Wolfram Demonstrations Project

The temperature dependence of the rate of chemical reactions and biological processes is frequently described by the Arrhenius equation. This implies the existence of a log-linear relationship between the rate constant and the reciprocal of the absolute temperature, which has been used to calculate the "energy of activation". It is shown here that there are many conditions in which data generated with a simpler exponential model can be fitted with the Arrhenius equation and vice versa. This suggests that an Arrhenius plot's linearity is insufficient to establish that there is a temperature-independent "energy of activation" unless its existence is confirmed independently.

Contributed by: Mark D. Normand and Micha Peleg

Slider Zoom
Gamepad Controls
Automatic Animation

Snapshot 1: data generated with an Arrhenius-like equation where the absolute temperature reciprocal is replaced by

and then fitted with the exponential model

Snapshot 2: data generated with an Arrhenius-like equation where the absolute temperature reciprocal is replaced by

and then fitted with the exponential model

Snapshot 3: data generated with the exponential model and fitted with the standard Arrhenius equation (notice the linearity of the Arrhenius plot in blue)

Snapshot 4: data generated with the exponential model and fitted with an Arrhenius-like equation where the absolute temperature reciprocal is replaced by

Snapshot 5: data generated with the exponential model and fitted with an Arrhenius-like equation where the absolute temperature reciprocal is replaced by

This Demonstration generates

versus

datasets using the Arrhenius or Arrhenius-like equations that are fitted with an exponential model. It also generates such datasets using the exponential model that are fitted by the Arrhenius or Arrhenius-like equations. The Arrhenius-like equation is presented as

, where

and

are the rates at temperature

and the reference temperature,

, respectively, both in °C, and

and

are constants having temperature dimension. Notice that setting

to 273.16 °C produces the standard Arrhenius equation. The exponential model equation is

) where

is a constant having temperature reciprocal units (°

The user chooses the data generation model by clicking the setter bar. The data so generated will be fitted by the other model. The number of points,

, the plot's temperature range,

and

, the reference temperature,

, and the generation or fit parameters

, and

, are entered with sliders.

The display includes the generated

versus

data and their fit by the opposite model (top plot) and the

versus

data fitted by the opposite model (bottom plot).

Notice that when

is large, the Arrhenius plot of the data generated by the exponential model (blue dots in bottom plot) is almost perfectly linear regardless of its absolute magnitude.

All curves generated by the Arrhenius equation change concavity at a high enough temperature. When the generated data has downward concavity at the chosen settings, the Demonstration forgoes the fitting by the exponential model and displays a message to that effect.

Generalized Arrhenius Function (Wolfram Demonstrations Project)

Arrhenius Equations for Reaction Rate and Viscosity (Wolfram Demonstrations Project)

Mark D. Normand and Micha Peleg

"Arrhenius versus Exponential Model for Chemical Reactions"
http://demonstrations.wolfram.com/ArrheniusVersusExponentialModelForChemicalReactions/
Wolfram Demonstrations Project
Published: July 25, 2011