= Stoichiometry
{title2=$\nu_i$}
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<Stoichiometry> relates the quantities consumed and formed in a <chemical reaction>. Its coefficients are ratios of entity counts, or equivalently of <amount of substance>, rather than ratios of <masses>. For the <water> <chemical equation>, consuming two <molecular hydrogen> <molecules> per <molecular oxygen> <molecule> gives the same $2:1$ ratio as consuming two <moles> of <molecular hydrogen> per <mole> of <molecular oxygen>. Multiplying every entity count by the same factor preserves the ratio. See https://openstax.org/books/chemistry-2e/pages/4-3-reaction-stoichiometry[Flowers et al., Chemistry 2e, reaction stoichiometry].
Coefficients and subscripts do different jobs. The coefficient in $2\mathrm{H}_2\mathrm{O}$ counts two <water> <molecules>; the subscript says that each contains two <hydrogen> <chemical atoms>. Changing coefficients scales quantities. Changing a subscript changes the specified <chemical substance>.
\Image[/stoichiometry-particle-counts.png]
{title=The same stoichiometric ratio at molecular and molar scales}
{description=The upper schematic counts individual <molecules>; the lower line multiplies each count by the <Avogadro constant> times one <mole>. Circle sizes and positions are illustrative.}
This distinction catches a common counting error: one <mole> of <water> <molecules> contains two <moles> of <hydrogen> <chemical atoms> and one <mole> of <oxygen> <chemical atoms>. Always specify what is counted.
<Stoichiometry> records reactant and product multiplicities in a <chemical reaction> or a <chemical reaction network>. The change caused by one reaction is its <stoichiometric vector>; multiplying by the reaction rate gives its contribution to the concentration equations. For two identical reactants the rate-constant convention absorbs any combinatorial factor.
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