## 2 Reaction Mechanisms and Kinetics of Electrocatalytic Nitrate Reduction
### Mechanistic Insight into the Electrochemical Nitrate Reduction  
From an electrochemical standpoint, several investigations have confirmed that eNO\({}_{3}\)R can involve different pathways, which produce a variety of products that enclose nitrogen gas and ammonia as well as undesired species such as nitrite, hydrazine, hydroxylamine, nitric oxide, nitrous oxide, and others as depicted in Figure 1.  
The electroreduction process of nitrates, as shown in various studies, initiates with the conversion of NO\({}_{3}^{-}\) to NO\({}_{2}^{-}\), which is commonly referred to as the rate-determining step (RDS). This step starts with the adsorption of nitrate as the electron is completely donated to the electrocatalyst surface. The adsorbed nitrate (NO\({}_{3\text{ads}}^{-}\)) could be reduced to the unstable nitrate danion radical (\({}^{\bullet}\)NO\({}_{3}^{2-}\)), which is hydrolyzed to form a nitrogen dioxide radical (NO\({}_{2}^{\bullet}\)) that is finally reduced to adsorbed nitrite (NO\({}_{2\text{ads}}^{-}\)) playing a critical role in the overall reaction pathway as given in Equations (1)-(4) [38]. \[\text{NO}_{3\text{aq}}^{-}+\ast\ \rightleftharpoons\text{NO}_{3\text{ads}}^{-} \tag{1}\]  
\[\text{NO}_{3\text{ads}}^{-}+\text{e}^{-}\rightarrow\text{NO}_{3\text{ads}}^{ 2-} \tag{2}\]  
\[\text{NO}_{3\text{ads}}^{2-}+\text{H}_{2}\text{O}\rightarrow\text{NO}_{2\text {ads}}^{\bullet}+2\text{OH}^{-} \tag{3}\]  
\[\text{NO}_{2\text{ads}}^{\bullet}+\text{e}^{-}\rightarrow\text{NO}_{2\text{ads }}^{-}+\text{H}_{2}\text{O} \tag{4}\]  
\begin{table}
\begin{tabular}{l l} \hline
**Reduction Reaction** & **Standard Redox Potential** \\ \hline \(2\text{NO}_{3\text{ (aq)}}^{-}+12\text{ H}^{+}+10\text{ e}^{-}=\text{ N}_{2\text{(g)}}+6\text{ H}_{2}\text{O}_{\text{(l)}}\) & \(\text{E}_{\text{NO}_{3}/\text{N}_{2}}^{0}=+1.25\text{ V}\) \\ \(\text{NO}_{3\text{ (aq)}}^{-}+10\text  
Furthermore, [PERSON] et al. [40] showed that the mechanism proceeds by dimerization of NO\({}_{\text{ads}}\) to form N\({}_{2}\)O\({}_{2}\), followed by protonation to HN\({}_{2}\)O\({}_{2}\) which is then reduced electrochemically to N\({}_{2}\)O\({}_{\text{ads}}\) as the following equations (Equations (7) and (8)). \[\text{NO}\ {}_{\text{ads}}+\text{NO}\ {}_{\text{(aq)}}+\ \text{H}^{+}+\ \text{e}^{-}\ \to\text{HN}_{2}\text{O}_{2,\ \text{ads}} \tag{7}\]  
\[\text{HN}_{2}\text{O}_{2,\ \text{ads}}+\ \text{H}^{+}+\ \text{e}^{-}\ \to\text{N}_{2}\text{O}\ {}_{\text{aq}}+\ \text{H}_{2}\text{O} \tag{8}\]  
Then, [PERSON] et al. [42], confirmed that N\({}_{2}\)O\({}_{\text{aq}}\) can then react with the hydrated electron and undergo the following reactions to form N\({}_{2}\) (Equations (9)-(11)). \[\text{N}_{2}\text{O}\ {}_{\text{aq}}+\text{e}^{-}\ \to\text{N}_{2}\text{O}^{-} \tag{9}\]  
\[\text{N}_{2}\text{O}^{-}+\text{H}_{2}\text{O}\to\text{N}_{2}+\text{OH}^{-}+ \text{OH}^{\bullet} \tag{10}\]  
\[\text{OH}^{\bullet}+\text{e}^{-}\ \to\text{OH}^{-} \tag{11}\]  
The third proposed pathway is the formation of hydroxylamine (NH\({}_{2}\)OH) and NH\({}_{4}^{+}\) due to the prevention of desorption of NO\({}_{\text{ads}}\) which allows its hydrogenation to HNO, H\({}_{2}\)NO, NH\({}_{2}\)OH, and finally NH\({}_{4}^{+}\) (Equations (12)-(16)) [40, 43, 44, 45, 46, 47].