Eyring Equation Information
The Eyring equation also known as Eyring–Polanyi equation in chemical kinetics relates the reaction rate to temperature. It was developed almost simultaneously in 1935 by Henry Eyring, M.G. Evans and Michael Polanyi. This equation follows from the transition state theory (aka, activated-complex theory) and is trivially equivalent to the empirical Arrhenius equation which are both readily derived from statistical thermodynamics in the kinetic theory of gases.[1]
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General form
The general form of the Eyring–Polanyi equation somewhat resembles the Arrhenius equation:
where ΔG‡ is the Gibbs energy of activation, kB is Boltzmann's constant, and h is Planck's constant.
It can be rewritten as:
To find the linear form of the Eyring-Polanyi equation:
where:
- = reaction rate constant
- = absolute temperature
- = enthalpy of activation
- = gas constant
- = Boltzmann constant
- = Planck's constant
- = entropy of activation
A certain chemical reaction is performed at different temperatures and the reaction rate is determined. The plot of versus gives a straight line with slope from which the enthalpy of activation can be derived and with intercept from which the entropy of activation is derived.
Accuracy
Transition state theory requires a value of the transmission coefficient as a prefactor in the Eyring equation above. This value is usually taken to be unity (i.e., the transition state always proceeds to products and never reverts back to reactants and ). As discussed by Winzor and Jackson in 2006, this assumption invalidates the description of an equilibrium between the transition state and the reactants and therefore the empirical Arrhenius equation is preferred with a phenomenological interpretation of the prefactor and activation energy . For more details, see discussion in Winzor and Jackson (2006) pages 399-400 in section "Transition-state theory."
To avoid specifying a value of the ratios of rate constants can be compared to the value of a rate constant at some fixed reference temperature (i.e., ) which eliminates the term in the resulting expression.
Notes
- ^ Chapman & Enskog 1939
References
- Evans, M.G.; Polanyi M. (1935). "Some applications of the transition state method to the calculation of reaction velocities, especially in solution". Trans. Faraday Soc. 31: 875. doi:10.1039/tf9353100875.
- Eyring, H. (1935). "The Activated Complex in Chemical Reactions". J. Chem. Phys. 3 (2): 107. Bibcode 1935JChPh...3..107E. doi:10.1063/1.1749604.
- Eyring, H.; Polanyi M. (1931). Z. Phys. Chem. Abt. B 12: 279.
- Laidler, K.J.; King M.C. (1983). "The development of Transition-State Theory". J. Phys. Chem. 87 (15): 2657–2664. doi:10.1021/j100238a002.
- Polanyi, J.C. (1987). Some concepts in reaction dynamics. Science. 236. pp. 680–690. doi:10.1126/science.236.4802.680.
- Winzor, D.J.; Jackson C.M. (2006). "Interpretation of the temperature dependence of equilibrium and rate constants". J. Mol. Recognit. 19 (5): 389–407. doi:10.1002/jmr.799. PMID 16897812.
- Chapman, S. and Cowling, T. G. The Mathematical Theory of Non-uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases
External links
- Eyring equation at the University of Regensburg
- Online-tool to calculate the reaction rate from an energy barrier (in kJ/mol) using the Eyring equation
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