# Reaction rate constant

## Overview

In chemical kinetics a **reaction rate constant** *k* or <math>\lambda</math> quantifies the speed of a chemical reaction.

For a chemical reaction where substance A and B are reacting to produce C, the reaction rate has the form:

- <math>\frac{d[C]}{dt} = k(T)[A]^{m}[B]^{n}</math>

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

[X] is the concentration of substance X in moles per volume of solution assuming the reaction is taking place throughout the volume of the solution. (for a reaction taking place at a boundary it would denote something like moles of X per area.)

The exponents *m* and *n* are called orders and depend on the reaction mechanism. They can be determined experimentally.

In a single-step reaction can also be written as

- <math>\frac{d[C]}{dt} = Ae^\frac{-E_a}{RT}[A]^m[B]^n</math>

*E _{a}* 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

*E*to vary with

_{a}*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.

The units of the rate coefficient depend on the global order of reaction:

- For order zero, the rate coefficient has units of mol L
^{-1}s^{-1}or mol dm^{-3}s^{-1} - For order one, the rate coefficient has units of s
^{-1} - For order two, the rate coefficient has units of L mol
^{-1}s^{-1}or mol^{-1}dm^{3}s^{-1} - For order n, the rate coefficient has units of mol
^{1-n}L^{n-1}s^{-1}or mol^{1-n}dm^{3n-3}s^{-1}