Stoichiometry

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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 (chemical equations).

1 Etymology
2 Definition
3 Different stoichiometries in competing reactions
4 Stoichiometric air-fuel ratios of common fuels
5 See also
6 External links
7 References

[edit] Etymology

"Stoichiometry" derives from the Greek words Στοικρειονε stoikheione (Gramatical translation) ("element") and metriā ("measure," from metron). 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.

[edit] 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 $H 2 O$ is 2:1. In stoichiometric compounds, the molar proportions are whole numbers (that is what the law of multiple proportions is about).

Compounds for which the molar proportions are not whole numbers are called non-stoichiometric compounds.

Stoichiometry is used not only to balance chemical equations but also is used in conversions — i.e. converting from grams to moles, or from grams to milliliters. For example, if there were 2.00 g of NaCl, to find the number of moles, one would do the following,

$\frac{2.00 \mbox{ g NaCl}}{58.44 \mbox{ g NaCl mol}^{-1}} = 0.034 \ mol$

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), as shown in the following equation,

$\left(\frac{2.00 \mbox{ g NaCl}}{1}\right)\left(\frac{1 \mbox{ mol NaCl}}{58.44 \mbox{ g NaCl}}\right) = 0.034\ mol$

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.

$\left(\frac{85.0 \mbox{ g }Fe_2O_3}{1}\right)\left(\frac{1 \mbox{ mol }Fe_2 O_3}{159.7 \mbox{ g }Fe_2 O_3}\right)\left(\frac{2 \mbox{ mol }Al}{1 \mbox{ mol }Fe_2 O_3}\right)\left(\frac{27.0 \mbox{ g }Al}{1 \mbox{ mol }Al}\right) = 28.7 \mbox{ g }Al$

[edit] 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 ( $C 6 H 6$ ) may produce singly-methylated $(C 6 H 5 C H 3)$ , doubly-methylated $(C 6 H 4 (C H 3) 2)$ , or still more highly-methylated $(C 6 H 6 - n (C H 3) n)$ products, as shown in the following example,

$C_6H_6 + \quad CH_3Cl \rightarrow C_6H_5CH_3 + HCl\,$

$C_6H_6 + 2\mbox{ }CH_3Cl \rightarrow C_6H_4(CH_3)_2 + 2HCl\,$

$C_6H_6 + n\mbox{ }CH_3Cl \rightarrow C_6H_{6-n}(CH_3)_n + nHCl\,$

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

[edit] Stoichiometric air-fuel ratios of common fuels