Law of Arrhenius

In chemical Cinétique the law of Arrhenius makes it possible to describe the variation of the speed of a Chemical reaction according to the Température. This law was stated by Svante August Arrhenius in 1889 in its article entitled " One the velocity off the inversion off duck sugar by acids" . But it is not that towards 1910 qu ' it was universally accepted by the chemists of its time. Indeed, the law of Arrhenius could be checked in experiments for a great number of chemical reactions. However, all the reactions do not follow this law (in particular enzymatic reactions).

The law of Arrhenius is thus an empirical law based on the results observed in experiments in a great number of cases. It took a great theoretical importance thereafter because it is compatible with the theory of the collisions and that of the complex activated of Eyring and Polanyi in 1935.

Statements

$\ frac {D \ ln K} {dT} = \ frac {E_a} {R.T^2}$ with:

K , the coefficient speed (in the past called " constant of vitesse")
T , the Temperature (in Kelvin )
$\ frac {D \ ln K} {dT}$ the derivative of the Napierian logarithm of the coefficient speed compared to the temperature
R , the constant of the Perfect gas S (usual value R = 8,314 J. mol ^-1.K^-1; value specifies R = 8,314 472 Pa.m³.K^-1.mol^-1 recommended by Codata)
E_a the energy of activation of Arrhenius

By supposing that E_a does not depend on the temperature, which is true only on one limited interval of temperature, the law of Arrhenius is integrated in:

$k = Ae^ {\ frac {- E_a} {R.T}}$

where has is the factor pre exponential (also called factor of frequency) taking account of the frequency of the collisions and the steric effects. At first approximation the pre-exponential factor does not depend on the temperature. The more precise measurements taken on a broad beach of temperature show than has utilized a factor in T ^1/2 or T ^3/2 according to the cases.

The form of the law of Arrhenius shows that the value of the energy of activation to the dominating importance on the speed of the reactions. One can say that the reactions having weakest energies of activation are fastest and conversely those which have highest energies of activation are slowest.

Order of magnitude of the energy of activation of Arrhenius

A great number of chemical reactions have an energy of activation ranging between 40 and 130 kJ.mol^-1. However certain reactions have weak energies of activation, even near to zero, (for example of the reactions between ions or radicals) and others have values higher than 200 kJ.mol^-1.
Dans the beach of above mentioned value, when the temperature increases 10°C, the coefficient speed is multiplied by a factor 2 to 3.

Here some examples (reactions in gas phase):

NO + Cl₂ → NOCl + Cl; E_a = 85 kJ.mol^-1

C₄H₆ + C₂H₄ → Cyclohexene; E_a = 115 kJ.mol^-1

2HI → H₂ + I₂; E_a = 184 kJ.mol^-1

Cyclobutane → 2 Ethylene; E_a = 262 kJ.mol^-1

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