Snapshot 1: generated with the Eyring–Polanyi and fitted with the Arrhenius model—low temperatures

Snapshot 2: generated with the Eyring–Polanyi and fitted with the Arrhenius model—very high temperatures

Snapshot 3: generated with the Arrhenius and fitted with the Eyring–Polanyi model—low temperatures

Snapshot 4: generated with the Arrhenius and fitted with the Eyring–Polanyi model—high temperatures

Snapshot 5: generated with the Arrhenius and fitted with the Eyring–Polanyi model—very high temperatures

The effect of temperature on the rate of chemical and biochemical reactions has been primarily described by the Arrhenius equation. It can be written in the form

, where

and

are the rate constants at absolute temperature

and

, respectively,

in

, and

,

being the activation energy and

the universal gas constant in the corresponding units. Although derived from statistical mechanics, the Arrhenius model is increasingly being treated as a successful

empirical model; see also [1]. An alternative model, also derived from statistical mechanics, is the

Eyring–Polanyi equation. It can be written in the form

, where

,

being the Gibbs energy of activation.

From a purely formal viewpoint, the main difference between the two models is the term

on the right side of the Eyring–Polanyi equation. Consequently, and in contrast with the Arrhenius model, the Eyring–Polanyi model implies that

can increase indefinitely, that is, as

,

. According to the Arrhenius model, as

rises, the

versus

relationship has an inflection point at

, and as

, it approaches an asymptotic value of

. Also, and again in contrast with the Arrhenius model, the plot of log

versus

need not be linear.

This Demonstration generates

data with the Arrhenius equation and compares them with the Eyring–Polanyi model. The choice is made with a setter bar. You can also select the temperature range, the reference temperature, and the

or

values with a slider.

The Demonstration plots the generated data points with their fitted curve superimposed. It also displays the fitted parameter value for

or

and the regression coefficient,

.

These plots show that over a wide range of temperatures, the Arrhenius and Eyring–Polanyi equations can be used interchangeably and that they diverge only at very high temperatures, around the Arrhenius equation's inflection point. This suggests that neither model can be considered superior on the basis of curve fitting alone.

It is not the purpose of this Demonstration to match any particular real system, and therefore some combinations of parameter values do not have a real-life

versus

relationship.

[1] M. Peleg, M. D. Normand, and M. G. Corradini, "The Arrhenius Equation Revisited,"

*Critical Reviews in Foods Science and Nutrition*,

**52**(9), 2012 pp. 830–851. doi:

10.1080/10408398.2012.667460.