HOME

TheInfoList



OR:

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 substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking ...
in the form of symbols and
chemical formula In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
s. The
reactant In chemistry, a reagent ( ) or analytical reagent is a substance or compound added to a system to cause a chemical reaction, or test if one occurs. The terms ''reactant'' and ''reagent'' are often used interchangeably, but reactant specifies a ...
entities are given on the left-hand side and the
product Product may refer to: Business * Product (business), an item that serves as a solution to a specific consumer problem. * Product (project management), a deliverable or set of deliverables that contribute to a business solution Mathematics * Produ ...
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 to show the direction of the reaction. The chemical formulas may be symbolic,
structural A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such ...
(pictorial diagrams), or intermixed. The coefficients next to the symbols and formulas of entities are the absolute values of the stoichiometric numbers. The first chemical equation was diagrammed by Jean Beguin in 1615.


Structure

A chemical equation (see an example below) consists of a list of reactants (the starting substances) on the left-hand side, an arrow symbol, and a list of products (substances formed in the chemical reaction) on the right-hand side. Each substance is specified by its
chemical formula In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
, optionally preceded by a number called stoichiometric coefficient. The coefficient specifies how many entities (e.g.
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
s) of that substance are involved in the reaction on a molecular basis. If not written explicitly, the coefficient is equal to 1. Multiple substances on any side of the equation are separated from each other by a
plus sign The plus and minus signs, and , are mathematical symbols used to represent the notions of positive and negative, respectively. In addition, represents the operation of addition, which results in a sum, while represents subtraction, res ...
. As an example, the equation for the reaction of
hydrochloric acid Hydrochloric acid, also known as muriatic acid, is an aqueous solution of hydrogen chloride. It is a colorless solution with a distinctive pungent smell. It is classified as a strong acid. It is a component of the gastric acid in the dige ...
with
sodium Sodium is a chemical element with the symbol Na (from Latin ''natrium'') and atomic number 11. It is a soft, silvery-white, highly reactive metal. Sodium is an alkali metal, being in group 1 of the periodic table. Its only stable ...
can be denoted: :2HCl + 2Na -> 2NaCl + H2 Given the formulas are fairly simple, this equation could be read as "two H-C-L plus two N-A yields two N-A-C-L and H two." Alternately, and in general for equations involving complex chemicals, the chemical formulas are read using
IUPAC nomenclature A chemical nomenclature is a set of rules to generate systematic names for chemical compounds. The nomenclature used most frequently worldwide is the one created and developed by the International Union of Pure and Applied Chemistry (IUPAC). Th ...
, which could verbalise this equation as "two hydrochloric acid molecules and two sodium atoms react to form two
formula unit In chemistry, a formula unit is the empirical formula of any ionic or covalent network solid compound used as an independent entity for stoichiometric calculations. It is the lowest whole number ratio of ions represented in an ionic compound. E ...
s of
sodium chloride Sodium chloride , commonly known as salt (although sea salt also contains other chemical salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of 22.99 and 35. ...
and a
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...
gas molecule."


Reaction types

Different variants of the arrow symbol are used to denote the type of a reaction: :


State of matter

To indicate
physical state In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, ...
of a chemical, a symbol in parentheses may be appended to its formula: (s) for a solid, (l) for a liquid, (g) for a gas, and (aq) for an
aqueous solution An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be r ...
. This is especially done when one wishes to emphasize the states or changes thereof. For example, the reaction of aqueous hydrochloric acid with solid (metallic) sodium to form aqueous sodium chloride and hydrogen gas would be written like this: :2HCl(aq) + 2Na(s) -> 2NaCl(aq) + H2(g) That reaction would have different
thermodynamic Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of ...
and
kinetic Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to: * Kinetic theory, describing a gas as particles in random motion * Kinetic energy, the energy of an object that it possesses due to its motion Art and ent ...
properties if gaseous
hydrogen chloride The compound hydrogen chloride has the chemical formula and as such is a hydrogen halide. At room temperature, it is a colourless gas, which forms white fumes of hydrochloric acid upon contact with atmospheric water vapor. Hydrogen chlorid ...
were to replace the hydrochloric acid as a reactant: :2HCl(g) + 2Na(s) -> 2NaCl(s) + H2(g) Alternately, an arrow without parentheses is used in some cases to indicate formation of a gas ↑ or precipitate ↓. This is especially useful if only one such species is formed. Here is an example indicating that hydrogen gas is formed: :2HCl + 2Na -> 2 NaCl + H2 ^


