Stoichiometry

Stoichiometry (/ˌstɔɪkiˈɒmɪtri/) is the

relationship between the weights 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 the total
mass of the products, leading to the
insight that the relations among A stoichiometric diagram of the combustion reaction of methane
quantities of reactants and products
typically form a ratio of positive
integers. This means that if the amounts of the separate reactants are known, then the amount of the product
can be calculated. Conversely, if one reactant has a known quantity and the quantity of the products can be
empirically determined, then the amount of the other reactants can also be calculated.

This is illustrated in the image here, where the balanced equation is:

CH4 + 2 O2 → CO2 + 2 H2O

Here, one molecule of methane reacts with two molecules of oxygen gas to yield one molecule of carbon
dioxide and two molecules of water. This particular chemical equation is an example of complete
combustion. Stoichiometry measures these quantitative relationships, and is used to determine the amount of
products and reactants that are produced or needed in a given reaction. Describing the quantitative
relationships among substances as they participate in chemical reactions is known as reaction stoichiometry.
In the example above, reaction stoichiometry measures the relationship between the quantities of methane
and oxygen that react to form carbon dioxide and water.

Because of the well known relationship of moles to atomic weights, the ratios that are arrived at by
stoichiometry can be used to determine quantities by weight in a reaction described by a balanced equation.
This is called composition stoichiometry.

Gas stoichiometry deals with reactions involving gases, where the gases are at a known temperature,
pressure, and volume and can be assumed to be ideal gases. For gases, the volume ratio is ideally the same
by the ideal gas law, but the mass ratio of a single reaction has to be calculated from the molecular masses
of the reactants and products. In practice, because of the existence of isotopes, molar masses are used
instead in calculating the mass ratio.

Etymology
The term stoichiometry was first used by Jeremias Benjamin Richter in 1792 when the first volume of
Richter's Anfangsgründe der Stöchyometrie oder Meßkunst chymischer Elemente (Fundamentals of
Stoichiometry, or the Art of Measuring the Chemical Elements) was published.[1] The term is derived from
the Ancient
Greek words
στοιχεῖον
stoikheîon
"element"[2]
and μέτρον
métron
"measure".

Definition

IUPAC definition for stoichiometry

A stoichiometric amount[3] or stoichiometric ratio of a reagent is the optimum amount or ratio where,
assuming that the reaction proceeds to completion:

1. All of the reagent is consumed

2. There is no deficiency of the reagent
3. There is no excess of the reagent.
Stoichiometry rests upon the very basic laws that help to understand it better, i.e., law of conservation of
mass, the law of definite proportions (i.e., the law of constant composition), the law of multiple proportions
and the law of reciprocal 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 number of
atoms of a given element X on the reactant side must equal the number of atoms of that element on the
product side, whether or not all of those atoms are actually involved in a reaction.[4]

Chemical reactions, as macroscopic unit operations, consist of simply a very large number of elementary
reactions, where a single molecule reacts with another molecule. As the reacting molecules (or moieties)
consist of a definite set of atoms in an integer ratio, the ratio between reactants in a complete reaction is also
in integer ratio. A reaction may consume more than one molecule, and the stoichiometric number counts
this number, defined as positive for products (added) and negative for reactants (removed).[5] The unsigned
coefficients are generally referred to as the stoichiometric coefficients.[6]
Each element has an atomic mass, and considering molecules as collections of atoms, compounds have a
definite molar mass. By definition, the atomic mass of carbon-12 is 12 Da, giving a molar mass of 12 g/mol.
The number of molecules per mole in a substance is given by the Avogadro constant, defined as
6.022 140 76 × 1023 mol−1 . Thus, to calculate the stoichiometry by mass, the number of molecules required
for each reactant is expressed in moles and multiplied by the molar mass of each to give the mass of each
reactant per mole of reaction. The mass ratios can be calculated by dividing each by the total in the whole
reaction.

Elements in their natural state are mixtures of isotopes of differing mass; thus, atomic masses and thus molar
masses are not exactly integers. For instance, instead of an exact 14:3 proportion, 17.04 g of ammonia
consists of 14.01 g of nitrogen and 3 × 1.01 g of hydrogen, because natural nitrogen includes a small
amount of nitrogen-15, and natural hydrogen includes hydrogen-2 (deuterium).

A stoichiometric reactant is a reactant that is consumed in a reaction, as opposed to a catalytic reactant,

which is not consumed in the overall reaction because it reacts in one step and is regenerated in another
step.

