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# Reaction rate constant

In chemical kinetics a reaction rate constant k or λ quantifies the speed of a chemical reaction.

For a chemical reaction n A + m B → C + D, the reaction rate is typically of the form

$\frac{d[C]}{dt} = k(T)[A]^{n'}[B]^{m'}$

Here [X] denotes, for a reaction between liquids, gases, or solutes, the concentration of X; for a reaction taking place at a boundary it would denote something like moles of X per area.

In this equation k(T) is the reaction rate constant that depends on temperature.

The exponents n' and m' are called orders and depend on the reaction mechanism. In a single-step reaction can also be written as

$\frac{d[C]}{dt} = Ae^\frac{-E_a}{RT}[A]^n[B]^m$

Ea is the activation energy and R is the Gas constant. Since at temperature T the molecules have energies according to a Boltzmann distribution, one can expect the proportion of collisions with energy greater than Ea to vary with e-Ea/RT. A is the pre-exponential factor or frequency factor.

The Arrhenius equation gives the quantitative basis of the relationship between the activation energy and the reaction rate at which a reaction proceeds.