Catalysis and other conditions

If the reaction requires energy, it is indicated above the arrow. A capital Greek letter delta (Δ) or a triangle (△) is put on the reaction arrow to show that energy in the form of heat is added to the reaction. The expression 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. Similarly, if a reaction requires a certain medium with certain specific characteristics, then the name of the acid or base that is used as a medium may be placed on top of the arrow. If no specific acid or base is required, another way of denoting the use of an acidic or basic medium is to write H+ or OH (or even "acid" or "base") on top of the arrow. Specific conditions of the temperature and pressure, as well as the presence of catalysts, may be indicated in the same way.


Notation variants

The standard notation for chemical equations only permits all reactants on one side, all products on the other, and all stoichiometric coefficients positive. For example, the usual form of the equation for
dehydration In physiology, dehydration is a lack of total body water, with an accompanying disruption of metabolic processes. It occurs when free water loss exceeds free water intake, usually due to exercise, disease, or high environmental temperature. Mil ...
of
methanol Methanol (also called methyl alcohol and wood spirit, amongst other names) is an organic chemical and the simplest aliphatic alcohol, with the formula C H3 O H (a methyl group linked to a hydroxyl group, often abbreviated as MeOH). It is ...
to dimethylether is: : 2 CH3OH -> CH3OCH3 + H2O Sometimes an extension is used, where some substances with their stoichiometric coefficients are moved above or below the arrow, preceded by a plus sign or nothing for a reactant, and by a minus sign for a product. Then the same equation can look like this: : 2 CH3OH -> overset\ceCH3OCH3 Such notation serves to hide less important substances from the sides of the equation, to make the type of reaction at hand more obvious, and to facilitate chaining of chemical equations. This is very useful in illustrating multi-step
reaction mechanism In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs. A chemical mechanism is a theoretical conjecture that tries to describe in detail what takes place at each stage o ...
s. Note that the substances above or below the arrows are not
catalyst Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
s in this case, because they are consumed or produced in the reaction like ordinary reactants or products. Another extension used in reaction mechanisms moves some substances to branches of the arrow. Both extensions are used in the example illustration of a mechanism. Use of negative stoichiometric coefficients at either side of the equation (like in the example below) is not widely adopted and is often discouraged. : 2 CH3OH \;-\; H2O -> CH3OCH3


Balancing chemical equations

Because no
nuclear reaction In nuclear physics and nuclear chemistry, a nuclear reaction is a process in which two nuclei, or a nucleus and an external subatomic particle, collide to produce one or more new nuclides. Thus, a nuclear reaction must cause a transformatio ...
s take place in a chemical reaction, the
chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical compounds, chemical elements canno ...
s pass through the reaction unchanged. Thus, each side of the chemical equation must represent the same number of atoms of any particular element (or
nuclide A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was co ...
, if different
isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers ( mass num ...
s are taken into account). The same holds for the total
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons res ...
, as stated by the
charge conservation In physics, charge conservation is the principle that the total electric charge in an isolated system never changes. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is al ...
law. An equation adhering to these requirements is said to be balanced. A chemical equation is balanced by assigning suitable values to the stoichiometric coefficients. Simple equations can be balanced by inspection, that is, by trial and error. Another technique involves solving a
system of linear equations In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example, :\begin 3x+2y-z=1\\ 2x-2y+4z=-2\\ -x+\fracy-z=0 \end is a system of three equations in t ...
. Balanced equations are usually written with smallest natural-number coefficients. Yet sometimes it may be advantageous to accept a fractional coefficient, if it simplifies the other coefficients. The introductory example can thus be rewritten as :HCl + Na -> NaCl + 1/2 H2 In some circumstances the fractional coefficients are even inevitable. For example, the reaction corresponding to the standard enthalpy of formation must be written such that one molecule 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 Lithium fluoride is an inorganic compound with the chemical formula LiF. It is a colorless solid, that transitions to white with decreasing crystal size. Although odorless, lithium fluoride has a bitter-saline taste. Its structure is analogous to ...
: :Li(s) + 1/2F2(g) -> LiF(s)


