Chemical kinetics is the branch of physical chemistry concerned with how rapidly chemical reactions occur and how their rates depend on experimental conditions. It connects measurements of changing composition with mathematical descriptions and molecular explanations of reaction pathways. Unlike thermodynamics, which establishes energetic constraints and equilibrium conditions, kinetics describes the timescale of chemical change. A thermodynamically favorable reaction may nevertheless proceed very slowly because its pathway contains a substantial barrier. (ocw.mit.edu)
Reaction rates and rate laws
For a reaction (aA+bB\rightarrow pP+qQ) in a closed, constant-volume system, with no appreciable accumulation of intermediates or competing reactions, the reaction rate is
[ v=-\frac{1}{a}\frac{d[A]}{dt} =-\frac{1}{b}\frac{d[B]}{dt} =\frac{1}{p}\frac{d[P]}{dt} =\frac{1}{q}\frac{d[Q]}{dt}. ]
Square brackets denote concentrations. The derivatives describe instantaneous changes, while the factors from stoichiometry ensure that the same reaction rate is obtained from each species. Concentration-based rates commonly have units of mol L(^{-1}) s(^{-1}). When intermediates accumulate or several reactions occur simultaneously, individual rates of formation and consumption require separate treatment. (goldbook.iupac.org)
A rate law expresses the dependence of rate on composition. A common form is
[ v=k[A]^\alpha[B]^\beta, ]
where (k) is a rate coefficient and the exponents are partial reaction orders. The overall order is (\alpha+\beta). Orders are determined experimentally and can be zero, fractional, or negative; they cannot generally be inferred from the balanced overall equation. The units of (k) depend on the overall order. Some reactions have more complicated rate laws for which a single, constant order is inadequate. (goldbook.iupac.org)
If one reactant remains effectively constant, its concentration can be absorbed into an observed coefficient. Thus, (v=k[A][B]) becomes (v=k_{\mathrm{obs}}[A]), with (k_{\mathrm{obs}}=k[B]), when (B) is maintained in large excess. This is pseudo-first-order behavior, not evidence that the underlying reaction is genuinely first order overall. (goldbook.iupac.org)
Concentration changes over time
Rate laws are differential equations. Integrating them gives concentration–time relationships. For the disappearance of a single reactant at constant volume and constant (k), three basic cases are
[ \begin{aligned} \text{Zero order:}\quad &[A]_t=[A]_0-kt,\ \text{First order:}\quad &[A]_t=[A]_0e^{-kt},\ \text{Second order:}\quad &\frac{1}{[A]_t}=\frac{1}{[A]_0}+kt. \end{aligned} ]
Here the second-order expression assumes (-d[A]/dt=k[A]^2). These equations apply only over the range where their respective rate laws remain valid. In particular, a zero-order expression cannot be extrapolated beyond reactant depletion. (ocw.mit.edu)
The half-life is the time required for a reactant concentration to fall to half its initial value. For first-order decay, (t_{1/2}=\ln 2/k), independent of initial concentration. For the zero- and second-order cases above, half-lives are ([A]_0/(2k)) and (1/(k[A]_0)), respectively. These contrasting dependencies help distinguish kinetic models. (ocw.mit.edu)
Temperature and molecular explanations
The dependence of many rate coefficients on temperature is described approximately by the Arrhenius equation:
[ k=Ae^{-E_a/(RT)}. ]
Here (A) is the pre-exponential factor, (E_a) the activation energy, (R) the molar gas constant, and (T) the absolute temperature. In the original formulation, (A) and (E_a) are treated as temperature-independent. A plot of (\ln k) against (1/T) then has slope (-E_a/R). Positive activation energy implies increasing (k) with increasing temperature within this approximation. (goldbook.iupac.org)
Collision models explain reaction rates in terms of encounters between molecules, with sufficient energy and suitable orientation for reaction. More generally, transition-state theory relates rates to passage through a transition state. For a unimolecular step, a commonly used expression is
[ k=\kappa\frac{k_BT}{h} \exp\left(-\frac{\Delta G^\ddagger}{RT}\right), ]
where (k_B) is the Boltzmann constant, (h) the Planck constant, (\Delta G^\ddagger) the activation Gibbs free energy, and (\kappa) a transmission coefficient. Activation free energy incorporates both enthalpic and entropic contributions; it is not identical to Arrhenius activation energy. (live.ocw.mit.edu)
Mechanisms and kinetic approximations
A reaction mechanism specifies the individual steps connecting reactants and products. For an elementary reaction, concentration exponents follow the reactant stoichiometry of that step under the usual mass-action description. An overall reaction, however, may contain intermediates and several elementary steps, producing a rate law unlike its overall stoichiometry. Agreement with an observed rate law is necessary for a proposed mechanism but does not establish its uniqueness. (goldbook.iupac.org)
The steady-state approximation simplifies mechanisms by assuming that an intermediate's rate of formation nearly balances its rate of consumption, so its concentration changes slowly. This does not mean that the entire system has reached chemical equilibrium. A distinct pre-equilibrium approximation assumes that a reversible step equilibrates rapidly before a slower subsequent reaction. Both approximations require an appropriate separation of timescales. (ocw.mit.edu)
Catalysis, transport, and applications
Catalysis accelerates reactions by providing alternative pathways with more favorable kinetic barriers. A catalyst participates in the mechanism but is regenerated overall. It does not change the equilibrium constant of the same overall reaction under fixed conditions. Enzymes are biological catalysts whose rates can show substrate saturation, making simple power-law descriptions insufficient across all concentrations. (mitocw.ups.edu.ec)
Observed rates may also depend on diffusion, mixing, or transport to a reactive surface. In heterogeneous systems, chemical conversion and transport must therefore be distinguished. Kinetic models support chemical engineering calculations of reactor performance and selectivity, including coupled reactions, heat effects, and heterogeneous catalytic processes. Experimental concentration–time measurements and initial-rate comparisons provide the information needed to estimate coefficients and test those models. (ocw.mit.edu)