Eyring equation

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 contrary to the empirical 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" is Planck'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 activation

A 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 the entropy 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 = 680–690

External links

* [http://www.chemie.uni-regensburg.de/Organische_Chemie/Didaktik/Keusch/eyr-e.htm Eyring equation at the University of Regensburg]