical reacti ...
(the numbers in front of the chemical formulas) result from the
law of conservation of mass In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through ...
and the law of conservation of charge (see "Balancing chemical equations" section below for more information).


Common symbols

Symbols are used to differentiate between different types of reactions. To denote the type of reaction: * "=" symbol is used to denote a
stoichiometric Stoichiometry is the calculation of reactants and products in chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical A chemical s ...
relation. * "\rightarrow" symbol is used to denote a net forward reaction. * "\rightleftarrows" symbol is used to denote a reaction in both directions. * "<=>" symbol is used to denote an
equilibrium List of types of equilibrium, the condition of a system in which all competing influences are balanced, in a wide variety of contexts. Equilibrium may also refer to: Film and television * Equilibrium (film), ''Equilibrium'' (film), a 2002 scien ...
. The physical state of chemicals is also very commonly stated in parentheses after the chemical symbol, especially for ionic reactions. When stating physical state, (s) denotes a solid, (l) denotes a liquid, (g) denotes a gas and (aq) denotes an
aqueous solution An aqueous solution is a solution Image:SaltInWaterSolutionLiquid.jpg, Making a saline water solution by dissolving Salt, table salt (sodium chloride, NaCl) in water. The salt is the solute and the water the solvent. In chemistry, a solution ...
. If the reaction requires energy, it is indicated above the arrow. A capital Greek letter delta (\Delta) is put on the reaction arrow to show that energy in the form of heat is added to the reaction. The expression h\nu is used as a symbol for the addition of energy in the form of light. Other symbols are used for other specific types of energy or radiation.


Balancing chemical equations

The
law of conservation of mass In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through ...
dictates that the quantity of each
element Element may refer to: Science * Chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all ...
does not change in a
chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and t ...

chemical reaction
. Thus, each side of the chemical equation must represent the same quantity of any particular element. Likewise, the charge is conserved in a
chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and t ...

chemical reaction
. Therefore, the same charge must be present on both sides of the balanced
equation In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...

equation
. One balances a chemical equation by changing the scalar number for each chemical formula. Simple chemical equations can be balanced by inspection, that is, by trial and error. Another technique involves solving a
system of linear equations In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
. Balanced equations are often written with smallest whole-number coefficients. If there is no coefficient before a chemical formula, the coefficient is 1. The method of inspection can be outlined as putting a coefficient of 1 in front of the most complex chemical formula and putting the other coefficients before everything else such that both sides of the arrows have the same number of each atom. If any fractional coefficient exists, multiply every coefficient with the smallest number required to make them whole, typically the
denominator A fraction (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Rom ...
of the fractional coefficient for a reaction with a single fractional coefficient. As an example, seen in the above image, the burning of methane would be balanced by putting a coefficient of 1 before the CH4: :1 CH4 + O2 → CO2 + H2O Since there is one carbon on each side of the arrow, the first atom (carbon) is balanced. Looking at the next atom (hydrogen), the right-hand side has two atoms, while the left-hand side has four. To balance the hydrogens, 2 goes in front of the H2O, which yields: :1 CH4 + O2 → CO2 + 2 H2O Inspection of the last atom to be balanced (oxygen) shows that the right-hand side has four atoms, while the left-hand side has two. It can be balanced by putting a 2 before O2, giving the balanced equation: :CH4 + 2 O2 → CO2 + 2 H2O This equation does not have any coefficients in front of CH4 and CO2, since a coefficient of 1 is dropped. Note that in some circumstances it is not correct to write a balanced reaction with all whole-number coefficients. For example, the reaction corresponding to the
standard enthalpy of formationThe standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements, with all substances in their standard states. The standard pre ...
must be written such that one mole of a single product is formed. This will often require that some reactant coefficients be fractional, as is the case with the formation of lithium fluoride: :Li(s) +  F2(g) → LiF(s)


Matrix method

Generally, any chemical equation involving ''J'' different molecules can be written as: :\sum_^J \nu_j R_j=0 where ''Rj'' is the symbol for the ''j-th'' molecule, and νj is the stoichiometric coefficient for the ''j-th'' molecule, positive for products, negative for reactants (or vice versa). A properly balanced chemical equation will then obey: :\sum_^J a_ \nu_j=0 where the composition matrix ''aij'' is the number of atoms of element ''i'' in molecule ''j''. Any vector which, when operated upon by the composition matrix yields a zero vector, is said to be a member of the
kernel Kernel may refer to: Computing * Kernel (operating system) In an operating system with a Abstraction layer, layered architecture, the kernel is the lowest level, has complete control of the hardware and is always in memory. In some systems it ...
or null space of the operator. Any member νj of the null space of ''aij'' will serve to balance a chemical equation involving the set of ''J'' molecules comprising the system. A "preferred" stoichiometric vector is one for which all of its elements can be converted to integers with no common divisors by multiplication by a suitable constant. Generally, the composition matrix is degenerate: That is to say, not all of its rows will be linearly independent. In other words, the
rank Rank is the relative position, value, worth, complexity, power, importance, authority, level, etc. of a person or object within a ranking, such as: Level or position in a hierarchical organization * Academic rank * Diplomatic rank * Hierarchy * Hi ...
(''JR'') of the composition matrix is generally less than its number of columns (''J''). By the theorem, the null space of ''aij'' will have ''J-JR'' dimensions and this number is called the nullity (''JN'') of ''aij''. The problem of balancing a chemical equation then becomes the problem of determining the ''JN''-dimensional null space of the composition matrix. It is important to note that only for ''JN''=1, will there be a unique solution. For ''JN''>1 there will be an infinite number of solutions to the balancing problem, but only ''JN'' of them will be independent: If ''JN'' independent solutions to the balancing problem can be found, then any other solution will be a linear combination of these solutions. If ''JN''=0, there will be no solution to the balancing problem. Techniques have been developed to quickly calculate a set of ''JN'' independent solutions to the balancing problem and are superior to the inspection and algebraic method in that they are determinative and yield all solutions to the balancing problem.


