= Order of reaction
{title2=$n$}
= Orders of reaction
{synonym}
= Reaction order
{synonym}
In a power-form <rate law> $v=k[\mathrm A]^\alpha[\mathrm B]^\beta$, the partial <orders of reaction> are $\alpha$ and $\beta$, and the overall <order of reaction> is $n=\alpha+\beta$. For example, doubling $[\mathrm A]$ at fixed $[\mathrm B]$ multiplies $v$ by $2^\alpha$: factors of one, two, and four correspond to partial <orders of reaction> zero, one, and two. These exponents can also be fractional or negative. A single constant <order of reaction> need not describe a <rate law> that is not a power form. See https://goldbook.iupac.org/terms/view/O04322[IUPAC Gold Book: order of reaction].
For a simple irreversible conversion $\mathrm A\longrightarrow\mathrm B$ with <rate equation> $-d[\mathrm A]/dt=k[\mathrm A]^n$, initial <concentration> $A_0>0$, and fixed $k>0$, compare <zero-order reactions>, <first-order reactions>, and <second-order reactions> using the <dimensionless quantities>
$$
X=\frac{[\mathrm A]}{A_0},\qquad \tau=kA_0^{n-1}t,\qquad \frac{dX}{d\tau}=-X^n.
$$
Their integrated curves, starting at $X(0)=1$, are
$$
\begin{aligned}
n=0:&\quad X=1-\tau\quad(0\leq\tau<1),\\
n=1:&\quad X=e^{-\tau},\\
n=2:&\quad X=\frac1{1+\tau}.
\end{aligned}
$$
For the <zero-order reaction>, the plotted extension $X=\max(1-\tau,0)$ stops conversion at depletion. It does not continue to obey $dX/d\tau=-1$ once $X=0$. A negative <concentration> would be unphysical. The <first-order reaction> and <second-order reaction> approach zero without reaching it at finite time in these models.
\Image[/reaction-order-concentration-curves.png]
{title=<Dimensionless> <concentration> decays for three <orders of reaction>, with <zero-order reaction> depletion and the corresponding linearizing plots}
The common $\tau$ axis compares curve shapes after each model's own time rescaling, rather than equal laboratory times for an identical numerical $k$. In the lower panels, $X$, $\ln X$, and $1/X$ respectively give straight lines with slopes $-1$, $-1$, and $+1$ for the matching <order of reaction>. The <natural logarithm> uses a <dimensionless quantity>. These transformed plots help test a proposed <rate law>; the <zero-order reaction> line applies only before depletion. See https://openstax.org/books/chemistry-2e/pages/12-4-integrated-rate-laws[Flowers et al., Chemistry 2e, §12.4: integrated rate laws].
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