# Reaction rate constant

## Overview

In chemical kinetics a reaction rate constant k or ${\displaystyle \lambda }$ 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:

${\displaystyle {\frac {d[C]}{dt}}=k(T)[A]^{m}[B]^{n}}$

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

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

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.

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 dm3 s-1
• For order n, the rate coefficient has units of mol1-n Ln-1 s-1 or mol1-n dm3n-3 s-1