Stoichiometry (sometimes called reaction stoichiometry to distinguish it from composition stoichiometry) is the calculation of quantitative (measurable) relationships of the reactants and products in chemical reactions (chemicals). A calculation is a deliberate process for transforming one or more inputs into one or more results with variable change A quantitative attribute is one that exists in a range of magnitudes and can therefore be measured. A reagent or reactant is a substance or compound consumed during a Chemical reaction. A product is a substance that forms as a result of a Biological - or Chemical reaction. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called A chemical substance is a Material with a definite chemical composition.

Contents 1 Etymology 2 Definition 3 Different stoichiometries in competing reactions 4 Stoichiometric coefficient 5 Stoichiometry matrix 6 Gas stoichiometry 7 Stoichiometric air-fuel ratios of common fuels 8 Methods to solving stoichiometry problems 8.1 Calculations 9 See also 10 References 11 External links

Etymology

"Stoichiometry" is derived from the Greek words στοιχειον (stoikheion, meaning element) and μετρον (metron, meaning measure. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly Many ancient philosophies used a set of archetypal classical "elements" to explain patterns in Nature. Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as ) In patristic Greek, the word Stoichiometria was used by Nicephorus to refer to the number of line counts of the canonical books of the New Testament and some of the Apocrypha. The Church Fathers, Early Church Fathers, or Fathers of the Church are the early and influential theologians and writers in the Christian Church A Biblical canon or canon of scripture is a list or Set of Biblical books considered to be authoritative as Scripture by a particular religious Huden Stoichiofaukrus (Θεος του Μετρο) read the measures and made provisions on the conceptual concepts of the era.

Definition

Stoichiometry rests upon the law of conservation of mass, the law of definite proportions (i. The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov - Lavoisier law says that the Mass of In Chemistry, the law of definite proportions and also the elements states that a Chemical compound always contains exactly the same proportion of elements e. , the law of constant composition) and the law of multiple proportions. In Chemistry, the law of definite proportions and also the elements states that a Chemical compound always contains exactly the same proportion of elements In Chemistry, the law of multiple proportions is one of the basic laws and a major tool of chemical measurement ( Stoichiometry) In general, chemical reactions combine in definite ratios of chemicals. Since chemical reactions can neither create nor destroy matter, nor transmute one element into another, the amount of each element must be the same throughout the overall reaction. Nuclear transmutation is the conversion of one Chemical element or Isotope into another which occurs through Nuclear reactions Natural transmutation occurs For example, the amount of element X on the reactant side must equal the amount of element X on the product side.

Stoichiometry is often used to balance chemical equations. For example, the two diatomic gases, hydrogen and oxygen, can combine to form a liquid, water, in an exothermic reaction, as described by the following equation:

The term stoichiometry is also often used for the molar proportions of elements in stoichiometric compounds. Diatomic molecules are molecules made only of two Atoms of either the same or different Chemical elements The prefix di- means two in Greek Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the An exothermic reaction is a Chemical reaction that releases Heat. The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this For example, the stoichiometry of hydrogen and oxygen in H₂O is 2:1. In stoichiometric compounds, the molar proportions are whole numbers (that is what the law of definite proportions is about).

Compounds for which the molar proportions are not whole numbers are called non-stoichiometric compounds. Non-stoichiometric compounds are Chemical compounds with an elemental composition that cannot be represented by a ratio of well-defined Natural numbers and

Stoichiometry is not only used to balance chemical equations but also used in conversions, i. e. , converting from grams to moles, or from grams to milliliters. For example, to find the number of moles in 2. 00 g of NaCl, one would do the following:

In the above example, when written out in fraction form, the units of grams form a multiplicative identity, which is equivalent to one (g/g=1), with the resulting amount of moles (the unit that was needed), is shown in the following equation,

Stoichiometry is also used to find the right amount of reactants to use in a chemical reaction. A reagent or reactant is a substance or compound consumed during a Chemical reaction. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called An example is shown below using the thermite reaction,

So, to completely react with 85. Thermite is a Pyrotechnic composition of Aluminium powder and a metal oxide which produces an Aluminothermic reaction known as a 0 grams of iron (III) oxide, 28. 7 grams of aluminum are needed.

