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WOLFRAM NOTEBOOK
Simple Arrhenius Model for Activation Energy and Catalysis
Simple Arrhenius Model for Activation Energy and Catalysis
The concept of activation energy was introduced by Svante Arrhenius in 1889. In order for a chemical reaction to occur, even one which is thermodynamically favorable—with a negative enthalpy of reaction <0—an energy of magnitude greater than or equal to , known as the activation energy, must be supplied to overcome a barrier. This is usually accomplished by heating the reaction mixture. The most rudimentary form of the Arrhenius equation, for the rate constant of the forward reaction, is given by . Clearly, the rate is increased at higher temperature . More advanced versions of the Arrhenius equation, which we do not consider here, take into account possible temperature dependence of the frequency factor , and even of the activation energy itself. There are also modifications dependent on the molecularity (bimolecular etc.) of the reaction. Near the peak of the activation curve, the reacting system goes through a short-lived intermediate state, which can be written as . In some theoretical treatments, this is known as an "activated complex".
ΔH
rx
E
a
k=A
-(RT)
E
a
e
T
A
E
a
ABC
This Demonstration considers the simple exchange reaction in which the fragments (possible single atoms) , , and are shown on the superimposed graphic in green, blue, and red, respectively. The progress of the reaction can be pictured as the reactants and "climbing a hill" of height and sliding down to the lower energy state of the products and . A parameter describes the extent of reaction as it varies between 0 and 1. We consider exothermal reactions in the moderate range of between -50 and -100 kJ/mol. Many other reaction enthalpy changes are as large as -1000 kJ/mol.
AB+C→A+BC
A
B
C
AB
C
E
a
A
BC
ξ
Δ
H
rx
Many reactions can be made to run many times faster by use of an appropriate catalyst. A catalyst, represented schematically on the graphic as a black rectangle, takes part in the mechanism of the reaction but is regenerated after the products are produced. A catalytic pathway is accompanied by a much-reduced activation energy , shown by a red curve on the energy plot. Catalysis can involve complex reactions on a molecular level, with possible intermediate species of the general form , , and . Ultimately the last species dissociates to produce the final products , with the regenerated catalyst now able to take part in repetitions of the reaction.
E
ca
cat-AB
cat-ABC
cat-BC
A+BC+cat
Almost all biological processes depend on the action of enzymes, which are catalysts usually composed of protein structures. Enzymes specific to a given biochemical reaction are able to speed up reaction rates by factors of several hundred thousand.
Moving the slider for the extent of reaction between and gives an idealized picture of the progress of the reaction.
ξ=0
ξ=1