Ionic equations

An ionic equation is a chemical equation in which
electrolyte An electrolyte is a medium containing ions that is electrically conducting Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that quantifies how strongly it resist ...

electrolyte
s are written as dissociated
ion An ion () is an atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ...
s. Ionic equations are used for
single Single may refer to: Arts, entertainment, and media * Single (music), a song release Songs * Single (Natasha Bedingfield song), "Single" (Natasha Bedingfield song), 2004 * Single (New Kids on the Block and Ne-Yo song), "Single" (New Kids on the B ...
and
double displacement reaction A salt metathesis reaction, sometimes called a double replacement reaction, double displacement reaction, is a chemical process involving the exchange of bonds between two reacting chemical species A chemical substance is a form of matter ...
s that occur in
aqueous solution An aqueous solution is a solution Image:SaltInWaterSolutionLiquid.jpg, Making a saline water solution by dissolving Salt, table salt (sodium chloride, NaCl) in water. The salt is the solute and the water the solvent. In chemistry, a solution ...
s. For example, in the following precipitation reaction: :CaCl2 + 2AgNO3 -> Ca(NO3)2 + 2 AgCl(v) the full ionic equation is: :Ca^2+ + 2Cl^- + 2Ag+ + 2NO3^- -> Ca^2+ + 2NO3^- + 2AgCl(v) or, with all physical states included: :Ca^2+(aq) + 2Cl^-(aq) + 2Ag+(aq) + 2NO3^(aq) -> Ca^2+(aq) + 2NO3^(aq) + 2AgCl(v) In this reaction, the Ca2+ and the NO3 ions remain in solution and are not part of the reaction. That is, these ions are identical on both the reactant and product side of the chemical equation. Because such ions do not participate in the reaction, they are called
spectator ion ''Spectator'' or ''The Spectator'' may refer to: *Spectator sport, a sport that is characterized by the presence of spectators, or watchers, at its matches *Audience Publications Canada * ''The Hamilton Spectator'', a Hamilton, Ontario, Canada, n ...
s. A ''net ionic'' equation is the full ionic equation from which the spectator ions have been removed. The net ionic equation of the proceeding reactions is: :2Cl^- + 2Ag+ -> 2AgCl(v) or, in ''reduced'' balanced form, :Ag+ + Cl^- -> AgCl(v) In a neutralization or
acid An acid is a or capable of donating a (hydrogen ion H+) (a ), or, alternatively, capable of forming a with an (a ). The first category of acids are the proton donors, or s. In the special case of , proton donors form the H3O+ and are ...
/
base Base or BASE may refer to: Brands and enterprises * Base (mobile telephony provider), a Belgian mobile telecommunications operator *Base CRM Base CRM (originally Future Simple or PipeJump) is an enterprise software company based in Mountain Vie ...
reaction, the net ionic equation will usually be: :H+(aq) + OH(aq) → H2O(l) There are a few acid/base reactions that produce a precipitate in addition to the water molecule shown above. An example is the reaction of
barium hydroxide Barium hydroxide is a chemical compound with the chemical formula Ba(OH)2(H2O)x. The monohydrate (x =1), known as baryta or baryta-water, is one of the principal compounds of barium. This white granular Hydrate, monohydrate is the usual commercial ...
with
phosphoric acid Phosphoric acid, also known as orthophosphoric acid or phosphoric(V) acid, is a weak acid with the chemical formula . The pure compound is a colorless solid. All three hydrogens are acidic to varying degrees and can be lost from the molecule a ...

phosphoric acid
, which produces not only water but also the insoluble salt barium phosphate. In this reaction, there are no spectator ions, so the net ionic equation is the same as the full ionic equation. :3Ba(OH)2 + 2H3PO4 -> 6H2O + Ba3(PO4)2(v) :\ce + \underbrace\ce_\ce \ce Double displacement reactions that feature a
carbonate In chemistry, a carbonate is a salt Salt is a mineral composed primarily of sodium chloride (NaCl), a chemical compound belonging to the larger class of Salt (chemistry), salts; salt in its natural form as a crystallinity, crystalline mi ...

carbonate
reacting with an acid have the net ionic equation: :\ce + \underbrace\ce_\ce \ce If every ion is a "spectator ion" then there was no reaction, and the net ionic equation is null. Generally, if ''zj'' is the multiple of elementary charge on the ''j-th'' molecule, charge neutrality may be written as: :\sum_^J z_j \nu_j=0 where the ''νj'' are the stoichiometric coefficients described above. The ''zj'' may be incorporated as an additional row in the ''aij'' matrix described above, and a properly balanced ionic equation will then also obey: :\sum_^J a_ \nu_j=0


References

{{Authority control Stoichiometry Equations Chemistry