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From Hammonds Postulate you know that if you have small activation energy, th reaction is exothermic: the reaction rate is fast.

But I cant figure out how to relate the with arrhenius:
k = A exp(-E/RT)

Small E gives small k....

Or do I miss something?

[Donaldson Tan]

I thought Hammond's postulate gives you an idea of how the transition state look like..

How does that gotta do with the Arrhenius equation?

I think you are looking for this equation:
dH_R = Ea₁-Ea₂

[mir]

Well, activation energy is closely related to the rate and temperature.
And Hammondspostulate is also saying TS occur early in highly exothermic reactions.
Exothermic reactions need only a small structural change to reach TS.
I guess there have to be only a small activationenergy to reach TS for such a small displacement of the structure.

So why doesn't Arrhenius work together with Hammons Postulate?
Perhaps there is a limitations in one of the two models.
Arrhenius work best in gas phase I have heard. But you may also use Hammonds Postulate in gas phase, right?

[Donaldson Tan]

Hammond's Postulate, also referred to as the Hammond-Leffler postulate, deals with the transition state of a chemical reaction.

    If two states, as for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have nearly the same energy content, their interconversion will involve only a small reorganization of the molecular structures.

    Hammond, G. S. A Correlation of Reaction Rates. J. Am. Chem. Soc. 1955, 77, 334-338.

This is my interpretation of Hammond's Postulate.

consider an exothermic elementary reaction of A -> B
1. the curve from A to B in energy diagram must be in the shape of an inverted U.
2. being in the shape of the inverted U, the energy level of the TS must be higher than the reactant (A).
3. the energy level of A is closer to the energy level of the TS, compared to that of B.
4. interconversion from reactant to TS requires a small molecular reorganisation
5. hence, the structure of the TS somehow resembles the reactant.

Hammond's Postulate is built on the basis of energy level, not time. It is a thermodynamic arguement.

There are 2 conflicting factors that decide the outcome of a chemical reaction. One is thermodynamics and the other is kinetics. The Arrhenius equation is a kinetics equation. Hammond's postulate is especially important when looking at the rate limiting step of a reaction. However, one must be cautious when examining a multistep reaction or one with the possibility of rearrangements during an intermediate stage. In some cases, the final products appear in skewed ratios in favor of a more unstable product (called the kinetic product) rather than the more stable product (the thermodynamic product). In this case one must examine the rate limiting step and the intermediates. Often times, the rate limiting step is the initial formation of an unstable species such as a carbocation. Then, once the carbocation is formed, subsequent rearrangements can occur. In these kinds of reactions, especially when run in cooler temperatures, the reactants simply react before the rearrangements necessary to form a more stable intermediate have time to occur. At higher temperatures when microscopic reversal is easier, the more stable thermodynamic product is favored because these intermediates have time to rearrange. Whether run in high or low temperatures, the mixture of the kinetic and thermodynamic products will eventually reach the same ratio, one in favor of the more stable thermodynamic product, when given time to equilibrate due to microreversal.

[mir]

“Studying tthe photograph of a racehorse cannot tell you how fast it can run..”
J. Knowles, Angew. Chemie Int. Ed. Eng. 1977

I will think about it.

Cool blog btw

[Donaldson Tan]

consider an exothermic elementary reaction of A -> B
1. the curve from A to B in energy diagram must be in the shape of an inverted U.
2. being in the shape of the inverted U, the energy level of the TS must be higher than the reactant (A).
3. the energy level of A is closer to the energy level of the TS, compared to that of B.
4. interconversion from reactant to TS requires a small molecular reorganisation
5. hence, the structure of the TS somehow resembles the reactant.

Hammond's Postulate merely stated that for an exothermic reaction, the TS energy level is nearer to the reactant energy level. It doesn't actually quantify that E_a is small.

Eg. Although 1 ton << 1000 tons, 1 ton is still a lot of mass.

[MarkDH]

Could you not link a small activation energy with a fast reaction rate through the Eyring equation?

k = (kB x T/h) K*

Where K* is the equilibrium constant between the ground and transition state. As:

dG* = -RT. lnK*

K* = exp(-dG*/RT)

So overall:

k = (kB x T/h) exp (-dG*/RT)

and from this, a small free energy of activation leads to an increase in reaction rate.

Might not be exactly what you're looking for but it could help?

[mir]

Hammond's Postulate merely stated that for an exothermic reaction, the TS energy level is nearer to the reactant energy level. It doesn't actually quantify that E_a is small.
Eg. Although 1 ton << 1000 tons, 1 ton is still a lot of mass.

But it says something about the kinetics:

As the stability of the product increases, the TS will shift toward the reactants, and closer and closer resemble the reactant in energy. So overall, a highly exothermic process will have smaller activation energy than a endothermic process.

[mir]

Could you not link a small activation energy with a fast reaction rate through the Eyring equation?
So overall:
k = (kB x T/h) exp (-dG*/RT)
and from this, a small free energy of activation leads to an increase in reaction rate.
Might not be exactly what you're looking for but it could help?

Eylers equation is the alternative to Arrhenius. Explained in Arhenius terms, the activation energy is resembling the activation enthalpy (plus a constant) in transition state theory. The Arrhenius constant, A, is logarithmic propotional to the activation enthropy.

Perhaps you have right, we learn more with  TS-theory, than with Arrhenius.

I gues syou have right, Transition state theory is explaining more about the facts.