Effect of concentration on reaction rate
Reaction rate describes how fast reactant concentrations decrease or product concentrations increase with time.
The Effect of Concentration on Reaction Rates is captured by a rate law that links the measured
initial rate to reactant concentrations.
Core definitions and essential formulas
For a reaction \(\nu_A A + \nu_B B + \cdots \rightarrow \text{products}\), a common form of the differential rate
law is
\[
\text{rate} = -\frac{1}{\nu_A}\frac{\mathrm{d}[A]}{\mathrm{d}t} = k[A]^m[B]^n\cdots
\]
Here \([A]\), \([B]\) are concentrations, \(k\) is the rate constant, and \(m\), \(n\) are reaction orders (found
experimentally, not from stoichiometric coefficients). The sign convention uses a minus sign for reactants so the
rate is positive for forward consumption; initial rate means the value at \(t \approx 0\), before concentrations
change significantly.
Comparing two experiments where only \([A]\) changes gives the order in \(A\):
\[
\frac{\text{rate}_2}{\text{rate}_1}=\left(\frac{[A]_2}{[A]_1}\right)^m
\quad \text{(other reactants held constant).}
\]
The overall order is \(n_{\text{overall}} = m + n + \cdots\). Once orders are known, compute \(k\) from any run:
\[
k=\frac{\text{rate}}{[A]^m[B]^n\cdots}.
\]
Units: if rate is in \(\mathrm{mol\cdot L^{-1}\cdot s^{-1}}\) and overall order is \(n_{\text{overall}}\), then
\(k\) has units \(\mathrm{(mol\cdot L^{-1})^{1-n_{\text{overall}}}\cdot s^{-1}}\). A larger \(k\) at the same
temperature indicates a faster reaction under comparable concentrations; larger orders mean the rate is more
sensitive to concentration changes.
Common pitfalls
- Using stoichiometric coefficients as reaction orders (orders must come from data).
- Comparing experiments where more than one reactant concentration changes.
- Mixing time units when computing rates or \(k\) (seconds vs minutes).
- Using non-initial rates in the method of initial rates (rate must be at \(t \approx 0\)).
Micro example
If \([A]\) doubles while other reactants stay constant and the initial rate increases by a factor of \(4\), then
\[
4 = 2^m \Rightarrow m = 2.
\]
Use this tool when initial-rate measurements from multiple experiments are available and the goal is reaction
order and a rate constant. Avoid applying it to concentration–time curves far from \(t=0\); a next-step concept
for deeper analysis is the integrated rate law and temperature dependence through the Arrhenius
equation.
