 Order of reaction

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 IUPAC Gold Book: order of reaction.

For a simple irreversible conversion $\mathrm{A}⟶\mathrm{B}$ 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 quantitiesTheir integrated curves, starting at $X(0)=1$, areFor 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.

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 Flowers et al., Chemistry 2e, §12.4: integrated rate laws.