Rate of Reaction
(Velocity Coefficent)

The rate of reaction is a measure of how quickly reactants are consumed or products formed. It is usually measured as the change in concentration of the reactants or products per unit time. It was found to depend directly on the concentrations of the reactants.1 Then for a simple reaction of the form A + B → C, the rate of reaction can be expressed in terms of the change in concentration of any of its components:

R = -d[A] / dt = -d[B] / dt = d[C] / dt = k [A]s [B]t

where k is the rate constant of the reaction (velocity coefficient) and the expressions in the square brackets are the concentrations of the reactants. The sum of the exponents s+t is called the order of reaction. It is a non-negative number that can be zero or any other number and does not need to be an integer.

Besides the reactant concentrations, other factors such as temperature, catalyst and pressure can affect the rate of reaction. Usually, one observes reactions occuring at higher temperatures have a higher rate. This is because an increase of the temperature results in more (successful) collisions between molecules. This can be seen through the Arrhenius equation of the rate constant:

k = A e-Ea/RT

where A is a simple prefactor and R is the gas constant. Thus, the rate constant depends on both the temperature T and the activation energy Ea. A simple rule of thumb is: for every 10 °C increase, the reaction rate doubles. However, this is not always true.

Another important equation for the calculation of rate constants was developed by Eyring and Polanyi:

k = (kBT/h) e-Ea/kT + ΔSa/k

where ΔSa and Ea and are the entropy and enthalpy of activation and kB and h are the Boltzmann and Planck constants.

The reaction rate can also be affected by special molecules, called catalysts that lower the activation energy required for reactants to form the products at a collision. Some are very powerful and can speed up a reaction by a factor of 1000 or more. In some cases, these compounds change the pathway of the reaction, i.e. different intermediates form during the reaction.

 

Chemical Kinetics for different Reaction Types

Zero-Order First-Order Second-Order
Rate Law R = k R = k [A] R = k [A]2
Linear Plot [A] = f(t) ln[A] = f(t) [A]-1 = f(t)
Integrated Law [A] = [A]0 - kt [A] = [A]0 e-kt [A]-1 = [A]0 -1 + kt
Half-life [A]0 / 2k ln2 / k 1 / k[A]0
Notes

  1. The law of mass action states that the rate of any chemical reaction is directly proportional to the product of the concentrations (activities) of the reactants. It also states that a reversible reaction reaches a dynamic equilibrium at which the rate of the forward and reverse reactions are equal.2

  2. J. Krenos and J. Potenza, Chemical Principles, 5th Ed, New York 2010

  • Summary

    The rate of reaction is measured as the change in concentration of the reactants or products per unit time.

  • The rate of reaction depends on the reactant concentrations, the temperature, the type and concentration of catalyst (if present) and the pressure.

  • A simple rule of thumb is: for every 10 °C increase, the reaction rate doubles.