Inspection method

The method of inspection can be outlined as setting the most complex substance's stoichiometric coefficient to 1 and assigning values to other coefficients step by step such that both sides of the equation end up with the same number of atoms for each element. If any fractional coefficients arise during this process, the presence of fractions may be eliminated (at any time) by multiplying all coefficients by their lowest common denominator. ; Example Balancing of the chemical equation for the complete
combustion Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combus ...
of
methane Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane ...
:::\mathord\, + \mathord\, -> \mathord\, + \mathord\, is achieved as follows: # A coefficient of 1 is placed in front of the most complex formula ( CH4): #:1 + \mathord\, -> \mathord\, + \mathord\, # The left-hand side has 1
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon ma ...
atom, so 1 molecule of CO2 will balance it. The left-hand side also has 4
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...
atoms, which will be balanced by 2 molecules of H2O: #:1 + \mathord\, -> 1 + 2 H2O # Balancing the 4
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
atoms of the right-hand side by 2 molecules of O2 yields the equation #:1 CH4 + 2 O2 -> 1 CO2 + 2 H2O # The coefficients equal to 1 are omitted, as they do not need to be specified explicitly: #:CH4 + 2 O2 -> CO2 + 2 H2O # It is wise to check that the final equation is balanced, i.e. that for each element there is the same number of atoms on the left- and right-hand side: 1 carbon, 4 hydrogen, and 4 oxygen.


System of linear equations

For each chemical element (or nuclide or unchanged
moiety Moiety may refer to: Chemistry * Moiety (chemistry), a part or functional group of a molecule ** Moiety conservation, conservation of a subgroup in a chemical species Anthropology * Moiety (kinship), either of two groups into which a society is ...
or charge) , its conservation requirement can be expressed by the
mathematical equation In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in F ...
:\sum_ \!\!\!\!\! a_ s_j \ = \!\!\!\!\! \sum_ \!\!\!\!\! a_ s_j where : is the number of atoms of element in a molecule of substance (per formula in the chemical equation), and : is the stoichiometric coefficient for the substance . This results in a homogeneous system of linear equations, which are readily solved using mathematical methods. Such system always has the all-zeros
trivial solution In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or an object which possesses a simple structure (e.g., groups, topological spaces). The noun triviality usually refers to a ...
, which we are not interested in, but if there are any additional solutions, there will be infinite number of them. Any non-trivial solution will balance the chemical equation. A "preferred" solution is one with whole-number, mostly positive stoichiometric coefficients with
greatest common divisor In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers ''x'', ''y'', the greatest common divisor of ''x'' and ''y'' is ...
equal to one.


Example

Let us assign variables to stoichiometric coefficients of the chemical equation from the previous section and write the corresponding linear equations: :\mathit_1 + \mathit_2 -> \mathit_3 + \mathit_4 \quad\;\;\; \begin \text && s_1 & = s_3 \\ \text && 4s_1 & = 2s_4 \\ \text && 2s_2 & = 2s_3 + s_4 \end All solutions to this system of linear equations are of the following form, where is any
real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every ...
: :\begin s_1 & = r \\ s_2 & = 2r \\ s_3 & = r \\ s_4 & = 2r \end The choice of yields the preferred solution, :\begin s_1 & = 1 \\ s_2 & = 2 \\ s_3 & = 1 \\ s_4 & = 2 \end which corresponds to the balanced chemical equation: :CH4 + 2 O2 -> CO2 + 2 H2O


