## 4 Model  
### Reaction Mechanism and Kinetic Model  
The results of our previous tests on CO adsorption/oxidation at room temperature provided insights into the reaction path [48]. Also based on results by others [13; 14; 32; 43; 51; 52], we concluded that, most probably, CO adsorption activates the copper redox cycle between +2 and +1 oxidation states. The main role of Ce is to provide oxygen to Cu sites through easily mobile lattice oxygen. We found that the most important parameters affecting the reaction path are the surface oxygen mobility/availability [15] and the CO\({}_{2}\) desorption rate [32]. The presence of O\({}_{2}\) activates the direct oxidation of copper and of oxygen vacancies of ceria in the area of copper sites. According to the above findings, the following mechanism is here derived:  
\[\sigma-\mathrm{O}+\mathrm{CO}\rightleftharpoons\sigma-\mathrm{O}-\mathrm{CO} \tag{1}\]  
\[\sigma-\mathrm{O}-\mathrm{CO}+\sigma^{\prime}-\mathrm{O}\rightarrow\sigma^{ \prime}-\mathrm{O}-\mathrm{CO}_{2}+\sigma \tag{2}\]  
\[\sigma^{\prime}-\mathrm{O}-\mathrm{CO}_{2}\rightarrow\sigma^{\prime}-\mathrm{O }+\mathrm{CO}_{2} \tag{3}\]  
\[\sigma+\sigma^{\prime}-\mathrm{O}\rightarrow\sigma-\mathrm{O}+\sigma^{\prime} \tag{4}\]  
With the presence of O\({}_{2}\) in the gas phase, the oxidation steps of sites \(\sigma^{\prime}\) and \(\sigma\) have to be considered:  
\[\sigma^{\prime}+\frac{1}{2}\mathrm{O}_{2}\rightarrow\sigma^{\prime}-\mathrm{O} \tag{5}\]  
\[\sigma+\frac{1}{2}\mathrm{O}_{2}\rightarrow\sigma-\mathrm{O} \tag{6}\]  
In Table 2, the nature of each site in the mechanism (1)-(6) is given. In the proposed mechanism, CO is adsorbed on Cu\({}^{2+}\) sites in strict contact with ceria, causing a partial reduction of copper (and adjacent cerium atom) (step 1). CO\({}_{2}\) is then formed and transferred onto ceria sites, causing copper reduction to Cu\({}^{+}\) (and adjacent cerium reduction to Ce\({}^{3+}\)) (step 2). The CO\({}_{2}\) adsorption onto sites different from copper is in agreement with [32]. Step 3 represents CO\({}_{2}\) desorption. As reported in [48], copper re-oxidation can occur also in the absence of molecular oxygen in the gas phase at the expense of an oxygen transfer from ceria sites, leading to a surface ceria reduction (step 4). When molecular oxygen is fed, re-oxidation of the surface can occur on both copper/ceria and ceria sites (steps 5 and 6). Based the mechanism (1)-(6), a kinetic model was developed. All steps are assumed irreversible except step 1. Rates of steps 1-6 are:  
\[R_{1}=k_{1}\;\theta_{1}\;\mathrm{C}_{\mathrm{CO}} \tag{7}\]  
\[R_{-1}=k_{-1}\;\theta_{2-1} \tag{8}\]  
\[R_{2}=k_{2}\;\theta_{2}\;\theta_{5} \tag{9}\] \begin{table}
\begin{tabular}{c c c} \hline
**Symbol of Site** & **Nature of Site** & **Site Fraction Symbol** \\ \hline \(\sigma\)-O & \(\mathrm{Cu}^{2+}-\mathrm{O}^{2-}-\mathrm{Ce}^{4+}\) & \(\theta_{1}\) \\ \(\sigma\)-O-CO & \(\mathrm{Cu}^{(2-8)+}-\mathrm{O}^{2-}-\mathrm{CO}^{(8+\varepsilon)+}-\) & \(\theta_{2}\) \\ \(\mathrm{Ce}^{(4-\varepsilon)+}\) & & \\ \(\sigma^{\prime}\)-O-CO\({}_{2}\) & \(\mathrm{CO}_{2}-\mathrm{Ce}^{4+}-\mathrm{O}^{2-}-\mathrm{Ce}^{4+}\) & \(\theta_{3}\) \\ \(\sigma\) & \(\mathrm{Cu}^{+}-\mathrm{\square}-\mathrm{Ce}^{3+}\) & \(\theta_{4}\) \\ \(\sigma^{\prime}\)-O & \(\mathrm{Ce}^{4+}-\mathrm{O}^{2-}-\mathrm{Ce}^{4+}\) & \(\theta_{5}\) \\ \(\sigma^{\prime}\) & \(\mathrm{Ce}^{3+}-\mathrm{\square}-\mathrm{Ce}^{3+}\) & \(\theta_{6}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Nature of the sites reported in the mechanism 1–6. \[R_{3}=k_{3}\,\theta_{3} \tag{10}\]  
\[R_{4}=k_{4}\,\theta_{4}\,\theta_{5} \tag{11}\]  
\[R_{5}=k_{5}\,\theta_{6}\,\,C_{O2}^{n} \tag{12}\]  
\[R_{6}=k_{6}\,\theta_{4}\,\,C_{O2}^{n} \tag{13}\]  
where \(\theta_{1-6}\) are the fractions of sites with respect to the total number of sites (Table 2). We assumed that both the activation energy (\(E_{i}\)) and the frequency factor (\(k^{\circ}{}_{i}\)) are not dependent of the adsorption degree (Redhead Approximation).