# Implicit dependence of reaction rate through reduction potential and activation energy

On one hand, the larger the reduction potential of a chemical reaction and the smaller its activation energy, the larger the reaction reaction. on the other hand the rate of a reaction depends on thermodynamic conditions, such as temperature and pressure, and the concentration of the species involved.

Now given that both the reduction potential and the activation energy of the reaction depend on thermodynamic conditions, can we deduce that the whole thermodynamic dependency of the rate of the reaction lies inside the reduction potential and the activation energy?

For the sake of clarification, that I said the larger is the reduction potential and the smaller is the activation energy the greater will be the rate of the reaction is a conclusion based on the analogy of a redox reaction and an electric circuit, the reduction potential being in place of the voltage difference, the activation energy as the energy consumer being in place of the electric resistance and the electron transferred during the reaction being in place of the electric current. It is clear that the greater the electric current, the greater the rate of reaction should be.

• What exactly do you mean by thermodynamics condition? What are the equations you draw your entering statement from: "On one hand, the larger is the reduction potential of the chemical reaction and the smaller is its activation energy the larger would be the rate of reaction, on the other hand the rate of reaction of a reaction depends on the thermodynamics condition upon which the reaction takes place."? – Philipp Sep 3 '14 at 14:14
• @Philipp, tried to clarify my point and also my background to the question. Please check if if the question is now clear and relevant. Thank you. – topology Sep 6 '14 at 7:18

## 1 Answer

The rate of a reaction depends on the thermodynamics of its transition state. It would be better to look at it in terms of Gibbs activation energy. Therefore there two factors affecting the rate of a reaction:

• the activation enthalpy $\Delta^‡ H$, that corresponds to the Arrhenius activation energy
• the activation entropy $\Delta^‡ S$ that takes into account the probability of a transition state.

The whole dependency of the kinetic constant on these parameters is expressed by the Eyring and Wynne-Jones equation: $$k = \frac{k_\text{B}T}h \operatorname{e}^{\frac {\Delta^‡ S} R }\operatorname{e}^{-\frac{\Delta^‡ H} {RT} }$$

Where $T$ is the temperature, $k_\text{B}$ is the Boltzman constant and $h$ is the Planck constant. Sometimes a reflection coefficient $\kappa$ is added to the equation to take into account some other dependencies. It is near to 1 for most of the simple reactions. $$k = \kappa \frac{k_\text{B}T}h \operatorname{e}^{\frac {\Delta^‡ S} R }\operatorname{e}^{-\frac{\Delta^‡ H} {RT} }$$