Matrix method

The system of linear equations introduced in the previous section can also be written using an efficient
matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** '' The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchi ...
formalism. First, to unify the reactant and product stoichiometric coefficients , let us introduce the quantity :\nu_j = \begin -s_j & \text \\ +s_j & \text \end called
stoichiometric number Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equals ...
, which simplifies the linear equations to :\sum_^J a_ \nu_j=0 where is the total number of reactant and product substances (formulas) in the chemical equation. Placement of the values at row and column of the composition matrix :\begin a_ & a_ & \cdots & a_ \\ a_ & a_ & \cdots & a_ \\ \vdots & \vdots & \ddots & \vdots \end and arrangement of the stoichiometric numbers into the stoichiometric vector :\begin \nu_1 \\ \nu_2 \\ \vdots \\ \nu_J \end allows the system of equations to be expressed as a single matrix equation: : Like previously, any nonzero stoichiometric vector , which solves the matrix equation, will balance the chemical equation. The set of solutions to the matrix equation is a linear space called the
kernel Kernel may refer to: Computing * Kernel (operating system), the central component of most operating systems * Kernel (image processing), a matrix used for image convolution * Compute kernel, in GPGPU programming * Kernel method, in machine learn ...
of the matrix . For this space to contain nonzero vectors , i.e. to have a positive
dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...
N, the columns of the composition matrix must not be
linearly independent In the theory of vector spaces, a set of vectors is said to be if there is a nontrivial linear combination of the vectors that equals the zero vector. If no such linear combination exists, then the vectors are said to be . These concepts are ...
. The problem of balancing a chemical equation then becomes the problem of determining the N-dimensional kernel of the composition matrix. It is important to note that only for N = 1 will there be a unique preferred solution to the balancing problem. For N > 1 there will be an infinite number of preferred solutions with N of them linearly independent. If N = 0, there will be only the unusable trivial solution, the zero vector. Techniques have been developed to quickly calculate a set of N independent solutions to the balancing problem, which are superior to the inspection and in that they are determinative and yield all solutions to the balancing problem. ; Example Let us take the same chemical equation again and write the corresponding matrix equation:
\mathit_1 + \mathit_2 -> \mathit_3 + \mathit_4
\begin \text \\ \text \\ \text \end \quad \begin 1 & 0 & 1 & 0 \\ 4 & 0 & 0 & 2 \\ 0 & 2 & 2 & 1 \end \begin \nu_1 \\ \nu_2 \\ \nu_3 \\ \nu_4 \end = \mathbf
Its solutions are of the following form, where is any real number: : \begin \nu_1 \\ \nu_2 \\ \nu_3 \\ \nu_4 \end = \begin -s_1 \\ -s_2 \\ s_3 \\ s_4 \end = r \begin -1 \\ -2 \\ 1 \\ 2 \end The choice of and a
sign A sign is an object, quality, event, or entity whose presence or occurrence indicates the probable presence or occurrence of something else. A natural sign bears a causal relation to its object—for instance, thunder is a sign of storm, or ...
-flip of the first two rows yields the preferred solution to the balancing problem: : \begin -\nu_1 \\ -\nu_2 \\ \nu_3 \\ \nu_4 \end = \begin s_1 \\ s_2 \\ s_3 \\ s_4 \end = \begin 1 \\ 2 \\ 1 \\ 2 \end


Ionic equations

An ionic equation is a chemical equation in which
electrolyte An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon ...
s are written as dissociated ions. Ionic equations are used for single and
double displacement reaction A salt metathesis reaction, sometimes called a double displacement reaction, is a chemical process involving the exchange of chemical bond, bonds between two reacting chemical species which results in the creation of products with similar or ident ...
s that occur in
aqueous solution An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be r ...
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 ions. 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 In computer science, ACID ( atomicity, consistency, isolation, durability) is a set of properties of database transactions intended to guarantee data validity despite errors, power failures, and other mishaps. In the context of databases, a se ...
/ base 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. The monohydrate (''x'' = 1), known as baryta or baryta-water, is one of the principal compounds of barium. This white granular monohydrate is the usual commercial form. ...
with
phosphoric acid Phosphoric acid (orthophosphoric acid, monophosphoric acid or phosphoric(V) acid) is a colorless, odorless phosphorus-containing solid, and inorganic compound with the chemical formula . It is commonly encountered as an 85% aqueous solution, w ...
, 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 A carbonate is a salt of carbonic acid (H2CO3), characterized by the presence of the carbonate ion, a polyatomic ion with the formula . The word ''carbonate'' may also refer to a carbonate ester, an organic compound containing the 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


History


Typesetting


Notes


References

{{Authority control Stoichiometry Equations Chemistry