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ChemWiki: The Dynamic Chemistry Textbook > Physical Chemistry > Kinetics > Complex Reactions > Transition State Theory > Eyring equation
Eyring equationFrom $1Table of contentsThe Eyring equation, developed by Henry Eyring in 1935, is based off of the transition-state theory and is used to describe the relationship between reaction rate and temperature. It is similar to the Arrhenius equation, which also describes temperature dependence on reaction rates. However, while Arrhenius equation can be applied only to the kinetics of gas reactions, the Eyring equation can be usful in the study of gas, condensed and mixed phase reactions that does not base on the collision model. IntroductionThe Eyring equation gives a more accurate calculation of rate constants and provides the knowledge of how a reaction progresses at the molecular level.
Consider a bimolecular reaction:
where K is the equilibrium constant. In a transition-state model, an activated complex, AB, is formed
There is an energy barrier, called activation energy, in the reaction pathway. A certain amount of energy is required for the reaction to occur. The transition state, AB, is formed at maximum energy. This high-energy complex represents an unstable intermediate. Once the energy barrier is overcome, the reaction is able to proceed downhill and product formation occurs.
The rate of a reaction is equal to the number of activated complexes decomposing to form products. In other words, it is the concentration of the high-energy complex multiplied by the frequency of it surmounting the barrier.
Rate can be rewritten as:
Combining equations 4 and 5, we get:
giving
where v is the frequency of vibration, k is the rate constant and K is the thermodynamic equilibrium constant. The frequency of vibration is given by:
where kB is the Boltzmann's constant (1.381 x 10-23 J/K), T is the absolute temperature in Kelvin (K) and h is Planck's constant (6.626 x 10-34 Js). Substituting equation 8 into equation 7, we get:
To further describe the equilibrium constant in thermodynamics, we have the equations:
Combining equations 10 and 11 to solve for lnK, we get:
The Eyring equation is finally given by substituting equation 12 into equation 9:
Application of the Eyring EquationThe linear form of the Eyring Equation is
The values for
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and 
can be determined from kinetic data obtained from a 
vs. 
plot. The plot should provide a straight line with negative slope, 
, and a y-intercept, 
.
