Average rate of a chemical reaction
The average rate describes how fast concentrations change over a finite time interval. The
Average rate of a chemical reaction is defined so the reaction progress is reported as a positive number
in the forward direction, even though reactant concentrations decrease.
Core definition and essential formulas
Definition (reaction-rate normalization by stoichiometry).
\[
r_{\text{avg}}
= -\,\frac{1}{\nu_{\text{react}}}\,\frac{\Delta[\text{reactant}]}{\Delta t}
= \frac{1}{\nu_{\text{prod}}}\,\frac{\Delta[\text{product}]}{\Delta t}
\]
Here \(\nu_i\) are stoichiometric coefficients, \([\text{species}]\) is concentration (commonly \(\mathrm{mol\cdot
L^{-1}}\)), and \(\Delta t\) is the measured time interval. For reactants, \(\Delta[\text{reactant}] < 0\), so
the leading minus sign makes \(r_{\text{avg}} > 0\) for forward reactions; for products,
\(\Delta[\text{product}] > 0\) so no minus sign is needed.
Convert the reaction rate to per-species rates.
\[
\frac{\Delta[i]}{\Delta t}
=
\begin{aligned}[t]
&-\nu_i\,r_{\text{avg}} \quad &\text{(reactant consumption)} \\
&\ \nu_i\,r_{\text{avg}} \quad &\text{(product formation)}
\end{aligned}
\]
Interpretation, common checks, and scope
A larger \(r_{\text{avg}}\) means a faster concentration change per unit time over the chosen interval; a smaller
value indicates slower progress. Typical units are \(\mathrm{mol\cdot L^{-1}\cdot s^{-1}}\) or \(\mathrm{mol\cdot
L^{-1}\cdot min^{-1}}\), matching the time unit used. Per-species results scale with \(\nu_i\), so species with
larger coefficients have larger magnitude consumption or formation rates.
Common pitfalls
- Mixing time units (seconds vs minutes) without converting \(\Delta t\).
- Using concentrations in \(\mathrm{mol\cdot m^{-3}}\) or \(\mathrm{mol\cdot L^{-1}}\) inconsistently.
- Forgetting stoichiometric normalization by \(\nu_i\), leading to mismatched rates between species.
- Dropping the sign convention (reactants should give positive \(r_{\text{avg}}\) after the minus sign).
Micro example
For \(2A \rightarrow B\), if \([A]\) changes from \(0.80\) to \(0.50\ \mathrm{mol\cdot L^{-1}}\) in \(60\
\mathrm{s}\):
\[
r_{\text{avg}} = -\frac{1}{2}\cdot\frac{-0.30}{60} = 2.50\times 10^{-3}\ \mathrm{mol\cdot L^{-1}\cdot s^{-1}}
\]
Use this approach when concentrations are known at two times and the goal is a single average rate and consistent
per-species rates. Avoid using it as an instantaneous rate at a specific time or to infer a reaction mechanism; a
next-step concept for deeper analysis is the rate law and integrated rate laws for
concentration–time behavior.