Converting grams to moles

Stoichiometry is not only used to balance chemical equations but also used in conversions, i.e., converting
from grams to moles using molar mass as the conversion factor, or from grams to milliliters using density.
For example, to find the amount of NaCl (sodium chloride) in 2.00 g, 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 in moles (the unit that was needed), as
shown in the following equation,

Molar proportion
Stoichiometry is often used to balance chemical equations (reaction stoichiometry). 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:

2 H2 + O2 → 2 H2O

Reaction stoichiometry describes the 2:1:2 ratio of hydrogen, oxygen, and water molecules in the above
equation.

The molar ratio allows for conversion between moles of one substance and moles of another. For example,
in the reaction

2 CH3OH + 3 O2 → 2 CO2 + 4 H2O

the amount of water that will be produced by the combustion of 0.27 moles of CH3 OH is obtained using
the molar ratio between CH3 OH and H2 O of 2 to 4.

The term stoichiometry is also often used for the molar proportions of elements in stoichiometric
compounds (composition stoichiometry). For example, the stoichiometry of hydrogen and oxygen in H2 O
is 2:1. In stoichiometric compounds, the molar proportions are whole numbers.

Determining amount of product

Stoichiometry can also be used to find the quantity of a product yielded by a reaction. If a piece of solid
copper (Cu) were added to an aqueous solution of silver nitrate (AgNO3 ), the silver (Ag) would be
replaced in a single displacement reaction forming aqueous copper(II) nitrate (Cu(NO3 )2 ) and solid silver.
How much silver is produced if 16.00 grams of Cu is added to the solution of excess silver nitrate?

The following steps would be used:

1. Write and balance the equation

2. Mass to moles: Convert grams of Cu to moles of Cu
3. Mole ratio: Convert moles of Cu to moles of Ag produced
4. Mole to mass: Convert moles of Ag to grams of Ag produced
The complete balanced equation would be:

Cu + 2 AgNO3 → Cu(NO3)2 + 2 Ag

For the mass to mole step, the mass of copper (16.00 g) would be converted to moles of copper by dividing
the mass of copper by its molar mass: 63.55 g/mol.

Now that the amount of Cu in moles (0.2518) is found, we can set up the mole ratio. This is found by
looking at the coefficients in the balanced equation: Cu and Ag are in a 1:2 ratio.

Now that the moles of Ag produced is known to be 0.5036 mol, we convert this amount to grams of Ag
produced to come to the final answer:

This set of calculations can be further condensed into a single step:

Further examples
For propane (C3 H8 ) reacting with oxygen gas (O2 ), the balanced chemical equation is:

C3H8 + 5 O2 → 3 CO2 + 4 H2O

The mass of water formed if 120 g of propane (C3 H8 ) is burned in excess oxygen is then

Stoichiometric ratio
Stoichiometry is also used to find the right amount of one reactant to "completely" react with the other
reactant in a chemical reaction – that is, the stoichiometric amounts that would result in no leftover reactants
when the reaction takes place. An example is shown below using the thermite reaction,

Fe2O3 + 2 Al → Al2O3 + 2 Fe

This equation shows that 1 mole of iron(III) oxide and 2 moles of aluminum will produce 1 mole of
aluminium oxide and 2 moles of iron. So, to completely react with 85.0 g of iron(III) oxide (0.532 mol),
28.7 g (1.06 mol) of aluminium are needed.

Limiting reagent and percent yield

The limiting reagent is the reagent that limits the amount of product that can be formed and is completely
consumed when the reaction is complete. An excess reactant is a reactant that is left over once the reaction
has stopped due to the limiting reactant being exhausted.

Consider the equation of roasting lead(II) sulfide (PbS) in oxygen (O2 ) to produce lead(II) oxide (PbO) and
sulfur dioxide (SO2 ):

2 PbS + 3 O2 → 2 PbO + 2 SO2

To determine the theoretical yield of lead(II) oxide if 200.0 g of lead(II) sulfide and 200.0 g of oxygen are
heated in an open container:
Because a lesser amount of PbO is produced for the 200.0 g of PbS, it is clear that PbS is the limiting
reagent.

