RRKM theory

The RRKM theory (Rice-Ramsperger-Kassel-Marcus) is a microcanonical theory of the transition state , which makes it possible to calculate rate constants of unimolecular gas phase reactions. It represents an extension of the RRK theory, which assumes that the rate constant depends on the energy of the reacting molecule:

   ${\displaystyle k=k(E)}$

It is assumed that the rate constant is proportional to the number of ways to distribute the energy among the various internal degrees of freedom of the reactant , so that the critical energy is localized in a certain degree of freedom.

In the RRKM theory , vibration and rotation energies are also considered, taking into account the zero point vibration energy.

It is named after Oscar K. Rice , Herman C. Ramsperger, Louis Kassel and Rudolph A. Marcus.

Assumptions

The molecule is viewed as a system of coupled harmonic oscillators that can exchange energies with each other.

• All states of the excited molecule with the energy can be reached and lead immediately to the formation of the product. ${\displaystyle E}$
• The energy redistribution in the molecule ( IVR ) is much faster than the reaction itself.

Derivation

Be an excited molecule: ${\displaystyle A^{*}}$

   ${\displaystyle A^{*}{\xrightarrow {k(E)}}A^{\ddagger }\rightarrow \mathrm {Produkte} }$

${\displaystyle A^{\ddagger }}$denotes the critical configuration with a certain minimum energy that is localized in the reaction coordinate. ${\displaystyle E_{0}}$

For the unimolecular rate constant we get:

   ${\displaystyle k_{\mathrm {uni} }={\frac {1}{hQ_{r}Q_{v}}}\int \limits _{E_{0}}^{\infty }dE\sum _{J=0}^{\infty }{\frac {(2J+1)G^{\ddagger }(E,J)\exp \!\left({\frac {-E}{k_{b}T}}\right)}{1+{\frac {k(E,J)}{\omega }}}}}$

See also

• Kinetics (chemistry)
• Eyring theory

Individual evidence

1. ↑ ^{a b} J. I. Steinfeld, JS Francisco, WL Hase, Chemical Kinetics and Dynamics , 2nd ed., Prentice Hall, 1998 , ISBN 978-0-13737123-5 .
2. ^ Entry on Rice-Ramsperger-Kassel-Marcus (RRKM) theory . In: IUPAC Compendium of Chemical Terminology (the “Gold Book”) . doi : 10.1351 / goldbook.R05391 Version: 2.3.2.
3. ^ Entry on Rice – Ramsperger – Kassel (RRK) theory . In: IUPAC Compendium of Chemical Terminology (the “Gold Book”) . doi : 10.1351 / goldbook.R05390 Version: 2.3.2.
4. ^ Rice, Ramsperger Theories of unimolecular gas reactions at low pressure , 2 parts, J. Am. Chem. Soc., Vol. 49, 1927, pp. 1617-1629, Vol. 50, 1928, pp. 617-620
5. ↑ Marcus Unimolecular Dissociations and Free Radical Recombination Reactions , Journal of Chemical Physics, Volume 20, 1952, p. 359
6. ^ Rice, Marcus The kinetics of the recombination of methyl radicals and iodine atoms , J. Phys. Colloid Chem., 55, 1951, 894-908
7. ↑ First RRK theory, then RRKM theory additionally after the later work of Marcus and in Rice, Marcus. Story according to Widom, Marcus Oscar K. Rice , Biographical Memoirs National Academy of Sciences, 1989, pdf

literature

• Physical chemistry # literature
• Kinetics (chemistry) #Literature