Figure 7. The Arrhenius plot of 104 and 1044 ppbv CH3I adsorptions on Ag0-Aerogel at 100, 150 and 200 ℃.
By fitting all three data points at each concentration, the ΔE ’s are 21.0 and 1.34 kJ/mol for 104 and 1044 ppbv adsorptions respectively. As stated above, both adsorption behaviors at 200 ℃ are relatively abnormal. If excluding the 200 ℃ data and consider the 100 and 150 ℃ results only, the ΔE ’s of 104 and 1044 ppbv adsorptions are well-agreed. The activation energy determined using 100 and 150℃ data of 104 ppbv adsorption is 10.4 kJ/mol, that of 1044 ppbv adsorption is 10.8 kJ/mol and the pre-exponential factors are 1.80×105and 1.47×105(cm/s)∙(mol/cm3)1-n respectively. In previous studies of CH3I adsorption on Ag-ZSM-5, Park et al.36 report the activation energy of 2.57 kJ/mol and Scheele et al.21 proposed 20 – 40 kJ/mol for CH3I adsorption on Ag0Z.
Another model describing the relationship between temperature and reaction rate constant is the Eyring equation,37
where k is the reaction rate (s-1),kB is Boltzmann’s constant, h is Planck’s constant and ΔG is the Gibbs free energy of activation. Since the unit and the physical meaning of k are different fromks determined using SCM, a quantified result may not be given. However, some valuable trends and predictions can be interpreted. Representing the Gibbs free energy of the activation of the reaction between iodoalkane and Ag0-Aerogel asΔG , dk/dT may be written as,
Eq. 24 indicates that the dependency of k to T may vary asΔG/R changes. For example, given a range of temperatureT1 to T3 , Figure 8 shows that how -ΔG/R changes the dependency of k to T . When -ΔG/R < T1 , dk/dT> 0, indicating the increasing temperature increases the reaction rate; when -ΔG/R >T3 , dk/dT < 0, and the reaction rate may decrease with increasing temperature. Interestingly, ifT1 < -ΔG/R <T3 , a minimum value of k may be observed at T = -ΔG/R . Generally, the ΔG is represented as a positive number, but can it be negative in some circumstances?
Proposed in the section above, iodoalkane molecules may cleave into free radicals and produce alkanes and AgI in the re-bindings of radicals. The negative activation energies have been reported in some radicals-engaged reactions.38,39 Therefore, in the adsorptions of iodoalkanes with larger alkane groups (e.g. C6H13I, C12H25I, etc.), the ΔG ’s may decrease (or become negative) due to their instabilities,40 and the rough estimation above suggests that the dependency of k to T may vary at certain circumstances.