## 4 Discussion
### Compensation Temperature  
[PERSON] has derived an equation describing the reaction rate constant as a function of temperature and the free enthalpy of activation \(\Delta G^{+}(p=p^{\varnothing}=0.1\text{MPa})\) depending on the reaction mechanism limited by the formation of the active complex \(\text{A}+\text{B}\rightarrow\left(\text{AB}\right)^{+}\) in gaseous phase [12]. The theses proposed in work [12] were adapted into the form of relations, in which the transmission coefficient and threshold energy distribution functions of the reactants were omitted [16; 50; 51; 52; 53; 54] and only the \"universal frequency term\" \(\frac{k_{B}T}{\hbar}\) was left [51]. This expression is directly proportional to the product of \((R\cdot T)\) half equal to potential and kinetic energy [16]. The equation in its most common form is as follows:  
\[k_{TST}=BTe^{-\frac{\mathrm{AG}^{+}}{RT}},\;B=\frac{k_{B}}{h}=2.08364\cdot 10^{10} \left(\mathrm{K}\cdot\mathrm{s}\right)^{-1} \tag{50}\]  
where:  
\[\Delta G^{+}=\Delta H^{+}-T\Delta S^{+} \tag{51}\]  
For the solid phase dissociation process following the reaction scheme: \(\mathrm{A}^{(\mathrm{s})}\rightarrow\mathrm{B}^{(\mathrm{s})}+\mathrm{C}^{( \mathrm{g})}\) or \(\mathrm{A}^{(\mathrm{s})}\rightarrow\mathrm{C}^{(\mathrm{g})}\) and the value of the stoichiometric coefficient for the substrate \(\mathrm{A}^{(\mathrm{s})}\) (\(\
u_{A}=1,\sum\
u^{+}=1-\
u_{A}=0\)) the equation is known in the form of Equations (50) and (51) [53]. The use of the presented approach seems to be common for thermal dissociation of the solid phase, such as for the complete decomposition of calcium oxalate (\(\mathrm{CaC_{2}O_{4}\cdot H_{2}O}\)) to CaO [16]. Using the concepts of a certain convergence between the Arrhenius \((k)\) and Eyring \((k_{TST})\) equations, from the equation \(\frac{\mathrm{dln}k}{\mathrm{d}T}=\frac{\mathrm{dln}k_{TST}}{\mathrm{d}T}\) we obtain:  
\[\Delta H^{+}=E-RT \tag{52}\]  
while from the direct comparison of the constant rates \((k=k_{TST})\) we obtain:  
\[\Delta G^{+}=E-RT\;\mathrm{ln}\;\frac{A}{BT} \tag{53}\]  
Therefore, from Equation (51) and Equations (52) and (53) we determine the entropy of activation:  
\[\Delta S^{+}=R\left[\mathrm{ln}\bigg{(}\frac{A}{BT}\bigg{)}-1\right] \tag{54}\]  
However, it should be noted that, despite the widespread acceptance of the presented comparison, there are premises which do not accept the concept of using the same set of input data [52]. On this basis, relationships between both activation thermodynamics and kinetics (parameters of the Arrhenius equation) are derived by taking the temperature of the maximum reaction rate as the activation temperature for dynamic conditions [53; 54]:  
\[\Delta H^{+}=E-RT_{m} \tag{55}\]  
\[\Delta S^{+}=R\left[\mathrm{ln}\bigg{(}\frac{A}{BT_{m}}\bigg{)}-1\right] \tag{56}\]  
Suppose that Equations (55) and (56) satisfy the _EEC_, with a slope called the compensation temperature \(T_{c}\) (see Equation (2)), which directly follows from the second law of thermodynamics:  
\[\Delta H^{+}=T_{c}\Delta S^{+}+H \tag{57}\]  
or:  
\[H=\Delta H^{+}-T_{c}\Delta S^{+}=\Delta G^{+}(T_{c})=\mathrm{const} \tag{58}\]  
By substituting Equations (55) and (56) into the form (57) and dividing the sides by \((R\cdot T_{C})\), after transformation we get:  
\[\frac{E}{RT_{c}}=\mathrm{ln}\;A-\mathrm{ln}\;(BT_{c})+\frac{H}{RT_{c}}-\mathrm{ ln}\bigg{(}\frac{T_{m}}{T_{c}}\bigg{)}+\frac{T_{m}}{T_{c}}-1 \tag{59}\]  
The sum of the last three components of Equation (59) is close to 0, which is evident either for \(T_{m}=T_{c}\) or by taking the approximation: \(\mathrm{ln}\;\Big{(}\frac{T_{m}}{T_{c}}\Big{)}\cong\frac{T_{m}}{T_{c}}-1\). The derivation is also valid by taking \(T=T_{m}\), so it shows features of generality, and Equation (59) takes the form \(KCE\):  
\[\Delta G^{+}=\Delta H^{+}-T\Delta S^{+} \tag{51}\]0  
The intercept in Equation (60) is:  
\[\Delta G^{+}=\Delta H^{+}-T\Delta S^{+} \tag{51}\]1  
and is the logarithmic form of Equation (50) containing the \(EEC\) expressed by Equation (58).