Different stoichiometries in competing reactions

Often, more than one reaction is possible given the same starting materials. The reactions may differ in their stoichiometry. For example, the methylation of benzene (C₆H₆) may produce singly-methylated (C₆H₅CH₃), doubly-methylated (C₆H₄(CH₃)₂), or still more highly-methylated (C₆H_{6 − n}(CH₃)_n) products, as shown in the following example,

In this example, which reaction takes place is controlled in part by the relative concentrations of the reactants. Methylation is a term used in the chemical sciences to denote the attachment or substitution of a methyl group on various substrates. Benzene, or benzol, is an organic Chemical compound and a known Carcinogen with the molecular formula C 6 H 6 In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance

Stoichiometric coefficient

The stoichiometric coefficient in a chemical reaction system of the i–th component is defined as

or

where N_i is the number of molecules of i, and ξ is the progress variable or extent of reaction (Prigogine & Defay, p. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called System (from Latin systēma, in turn from Greek systēma is a set of interacting or interdependent Entities, real or abstract In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by A variable (ˈvɛərɪəbl is an Attribute of a physical or an abstract System which may change its Value while it is under Observation.  18; Prigogine, pp.  4–7; Guggenheim, p.  37 & 62). The extent of reaction can be regarded as a real (or hypothetical) product, one molecule of which is produced each time the reaction event occurs.

The stoichiometric coefficient ν_i represents the degree to which a chemical species participates in a reaction. The convention is to assign negative coefficients to reactants (which are consumed) and positive ones to products. However, any reaction may be viewed as "going" in the reverse direction, and all the coefficients then change sign (as does the free energy). In Thermodynamics, the term thermodynamic free energy refers to the amount of work that can be extracted from a System, and is helpful in Engineering Whether a reaction actually will go in the arbitrarily-selected forward direction or not depends on the amounts of the substances present at any given time, which determines the kinetics and thermodynamics, i. A chemical substance is a Material with a definite chemical composition. Chemical kinetics, also known as reaction kinetics is the study of rates of chemical processes In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and e. , whether equilibrium lies to the right or the left. In a Chemical process, chemical equilibrium is the state in which the chemical activities or Concentrations of the reactants and products have no net change

If one contemplates actual reaction mechanisms, stoichiometric coefficients will always be integers, since elementary reactions always involve whole molecules. Chemistry, a reaction mechanism is the step by step Sequence of Elementary reactions by which overall Chemical change occurs. The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French If one uses a composite representation of an "overall" reaction, some may be rational fractions. In Mathematics, a rational number is a number which can be expressed as a Ratio of two Integers Non-integer rational numbers (commonly called fractions In Mathematics, a fraction (from the Latin fractus, broken is a concept of a proportional relation between an object part and the object There are often chemical species present that do not participate in a reaction; their stoichiometric coefficients are therefore zero. Any chemical species that is regenerated, such as a catalyst, also has a stoichiometric coefficient of zero. Catalysis is the process in which the rate of a Chemical reaction is increased by means of a Chemical substance known as a catalyst

The simplest possible case is an isomerism

in which ν_B = 1 since one molecule of B is produced each time the reaction occurs, while ν_A = −1 since one molecule of A is necessarily consumed. This article is about the chemical concept For "isomerism" of atomic nuclei see Nuclear isomer. In any chemical reaction, not only is the total mass conserved, but also the numbers of atoms of each kind are conserved, and this imposes a corresponding number of constraints on possible values for the stoichiometric coefficients. The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov - Lavoisier law says that the Mass of History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny The periodic table of the chemical elements is a tabular method of displaying the Chemical elements Although precursors to this table exist its invention is Of course, only a small subset of the possible atomic rearrangements will occur.

There are usually multiple reactions proceeding simultaneously in any natural reaction system, including those in biology. Nature, in the broadest sense is equivalent to the natural world, physical universe, material world or material universe. Foundations of modern biology There are five unifying principles Since any chemical component can participate in several reactions simultaneously, the stoichiometric coefficient of the i–th component in the k–th reaction is defined as

so that the total (differential) change in the amount of the i–th component is

.

Extents of reaction provide the clearest and most explicit way of representing compositional change, although they are not yet widely used.

