## 3 Theoretical Approach
### The Formulation of the Arrhenius Form  
When considering a reaction at equilibrium in which a reactant \(A\) is transformed to a product \(B\) (reactants and products can be solids, liquids or gaseous). \(A\) and \(B\) form a system, and this system can, therefore, be described by using Equation (5). The equilibrium constant of the reaction can be expressed as (for more details, see Appendix B, Equation (A24)):  
\[K_{c}=\frac{z_{B}}{z_{A}}e^{-\frac{\Delta E_{0}}{kT}} \tag{6}\]  
where \(z_{B}\) and \(z_{A}\) are the partition function for \(A\) and \(B\), respectively and \(\Delta E_{0}\) is the separation of zero-point energies. In the conversion of molecular energy to molar energy, the constant \(k_{b}\) is further substituted by the constant \(R\) in light of the following relation \(k_{b}=RN_{Ab}\) where \(N_{Ab}\) is the Avogadro number. This expression serves as a link between [PERSON]'s work (Equation (5)) and the transition state theory (TST). More details and explanations about this development are given in Appendices A and B and in the following references [27; 30]. The basis of kinetic theory can be found in [PERSON], [PERSON] [11], [PERSON] [19] and [PERSON] [10]. In parallel to the kinetic theory, developments in statistical physics led to the transition state theory (TST) [11; 25; 31] and the activated complex theory [25; 32; 33]. Using transition state theory (TST) as described in [32], the following well-known expression can be established (see Appendix B for details):  
\[k=A^{pf}e^{-\frac{E_{ext}}{kT}} \tag{7}\]  
In this equation, \(k\) is the kinetic equation (Arrhenius form), \(A^{pf}\) is the pre-exponential factor and \(E_{act}\) is the activation energy. For [PERSON] [34], the TST approach enables the possibility of describing a greater variety of reactions, including those due to the vibrational mode. Nevertheless, this remains in the context of homogeneous gas-phase reactions consistent with the statistical formulations. The question is now how to interpret the pre-exponential factor (and the partition function, which is part of this factor, (see Appendix B)) for different types of reactions, in particular those occurring in a solid (ex. reference [35]). In gas-phase theory, collision theory was developed in 1916 by [PERSON] and in 1918 by [PERSON] [32; 36; 37] and allows interpreting the kinetic law and its parameters. Subsequently, developing TST allowed [PERSON] and [PERSON] (from 1935) to apply these concepts to a large diversity of reactions [25; 38], such as:  
* Elementary reactions in solutions;Surface reactions, adsorption, chemisorption, etc. ;
* Gas-phase reactions, single-molecule or multi-molecule. In all of these cases, each time, these authors found a different form for the pre-exponential factor, but the general expression of Equation (7) remained. Given that the differences can be described through the pre-exponential factor, it is possible to infer that for conventional (chemical reaction) and unconventional applications, the Arrhenius expression is applicable so long the differences are confined to the pre-exponential factor. For this to be the case, the reaction needs to possess an energy barrier. [PERSON]'s work [25; 38] well described the transition from a stable state to an activated state. This transition needs a supply of energy called the energy barrier [25; 38]. Thus, on this basis, [PERSON] et al. argue the universality of the Arrhenius law [39]. Further, studies have shown that it is possible to successfully fit a form of the Arrhenius equation to represent the kinetics of any reactions that possess an energy barrier [40]. It can, therefore, be concluded that it is possible to use these representations of a reaction rate for the reactions involved in the thermal decomposition of a solid despite the absence of a clear theoretical basis. In solid matter, all the atoms vibrate but stay in fixed, meaning positions because of their strong attractions.