= Reaction rate
{title2=$v$}
{wiki}
For one <chemical reaction> in a <closed system> of fixed <volume> $V$, with uniform <concentrations> and no competing reactions or appreciable accumulation of unlisted species, choose the <chemical equation>
$$
a\mathrm A+b\mathrm B\longrightarrow c\mathrm C,\qquad a,b,c>0.
$$
Brackets denote <amount of substance> per <volume>, for example $[\mathrm A]=n_{\mathrm A}/V$. The <stoichiometry> gives one instantaneous <reaction rate>
$$
v=-\frac1a\frac{d[\mathrm A]}{dt}
=-\frac1b\frac{d[\mathrm B]}{dt}
=\frac1c\frac{d[\mathrm C]}{dt}
=\frac1V\frac{d\xi}{dt},
$$
where $\xi$ is the existing <extent of reaction>. The minus signs make forward consumption positive; dividing by the coefficients makes measurements of different <chemical species> agree. Units can be $\mathrm{mol\,L^{-1}\,s^{-1}}$. See https://goldbook.iupac.org/terms/view/R05156[IUPAC Gold Book: rate of reaction] and https://openstax.org/books/chemistry-2e/pages/12-1-chemical-reaction-rates[Flowers et al., Chemistry 2e, §12.1: chemical reaction rates].
For the illustrative <chemical equation> $2\mathrm A+\mathrm B\longrightarrow3\mathrm C$, a measured $d[\mathrm C]/dt=0.060\,\mathrm{mol\,L^{-1}\,s^{-1}}$ implies $v=0.020\,\mathrm{mol\,L^{-1}\,s^{-1}}$, $d[\mathrm A]/dt=-0.040\,\mathrm{mol\,L^{-1}\,s^{-1}}$, and $d[\mathrm B]/dt=-0.020\,\mathrm{mol\,L^{-1}\,s^{-1}}$. These numbers express <stoichiometry>, without supplying a <rate law>.
Each <derivative> is the slope of a <concentration> curve at one instant. Over a finite interval, $-\Delta[\mathrm A]/(a\Delta t)$ instead gives an average <reaction rate>. For A converting reversibly to B, the net <reaction rate> is $v=d[\mathrm B]/dt=J_f-J_r$; both directional <reaction rates> can remain positive when $v=0$ at <chemical equilibrium>.
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