With complex reaction systems, it is often useful to consider both the representation of a reaction system in terms of the amounts of the chemicals present { N_i } (state variables), and the representation in terms of the actual compositional degrees of freedom, as expressed by the extents of reaction { ξ_k }. In Thermodynamics, state variables, state parameters or thermodynamic variables describe the momentary condition of a system. The transformation from a vector expressing the extents to a vector expressing the amounts uses a rectangular matrix whose elements are the stoichiometric coefficients [ ν_i k ]. In Mathematics, a vector space (or linear space) is a collection of objects (called vectors) that informally speaking may be scaled and added In Mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries) which may be Numbers or more generally

The maximum and minimum for any ξ_k occur whenever the first of the reactants is depleted for the forward reaction; or the first of the "products" is depleted if the reaction as viewed as being pushed in the reverse direction. This is a purely kinematic restriction on the reaction simplex, a hyperplane in composition space, or N‑space, whose dimensionality equals the number of linearly-independent chemical reactions. Kinematics ( Greek κινειν, kinein, to move is a branch of Classical mechanics which describes the motion of objects without In Geometry, a simplex (plural simplexes or simplices) or n -simplex is an n -dimensional analogue of a triangle A hyperplane is a concept in Geometry. It is a higher-dimensional generalization of the concepts of a line in Euclidean plane geometry and a In mathematics the dimension of a Space is roughly defined as the minimum number of Coordinates needed to specify every point within it In Linear algebra, a family of vectors is linearly independent if none of them can be written as a Linear combination of finitely many other vectors This is necessarily less than the number of chemical components, since each reaction manifests a relation between at least two chemicals. The accessible region of the hyperplane depends on the amounts of each chemical species actually present, a contingent fact. Different such amounts can even generate different hyperplanes, all of which share the same algebraic stoichiometry.

In accord with the principles of chemical kinetics and thermodynamic equilibrium, every chemical reaction is reversible, at least to some degree, so that each equilibrium point must be an interior point of the simplex. Chemical kinetics, also known as reaction kinetics is the study of rates of chemical processes In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and In Mathematics, the interior of a set S consists of all points of S that are intuitively "not on the edge of S " As a consequence, extrema for the ξ's will not occur unless an experimental system is prepared with zero initial amounts of some products.

The number of physically-independent reactions can be even greater than the number of chemical components, and depends on the various reaction mechanisms. For example, there may be two (or more) reaction paths for the isomerism above. The reaction may occur by itself, but faster and with different intermediates, in the presence of a catalyst.

The (dimensionless) "units" may be taken to be molecules or moles. In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this Moles are most commonly used, but it is more suggestive to picture incremental chemical reactions in terms of molecules. The N's and ξ's are reduced to molar units by dividing by Avogadro's number. The Avogadro constant (symbols L, N A also called Avogadro's number, is the number of "elementary entities" (usually Atoms While dimensional mass units may be used, the comments about integers are then no longer applicable. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object

Stoichiometry matrix

In complex reactions, stoichiometries are often represented in a more compact form called the stoichiometry matrix. The stoichiometry matrix is denoted by the symbol, .

If a reaction network has n reactions and m participating molecular species then the stoichiometry matrix will have corresponding n columns and m rows.

For example, consider the system of reactions shown below:

S₁ → S₂

5S₃ + S₂ → 4S₃ + 2S₂

S₃ → S₄

S₄ → S₅

This systems comprises four reactions and five different molecular species. The stoichiometry matrix for this system can be written as:

where the rows correspond to S₁, S₂, S₃, S₄ and S₅, respectively. Note that the process of converting a reaction scheme into a stoichiometry matrix can be a lossy transformation, for example, the stoichiometries in the second reaction simplify when included in the matrix. This means that it is not always possible to recover the original reaction scheme from a stoichiometry matrix.

Often the stoichiometry matrix is combined with the rate vector, v to form a compact equation describing the rates of change of the molecular species:

Gas stoichiometry

Gas stoichiometry is the quantitative relationship between reactants and products in a chemical reaction when it is employed for reactions that produce gases. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called This page is about the physical properties of gas as a state of matter Gas stoichiometry applies when the gases produced are assumed to be ideal, and the temperature, pressure, and volume of the gases are all known. These four properties that constitute an ideal gas can be easily remembered by the acronym RIPE which stands for - R andom Motion (molecules are in constant random motion Often, but not always, the standard temperature and pressure (STP) are taken as 0°C and 1 bar and used as the conditions for gas stoichiometric calculations. In Physical sciences standard conditions for temperature and pressure are Standard sets of conditions for experimental measurements to allow comparisons to be made

