# Dictionary Definition

stoichiometry n : (chemistry) the relation
between the quantities of substances that take part in a reaction
or form a compound (typically a ratio of whole integers)

# User Contributed Dictionary

## English

### Noun

- uncountable chemistry The study and calculation of quantitative (measurable) relationships of the reactants and products in chemical reactions (chemical equations).
- countable chemistry The quantitative relationship between the reactants and products of a specific reaction or equation.

#### Translations

the study of the relationships of reactants and
products in chemical reactions

- Finnish: stokiometria
- French: stoechiométrie
- German: Stöchiometrie
- Greek: στοιχειομετρία
- Italian: stechiometria
- Latvian: stehiometrija
- Spanish: estequiometría
- Swedish: stökiometri

### See also

# Extensive Definition

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).

## Etymology

"Stoichiometry" is derived from the Greek words στοιχειον (stoikheion, meaning element) and μετρον (metron, meaning measure.) 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. 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.e., the law of constant composition) and the law of multiple proportions. 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. 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:

- 2H_2 + O_2 \rightarrow 2H_2O\,

The term stoichiometry is also often used for the
molar
proportions of elements in stoichiometric compounds. For example,
the stoichiometry of hydrogen and oxygen in H_2O 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.

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:

- \frac = 0.034 \ mol

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,

- \left(\frac\right)\left(\frac\right) = 0.034\ mol

Stoichiometry is also used to find the right
amount of reactants to
use in a chemical
reaction. An example is shown below using the thermite
reaction,

- Fe_2O_3 + 2Al \rightarrow Al_2O_3 + 2Fe

So, to completely react with 85.0 grams of iron
(III) oxide, 28.7 grams of aluminum are needed.

- m Al = \left(\frac\right)\left(\frac\right)\left(\frac\right)\left(\frac\right) = 28.7 \mboxAl

## 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 (C_6H_6) may produce
singly-methylated (C_6H_5CH_3), doubly-methylated (C_6H_4(CH_3)_2),
or still more highly-methylated (C_6H_(CH_3)_n) products, as shown
in the following example,

- C_6H_6 + \quad CH_3Cl \rightarrow C_6H_5CH_3 + HCl\,
- C_6H_6 + 2\mboxCH_3Cl \rightarrow C_6H_4(CH_3)_2 + 2HCl\,
- C_6H_6 + n\mboxCH_3Cl \rightarrow C_6H_(CH_3)_n + nHCl\,

In this example, which reaction takes place is
controlled in part by the relative concentrations of the
reactants.

## Stoichiometric coefficient

The stoichiometric coefficient in a chemical reaction system of the i–th component is defined as- \nu_i = \frac \,

or

- dN_i = \nu_i d\xi \,

where Ni is the number of molecules of i, and ξ is the
progress variable or
extent of reaction''' (Prigogine & Defay, p. 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 νi
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). 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.e., whether equilibrium
lies to the right or the left.

If one contemplates actual reaction
mechanisms, stoichiometric coefficients will always be integers, since elementary
reactions always involve whole molecules. If one uses a composite
representation of an "overall" reaction, some may be rational
fractions.
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.

The simplest possible case is an isomerism

- A \iff B

in which νB = 1 since one molecule of B is
produced each time the reaction occurs, while νA = −1
since one molecule of A is necessarily consumed. 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. 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. 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

- \nu_ = \frac \,

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

- dN_i = \sum_k \nu_ d\xi_k \, .

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 (state
variables), and the representation in terms of the actual
compositional degrees
of freedom, as expressed by the extents of reaction . The
transformation from a vector
expressing the extents to a vector expressing the amounts uses a
rectangular matrix
whose elements are the stoichiometric coefficients
[ νi k ].

The maximum and
minimum for any ξk 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. 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. 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. Moles
are most commonly used, but it is more suggestive to picture
incremental chemical reactions in terms of molecules. The Ns and
ξ's are reduced to molar units by dividing by Avogadro's
number. While dimensional mass units may be used, the
comments about integers are then no longer applicable.

## 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, \mathbf.If a reaction network has \mathit reactions and
\mathit participating molecular species then the stoichiometry
matrix will have corresponding \mathit columns and \mathit
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:

\mathbf = \begin -1 & 0 & 0 & 0 \\ 1
& 1 & 0 & 0 \\ 0 & -1 & -1 & 0 \\ 0 & 0
& 1 & -1 \\ 0 & 0 & 0 & 1 \\ \end

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:

\frac = \mathbf \cdot \mathbf

## 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. Gas stoichiometry applies when the gases produced are assumed to be ideal, and the temperature, pressure, and volume of the gases are all known. 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.Gas stoichiometry calculations solve for the
unknown volume or
mass of a gaseous product
or reactant. 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:

- 100 \ \mbox\,NH_3 \cdot \frac = 5.871 \ \mbox\,NH_3\

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 (273.15 K) and 1 atmosphere
using the gas law
constant of R = 0.08206 L · atm · K-1 · mol-1 :

Gas stoichiometry often involves having to know
the molar
mass of a gas, given the density of that gas. The ideal
gas law can be re-arranged to obtain a relation between the
density and the molar mass of
an ideal gas:

- \rho = \frac and n = \frac

and thus:

- \rho = \frac

## Stoichiometric air-fuel ratios of common fuels

## 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.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. When choosing primary
standards in analytical
chemistry, compounds with higher "equivalent weights" are, in
general, more desirable because weighing errors are reduced or
minimized. For example, hydrogen, with atomic weight
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 15.9994, 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.\frac = \frac

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

\mbox \times \frac = \mbox

## See also

## References

- Chemical Thermodynamics
- Thermodynamics of Irreversible Processes, 3rd ed. Library of Congress Catalog No. 67-29540
- Thermodynamics: An Advanced Treatment for Chemists and Physicists, 5th ed. 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

stoichiometry in German: Stöchiometrie

stoichiometry in Spanish: Estequiometría

stoichiometry in French: Stœchiométrie

stoichiometry in Indonesian: Stoikiometri

stoichiometry in Italian: Stechiometria

stoichiometry in Hebrew: סטויכיומטריה

stoichiometry in Dutch: Stoichiometrie

stoichiometry in Japanese: 化学量論

stoichiometry in Polish: Stechiometria

stoichiometry in Portuguese:
Estequiometria

stoichiometry in Russian: Стехиометрия

stoichiometry in Slovenian: Stehiometrija

stoichiometry in Serbian: Стехиометрија

stoichiometry in Finnish: Stoikiometria

stoichiometry in Swedish: Stökiometri

stoichiometry in Tamil: விகிதவியல்

stoichiometry in Turkish: Stokiyometri

stoichiometry in Chinese:
化学计量