In reality, the actual yield is not the same as the stoichiometrically-calculated theoretical yield. Percent yield,
then, is expressed in the following equation:

If 170.0 g of lead(II) oxide is obtained, then the percent yield would be calculated as follows:

Example
Consider the following reaction, in which iron(III) chloride reacts with hydrogen sulfide to produce iron(III)
sulfide and hydrogen chloride:

2 FeCl3 + 3 H2S → Fe2S3 + 6 HCl

The stoichiometric masses for this reaction are:

324.41 g FeCl3, 102.25 g H2S, 207.89 g Fe2S3, 218.77 g HCl

Suppose 90.0 g of FeCl3 reacts with 52.0 g of H2 S. To find the limiting reagent and the mass of HCl
produced by the reaction, we change the above amounts by a factor of 90/324.41 and obtain the following
amounts:

90.00 g FeCl3, 28.37 g H2S, 57.67 g Fe2S3, 60.69 g HCl

The limiting reactant (or reagent) is FeCl3 , since all 90.00 g of it is used up while only 28.37 g H2 S are
consumed. Thus, 52.0 − 28.4 = 23.6 g H2 S left in excess. The mass of HCl produced is 60.7 g.

By looking at the stoichiometry of the reaction, one might have guessed FeCl3 being the limiting reactant;
three times more FeCl3 is used compared to H2 S (324 g vs 102 g).

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 (C6 H6 ), through a Friedel–Crafts reaction using
AlCl3 as a catalyst, may produce singly methylated (C6 H5 CH3 ), doubly methylated (C6 H4 (CH3 )2 ), or still
more highly methylated (C6 H6−n (CH3 )n ) products, as shown in the following example,

C6H6 + CH3Cl → C6H5CH3 + HCl

C6H6 + 2 CH3Cl → C6H4(CH3)2 + 2 HCl
C6H6 + n CH3Cl → C6H6−n(CH3)n + n HCl
In this example, which reaction takes place is controlled in part by the relative concentrations of the
reactants.

Stoichiometric coefficient and stoichiometric number

In lay terms, the stoichiometric coefficient of any given component is the number of molecules and/or
formula units that participate in the reaction as written. A related concept is the stoichiometric number
(using IUPAC nomenclature), wherein the stoichiometric coefficient is multiplied by +1 for all products and
by −1 for all reactants.

For example, in the reaction CH4 + 2 O2 → CO2 + 2 H2 O, the stoichiometric number of CH4 is −1, the
stoichiometric number of O2 is −2, for CO2 it would be +1 and for H2 O it is +2.

In more technically precise terms, the stoichiometric number in a chemical reaction system of the i-th
component is defined as

or

where is the number of molecules of i, and is the progress variable or extent of reaction.[7][8]

The stoichiometric number represents the degree to which a chemical species participates in a reaction.
The convention is to assign negative numbers to reactants (which are consumed) and positive ones to
products, consistent with the convention that increasing the extent of reaction will correspond to shifting the
composition from reactants towards products. However, any reaction may be viewed as going in the reverse
direction, and in that point of view, would change in the negative direction in order to lower the system's
Gibbs 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 of the initial state,

In reaction mechanisms, stoichiometric coefficients for each step are always 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 isomerization

A→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 corresponding constraints on
possible values for the stoichiometric coefficients.
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 number 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 { Ni } (state variables), and the representation in terms of the
actual compositional degrees of freedom, as expressed by the extents of reaction { ξk }. The transformation
from a vector expressing the extents to a vector expressing the amounts uses a rectangular matrix whose
elements are the stoichiometric numbers [ 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 sharing 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 ξs 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 ξs are
reduced to molar units by dividing by the Avogadro constant. 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 N.[9][10][11]
If a reaction network has n reactions and m participating molecular species, then the stoichiometry matrix
will have correspondingly m rows and n columns.

For example, consider the system of reactions shown below:

S1 → S2
5 S3 + S2 → 4 S3 + 2 S2
S3 → S4
S4 → S5

This system 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. 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, and the species vector, x to form a
compact equation, the biochemical systems equation, describing the rates of change of the molecular
species:

Gas stoichiometry
Gas stoichiometry is the quantitative relationship (ratio) between reactants and products in a chemical
reaction with 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. The ideal gas law is used
for these calculations. 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:

4 NH3 (g) + 7 O2 (g) → 4 NO2 (g) + 6 H2O (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 (273.15 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:

and

and thus:

where:

P = absolute gas pressure

V = gas volume
n = amount (measured in 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-to-fuel ratios of common fuels

In the combustion reaction, oxygen reacts with the fuel, and the point where exactly all oxygen is consumed
and all fuel burned is defined as the stoichiometric point. With more oxygen (overstoichiometric
combustion), some of it stays unreacted. Likewise, if the combustion is incomplete due to lack of sufficient
oxygen, fuel remains unreacted. (Unreacted fuel may also remain because of slow combustion or
insufficient mixing of fuel and oxygen – this is not due to stoichiometry.) Different hydrocarbon fuels have
different contents of carbon, hydrogen and other elements, thus their stoichiometry varies.