Gas stoichiometry calculations solve for the unknown volume or mass of a gaseous product or reactant. The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object For example, if we wanted to calculate the volume of gaseous NO₂ produced from the combustion of 100 g of NH₃, by the reaction:

4NH₃ (g) + 7O₂ (g) → 4NO₂ (g) + 6H₂O (l)

we would carry out the following calculations:

There is a 1:1 molar ratio of NH₃ to NO₂ in the above balanced combustion reaction, so 5. 871 mol of NO₂ will be formed. We will employ the ideal gas law to solve for the volume at 0 °C (273. The ideal gas law is the Equation of state of a hypothetical Ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834 15 K) and 1 atmosphere using the gas law constant of R = 0. Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working 08206 L · atm · K^-1 · mol^-1 :

PV	= nRT
V

Gas stoichiometry often involves having to know the molar mass of a gas, given the density of that gas. Molar mass, symbol M, is the Mass of one mole of a substance ( Chemical element or Chemical compound) The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different The ideal gas law can be re-arranged to obtain a relation between the density and the molar mass of an ideal gas:

    and    

and thus:

where:
P	= absolute gas pressure
V	= gas volume
n	= number of moles
R	= universal ideal gas law constant
T	= absolute gas temperature
ρ	= gas density at T and P
m	= mass of gas
M	= molar mass of gas

Stoichiometric air-fuel ratios of common fuels

Fuel	By weight	By volume [1]	Percent fuel by weight
Gasoline	14. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Molar mass, symbol M, is the Mass of one mole of a substance ( Chemical element or Chemical compound) Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature 7 : 1	-	6. 8%
Natural Gas	17. 2 : 1	9. 7  : 1	5. 8%
Propane (LP)	15. 5 : 1	23. 9 : 1	6. 45%
Ethanol	9 : 1	-	11. 1%
Methanol	6. 4 : 1	-	15. 6%
Hydrogen	34 : 1	2. 39 : 1	2. 9%
Diesel	14. 6 : 1	-	6. 8%

Methods to solving stoichiometry problems

To use the following methods, you must first determine the molar mass of the reagents and the products, and balance the reaction. Using the known masses of compounds in the reaction, calculate the number of moles there are of each known. Then determine which chemical is the limiting reagent. In Chemistry, the limiting reagent, also known as the " limiting reactant " is the Chemical that determines how far the reaction will go before

One method has been commonly taught in various text books. Like equivalent weight, it is the amount of an element that reacts, or is involved in reaction with, 1 mole of electrons. Equivalent weight is the amount of an element that reacts or is involved in reaction with 1 mole of electrons The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this When choosing primary standards in analytical chemistry, compounds with higher "equivalent weights" are, in general, more desirable because weighing errors are reduced or minimized. In Metrology, a primary standard is a standard that is accurate enough that it is not calibrated by or subordinate to other standards Analytical chemistry is the study of the Chemical composition of natural and artificial Materials. For example, hydrogen, with atomic weight 1. Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 008 and valence of 1, has an equivalent weight of 1. 008. Oxygen assumes a valence of 2 and has an atomic weight of 15. Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the 9994, so it has an equivalent weight of 7. 9997.

Calculations

A simple equation with moles and the coefficient number of limiting reagents and products, known as the Moum method, will give the number of moles of the unknown quite simply.

This can be re-arranged to give the Lecce method:

See also

• Equivalence ratio

References

• Ilya Prigogine & R. Defay, translated by D. H. Everett; Chapter IV (1954). Chemical Thermodynamics. Longmans, Green & Co. Exceptionally clear on the logical foundations as applied to chemistry; includes non-equilibrium thermodynamics. Non-equilibrium thermodynamics is a branch of Thermodynamics concerned with studying Time -dependent Thermodynamic systems irreversible transformations  
• Ilya Prigogine (1967). Thermodynamics of Irreversible Processes, 3rd ed. . Interscience: John Wiley & Sons. A simple, concise monograph.   Library of Congress Catalog No. 67-29540
• E. A. Guggenheim (1967). Thermodynamics: An Advanced Treatment for Chemists and Physicists, 5th ed. . North Holland; John Wiley & Sons (Interscience). A remarkably astute treatise.   Library of Congress Catalog No. 67-20003
• Zumdahl, Steven S. Chemical Principles. Houghton Mifflin, New York, 2005, pp 148-150.

External links

• University of Plymouth :Engine Combustion primer
• Carnegie Mellon's ChemCollective :Free Stoichiometry Tutorials

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