Unformatted text preview: e elapsing can be compared with theoretical simulations based on results of quantum chemical calculations
http://www.nobel.se/chemistry/laureates/1999/press.html Activated Complex Theory
An activated complex (forms in the transition state), AB‡, forms between reactants as they collide.
The nuclear and electronic configurations are in between those of products and reactants. Zewail showed with femtosecond spectroscopy that the intermediate product was formed. It has a lifetime of 700 fs. http://www.nobel.se/chemistry/laureates/1999/press.html Henry Eyring
(1935) L Grondahl CHEM2056 Activated Complex Theory k = k‡ K ‡ 1) Pre‐equilibrium between reactants and the activated complex
2) The reaction coordinate can be ‘mapped’ on a single degree of freedom (e.g. vibrational). The activated complex falls apart in a unimolecular decay
Using pre‐equilibrium approximation: K‡
A+B AB‡ [AB‡] = K‡[A][B] k‡ AB‡ P Statistical mechanics: Thermodynamics: is the transmission coefficient, ~ 1. R = k‡ [AB‡] k k ‡K ‡ Combine these two expressions to get: R = k‡ K‡[A][B]
= k [A][B]
Use standard concentration, co = 1M, in expression. Use k2 and not k‡.
Goes about the pre‐equilibrium approximation in a different way ‡G RT ln K ‡ kT kT
k b b
h
h
‡ kbT ‡G / RT
e
h This equation can be used to calculate the free energy of activation ‡G for a rate constant at a known temperature
kb Boltzmann constant; h Planck constant L Grondahl CHEM2056 L Grondahl CHEM2056 Example Question
k k ‡K ‡ A second‐order reaction has a rate constant of 5.7x10‐5 M‐1s‐1 at 25°C. Calculate the Gibb’s energy of activation for this reaction at 25°C. kb = 1.380 x 1023 J K1
h = 6.6261034 J s
T = 298 K
R = 8.3145 J K1 mol1 Thermodynamics : kbT ‡G / RT
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h ‡G ‡ H T‡ S
k kbT ‡S / R ‡ H / RT
e
e
h Try problem 1 on ‘Practice problem sheet week 7’.
L Grondahl CHEM2056 L Grondahl CHEM2056 Eyring Equation Ea RT ‡U
‡ ‡ ‡ ‡ H U p V ‡ Ea H p V RT p ‡V ‡n RT k e2 kbT ‡S / R Ea / RT
e
e
h where e2 = 7.389 k a T e Ea / RT k e2 k e kbT ‡S / R Ea / RT
e
e
h k a T e Ea / RT
L Grondahl CHEM2056 Summary of activated complex theory kbT ‡S / R Ea / RT
e
e
h Solution + unimolecular gas reactions: Ea ‡ H RT Empirical relationship: k a T e Ea / RT Bimolecular gas reactions: Unimolecular gas reactions: A → A‡; ∆‡n = 0
Solution reactions: no volume change upon formation of activated complex e = 2.718; ln(e) = 1 L Grondahl CHEM2056 Empirical relationship: ‡ H ‡U p ‡V Ea ‡ H p ‡V RT p ‡V ‡n RT Bimolecular gas reactions: A + B → AB‡; ∆‡n = 1 – 2 = 1
Ea ‡ H p ‡V RT ‡ H RT RT
Ea ‡ H 2 RT Empirical relationship: Ea RT ‡U k e kbT ‡S / R Ea / RT
e
e
h Assumes the presence of an activated complex and models the temperature dependence on the rate constant based on formation and reaction of this activated complex
Uses thermodynamic relationships to evaluate the meaning of the pre‐
exponential factor which contains an entropy term in agreement with the steric requirement The pre‐exponential factor in the Arrhenius‐like equation contains an entropy term!
The entropy of activation is always negative (A and B come together), however, if the reduction in entropy is below what would be expected from collision of A and B; then that additional reduction in entropy is of steric origin.
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 Mole, Kinetics, ea, Grondahl CHEM2056

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