In chemistry and chemical engineering, the reaction rate (or rate of reaction) quantifies the speed at which reactants are converted into products in a chemical reaction. It is expressed as the change in concentration of a reactant or product per unit time. Mathematically, for a reaction
$$ aA + bB \rightarrow cC + dD, $$
the reaction rate $r$ can be defined in terms of any species $i$ as
$$ r = -\frac{1}{ u_i}\frac{d[\text{species }i]}{dt}, $$
where $[\text{species }i]$ denotes the molar concentration (typically in mol L$^{-1}$) of species $i$, $t$ is time, and $ u_i$ is the stoichiometric coefficient (positive for products, negative for reactants). The negative sign ensures that the rate is a positive quantity for reactants that decrease in concentration.
Dependence on Concentration
The quantitative relationship between reaction rate and the concentrations of reactants is described by a rate law. For an elementary reaction, the rate law often follows the law of mass action:
$$ r = k,[A]^{m}[B]^{n}, $$
where $k$ is the rate constant, $[A]$ and $[B]$ are the concentrations of reactants, and $m$ and $n$ are the reaction orders with respect to each reactant. The overall order of the reaction is $m+n$. Rate constants are temperature‑dependent and are commonly expressed by the Arrhenius equation:
$$ k = A \exp!\left(-\frac{E_a}{RT}\right), $$
with $A$ the pre‑exponential factor, $E_a$ the activation energy, $R$ the universal gas constant, and $T$ the absolute temperature.
Factors Influencing Reaction Rate
- Concentration or Partial Pressure – Higher concentrations of reactants increase the frequency of effective collisions, generally accelerating the reaction.
- Temperature – Raising temperature increases kinetic energy, leading to more collisions with sufficient energy to overcome the activation barrier; this typically raises $k$.
- Catalysts – Catalysts provide alternative reaction pathways with lower activation energies, thereby increasing the rate without being consumed.
- Surface Area – For heterogeneous reactions, a larger surface area of solid reactants or catalysts enhances the rate.
- Solvent Effects – Solvent polarity, viscosity, and dielectric constant can affect reaction mechanisms and thus rates.
- Light (Photochemical Reactions) – Absorption of photons can initiate reactions, altering the effective rate.
Units
In the International System of Units (SI), reaction rate is expressed as concentration change per time, typically mol L$^{-1}$ s$^{-1}$. When expressed in terms of extent of reaction, units of mol s$^{-1}$ may be used.
Measurement Techniques
- Spectroscopy (e.g., UV‑Vis, IR, NMR) to monitor concentration changes of reactants or products in real time.
- Gas Chromatography and Mass Spectrometry for analyzing volatile reactants or products.
- Conductivity or pH measurements when the reaction involves ionic species.
- Calorimetry to infer rates from heat evolution or absorption.
Applications
Understanding and controlling reaction rates is essential in:
- Industrial synthesis to optimize yield, safety, and energy consumption.
- Pharmacokinetics for drug metabolism and efficacy.
- Environmental chemistry (e.g., atmospheric pollutant degradation).
- Biochemistry where enzyme kinetics describe catalytic rates in living systems.
Related Concepts
- Half‑life: The time required for the concentration of a reactant to decrease by 50 % in a first‑order reaction.
- Rate-determining step: The slowest elementary step that controls the overall reaction rate.
- Transition state theory: Provides a theoretical framework linking the structure of the activated complex to the rate constant.
The reaction rate is a central parameter in chemical kinetics, linking microscopic molecular interactions to macroscopic observable changes in chemical systems.