- Eyring equation
The Eyring equation also known as Eyring–Polanyi equation in
chemical kinetics relates thereaction rate totemperature . It was developed almost simultaneously in 1935 byHenry Eyring , M.G.Evans andMichael Polanyi . This equation follows from thetransition state theory ("aka", activated-complex theory) and contrary to theempirical Arrhenius equation this model is theoretical and based on statistical thermodynamics.The general form of the Eyring–Polanyi equation somewhat resembles the Arrhenius equation:
k = frac{k_mathrm{B}T}{h}mathrm{e}^{-frac{Delta G^Dagger}{RT
where Δ"G"‡ is the Gibbs energy of activation, "k"B is
Boltzmann's constant , and "h" isPlanck's constant .It can be rewritten as:
k = left(frac{k_mathrm{B}T}{h} ight) mathrm{exp}left(frac{Delta S^ddagger}{R} ight) mathrm{exp}left(-frac{Delta H^ddagger}{RT} ight)
To find the linear form of the Eyring-Polanyi equation:
ln frac{k}{T} = frac{-Delta H^ddagger}{R} cdot frac{1}{T} + ln frac{k_mathrm{B{h} + frac{Delta S^ddagger}{R}
where:
*k =reaction rate constant
*T =absolute temperature
*Delta H^ddagger = enthalpy of activation
*R =gas constant
*k_mathrm{B} =Boltzmann constant
*h =Planck's constant
*Delta S^ddagger = entropy of activationA certain chemical reaction is performed at different temperatures and the reaction rate is determined. The plot of ln(k/T) versus 1/T gives a straight line with slope Delta H^ddagger / R from which the
enthalpy of activation can be derived and with intercept ln(k_mathrm{B}/h) + Delta S^ddagger / R from which theentropy of activation is derived.References
* Cite journal
last = Evans
first = M.G.
coauthors = Polanyi M.
year = 1935
date = 1935
title =
journal = Trans. Faraday Soc.
volume = 31
pages = 875* Cite journal
last = Eyring
first = H.
year = 1935
date = 1935
title =
journal = J. Chem. Phys.
volume = 3
pages = 107* Cite journal
last = Eyring
first = H.
coauthors = Polanyi M.
year = 1931
date = 1931
title =
journal = Z. Phys. Chem. Abt. B
volume = 12
pages = 279* Cite journal
last = Laidler
first = K.J.
coauthors = King M.C.
year = 1983
date = 1983
title = The development of Transition-State Theory
journal = J. Phys. Chem.
volume = 87
pages = 2657–2664
doi = 10.1021/j100238a002* Cite journal
last = Polanyi
first = J.C.
year = 1987
date = 1987
title = Some concepts in reaction dynamics. Science
volume = 236
issue = 4802
pages = 680–690External links
* [http://www.chemie.uni-regensburg.de/Organische_Chemie/Didaktik/Keusch/eyr-e.htm Eyring equation at the University of Regensburg]
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