Oxygen makes up only 20.95% of the volume of air, and only 23.20% of its mass.[12] The air-fuel ratios
listed below are much higher than the equivalent oxygen-fuel ratios, due to the high proportion of inert
gasses in the air.
 Ratio by mass Ratio by Percent fuel by
Fuel [13] Main reaction
volume [14] mass

Gasoline 14.7 : 1 — 6.8% 2 C8H18 + 25 O2 → 16 CO2 + 18 H2O

Natural gas 17.2 : 1 9.7 : 1 5.8% CH4 + 2 O2 → CO2 + 2 H2O

Propane C3H8 + 5 O2 → 3 CO2 + 4 H2O

15.67 : 1 23.9 : 1 6.45%
(LP)

Ethanol 9:1 — 11.1% C2H6O + 3 O2 → 2 CO2 + 3 H2O

Methanol 6.47 : 1 — 15.6% 2 CH4O + 3 O2 → 2 CO2 + 4 H2O

n-Butanol 11.2 : 1 — 8.2% C4H10O + 6 O2 → 4 CO2 + 5 H2O

Hydrogen 34.3 : 1 2.39 : 1 2.9% 2 H2 + O2 → 2 H2O

Diesel 14.5 : 1 — 6.8% 2 C12H26 + 37 O2 → 24 CO2 + 26 H2O

Methane 17.19 : 1 9.52 : 1 5.5% CH4 + 2 O2 → CO2 + 2 H2O

Acetylene 13.26 : 1 11.92 : 1 7.0% 2 C2H2 + 5 O2 → 4 CO2 + 2 H2O

Ethane 16.07 : 1 16.68 : 1 5.9% 2 C2H6 + 7 O2 → 4 CO2 + 6 H2O

Butane 15.44 : 1 30.98 : 1 6.1% 2 C4H10 + 13 O2 → 8 CO2 + 10 H2O

Pentane 15.31 : 1 38.13 : 1 6.1% C5H12 + 8 O2 → 5 CO2 + 6 H2O

Gasoline engines can run at stoichiometric air-to-fuel ratio, because gasoline is quite volatile and is mixed
(sprayed or carburetted) with the air prior to ignition. Diesel engines, in contrast, run lean, with more air
available than simple stoichiometry would require. Diesel fuel is less volatile and is effectively burned as it
is injected.[15]

See also
Non-stoichiometric compound
Biochemical systems equation
Chemical reaction
Chemical equation
Molecule
Molar mass
Ideal gas law

