## 4 Solketal Synthesis
### Catalyst Study
#### 4.2.2 Kinetics and Mechanisms of Reaction  
Solketal synthesis is a relatively simple reaction, with controlled potential hazards; therefore, it could be carried in less carefully designed reactors when compared to inflammable or explosive reactions. However, since it is also a limited reaction, to make it industrially viable, it is necessary to rely on kinetic and thermodynamic data to design efficient equipment. The most-cited kinetic models in the open literature are the Pseudo-homogeneous (PH), Langmuir-Hinshelwood-Hougen-Watson (LHHW), and Eley-Rideal (ER) models. The simplest approach is the Pseudo-homogeneous (PH) model, based on Potential Laws and often referred to with this term. It considers a reversible reaction of the first order in each species with virtually no adsorption of the species on the catalyst; therefore, the reaction would occur exclusively in the fluid phase [10, 70]. It is usually represented by the following expression:  
\[\Re=k\left(C_{gly}C_{acetone}-\frac{C_{solketal}C_{water}}{K_{eq}}\right) \tag{1}\]  
where \(C\) represents the concentration of each species, \(k\) the reaction kinetic constant, and \(K_{eq}\) the thermodynamic equilibrium constant. In the Langmuir-Hinshelwood-Hougen-Watson (LHHW), the mechanism comprises three steps: in the first, there is the adsorption of acetone and glycerol on the catalyst surface; in the second, a bimolecular reaction of adjacent molecules occurs to form a short-lived hemiketal (rate-controlling step), followed by two reactions that originate solketal and water; finally, in the third step, both products desorb from the surface of the catalyst [10, 70]. The usual equation is:  
\[\Re=k\frac{C_{glycerol}C_{acetone}-\frac{C_{solketalC_{water}}}{K_{eq}}}{(1+K_{water}C_{ water})^{2}} \tag{2}\]  
where \(K_{water}\) is the adsorption equilibrium constant for water. Equation (2) is a simplification of the actual rate law, as the adsorption of water is usually much stronger than the other compounds; therefore, these terms are neglected in the denominator [10, 70]. The Eley-Rideal (ER) model considers that only one of the molecules adsorb into the catalyst surface, while the other reacts directly from the fluid phase. It is expressed as follows:  
\[\Re=k\frac{C_{glycerol}C_{acetone}-\frac{C_{solketalC_{water}}}{K_{eq}}}{1+K_{water}C_{water}} \tag{3}\]  
All the studies reviewed report the use of one of these three models. Table 2 summarizes the recent literature (from 2015 on) on kinetic studies for solketal synthesis over a range of catalysts. Being mindful that the PH model does not consider the adsorption of molecules onto the catalyst surface, it is intuitive to think that reactions with homogeneous catalysts are well described by this model. Dmitriev et al. proposed a mechanism (Figure 6) for the reaction with sulfuric acid (strong Bronsted acid) as a catalyst comprising a nucleophilic addition of glycerol to the carbonyl group of acetone, forming a semiketal. Then, the ring closure takes place, forming a carbenium ion (limiting step). Finally, the H\({}^{+}\) ion is released and solketal is formed [102]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Author** & **Catalyst** & **E\({}_{\mathbf{A}}\) (kJ\(\cdot\)mol\({}^{-1}\))** & **Other Parameters 12,3,4,5** & **Ref. ** \\ \hline Pseudo-homogeneous (PH) & & & & \\ \hline Rossa, 2017 & Zeolite H-Beta & 44.77 \(\pm\) 1.2 & \ \begin{tabular}{c} \(E_{A\cdot 1}\) = 41.40 \(\pm\) 1.8 kJ\(\cdot\)mol\({}^{-1}\) \\ \(K_{eq}\) = 0.5159 (313 K) \\ \end{tabular}  & [76] \\ \hline Dmitriev, 2018 & Sulfuric acid & 87.1 & \begin{tabular}{c} \(E_{A\cdot 1}\) = 101.67 kJ\(\cdot\)mol\({}^{-1}\) \\ \(K_{eq}\) = 0.77 (303 K) \\ \end{tabular}  & [102] \\ \hline Cornejo, 2019 & Purolite® CT275 & 39.78 \(\  
It is important to notice, however, that the mechanism proposed by Dmitriev et al.