References
1. Richter, J.B. (1792). Anfangsgründe der Stöchyometrie ... (in 3 vol.s) (https://books.google.co
m/books?id=NhFQAAAAcAAJ&pg=RA1-PA121) [Rudiments of Stoichiometry ...] (in
German). Vol. 1. Breslau and Hirschberg, (Germany): Johann Friedrich Korn der Aeltere.
p. 121. From p. 121: "Die Stöchyometrie (Stöchyometria) ist die Wissenschaft die
quantitativen oder Massenverhältnisse ... zu messen, in welchen die chemischen Elemente
... gegen einander stehen." (Stoichiometry (stoichiometria) is the science of measuring the
quantitative or mass relations in which the chemical "elements" exist in relation to each
other.) [On pp. 3–7, Richter explains that an "element" is a pure substance, and that a
"chemical element" (chymisches Element (Elementum chymicum)) is a substance that
cannot be resolved into dissimilar substances by known physical or chemical means. Thus,
 for example, aluminium oxide was a "chemical element" because in Richter's time, it couldn't
be resolved further into its component elements.]
2. Sinnott, R. K. (2005). Coulson and Richardson's Chemical Engineering (4th ed.). Amsterdam
Paris: Elsevier Butterworth-Heinemann. p. 36. ISBN 978-0-7506-6538-4.
3. What's in a Name? Amount of Substance, Chemical Amount, and Stoichiometric Amount
Carmen J. Giunta Journal of Chemical Education 2016 93 (4), 583-586
doi:10.1021/acs.jchemed.5b00690 (https://doi.org/10.1021%2Facs.jchemed.5b00690)
4. "Stoichiometry of Chemical Reactions" (https://web.ung.edu/media/chemistry/Chapter4/Cha
pter4-StoichiometryOfChemicalReactions.pdf) (PDF).
5. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online
corrected version: (2006–) "stoichiometric number, ν (https://goldbook.iupac.org/terms/view/S
06025.html)". doi:10.1351/goldbook.S06025 (https://doi.org/10.1351%2Fgoldbook.S06025)
6. Nijmeh, Joseph; Tye, Mark (2 October 2013). "Stoichiometry and Balancing Reactions" (http
s://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Modules_and_Websites_(Inorgani
c_Chemistry)/Chemical_Reactions/Stoichiometry_and_Balancing_Reactions#:~:text=The%
20stoichiometric%20coefficient%20is%20the,product%20sides%20of%20the%20equation.).
LibreTexts. Retrieved 5 May 2021.
7. Prigogine & Defay, p. 18; Prigogine, pp. 4–7; Guggenheim, p. 37 & 62
8. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online
corrected version: (2006–) "extent of reaction, ξ (https://goldbook.iupac.org/terms/view/E0228
3.html)". doi:10.1351/goldbook.E02283 (https://doi.org/10.1351%2Fgoldbook.E02283)
9. {{cite journal |last1=Ghaderi |first1=Susan |last2=Haraldsdóttir |first2=Hulda S.
|last3=Ahookhosh |first3=Masoud |last4=Arreckx |first4=Sylvain |last5=Fleming |first5=Ronan
M.T. |title=Structural conserved moiety splitting of a stoichiometric matrix |journal=Journal of
Theoretical Biology |date=August 2020 |volume=499 |pages=110276
|doi=10.1016/j.jtbi.2020.110276|pmid=32333975 |bibcode=2020JThBi.49910276G |doi-
access=free |hdl=1887/3134882 |hdl-access=free }}
10. Hofmeyr, Jan-hendrik S. (2001). "Metabolic control analysis in a nutshell". In Proceedings of
the 2 Nd International Conference on Systems Biology: 291–300. CiteSeerX 10.1.1.324.922
(https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.324.922).
11. Reder, Christine (21 November 1988). "Metabolic control theory: A structural approach".
Journal of Theoretical Biology. 135 (2): 175–201. Bibcode:1988JThBi.135..175R (https://ui.a
dsabs.harvard.edu/abs/1988JThBi.135..175R). doi:10.1016/s0022-5193(88)80073-0 (https://
doi.org/10.1016%2Fs0022-5193%2888%2980073-0). PMID 3267767 (https://pubmed.ncbi.n
lm.nih.gov/3267767).
12. "Universal Industrial Gases, Inc: Composition of Air - Components & Properties of Air -
Answers to "What is air?" - "What is air made up of?" -" What are air products and what are
they used for?" " (http://www.uigi.com/air.html).
13. John B. Heywood: "Internal Combustion Engine Fundamentals page 915", 1988
14. North American Mfg. Co.: "North American Combustion Handbook", 1952
15. "Air-fuel ratio, lambda and engine performance" (https://x-engineer.org/automotive-engineeri
ng/internal-combustion-engines/performance/air-fuel-ratio-lambda-engine-performance/).
Retrieved 2019-05-31.
Zumdahl, Steven S. Chemical Principles. Houghton Mifflin, New York, 2005, pp 148–150.
 Internal Combustion Engine Fundamentals, John B. Heywood

External links
Engine Combustion primer (https://web.archive.org/web/20070206060439/http://www.tech.pl
ym.ac.uk/sme/ther305-web/Combust1.PDF) from the University of Plymouth
Free Stoichiometry Tutorials (https://chemcollective.org/tutorials.php) from Carnegie Mellon's
ChemCollective
Stoichiometry Add-In for Microsoft Excel (http://chemistry-in-excel.jimdo.com/) Archived (http
s://web.archive.org/web/20110511073820/http://chemistry-in-excel.jimdo.com/) 2011-05-11
at the Wayback Machine for calculation of molecular weights, reaction coëfficients and
stoichiometry.
Reaction Stoichiometry Calculator (http://www.thermobook.net/stoichiometry/) a
comprehensive free online reaction stoichiometry calculator.

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