## 1 Introduction
To promote the absorption rate, and decrease oxygen degradation and thermal degradation, aqueous piperazine [40], and a cyclic diamine shown in Figure 1e, solution was used to test for the capture of CO\({}_{2}\)[10; 22]. Figure 1: Structures of various amines showing the difference in functional groups. The absorption process of CO\({}_{2}\) using an amine solution generally includes diffusion from the bulk gas phase to the gas-liquid interface, from interface diffusion into the liquid bulk phase, and reaction with an amine. The reaction between CO\({}_{2}\) and the amine can be described by a two-step zwitterions mechanism [43]. First, the reactions of CO\({}_{2}\) with a primary amine and secondary amine (CO\({}_{2}\)/H\({}_{2}\)O/R\({}_{1}\)R\({}_{2}\)NH\({}_{2}\)) systems, based on the zwitterion system, are found to be [43; 44]:  
\[\mathrm{H_{2}O}\rightleftharpoons H^{+}+\mathrm{OH^{-}}, \tag{1}\]  
\[\mathrm{CO_{2}+OH^{-}}\rightleftharpoons HCO_{3}^{-} \tag{2}\]  
\[\mathrm{CO_{2}+H_{2}O}\rightleftharpoons HCO_{3}^{-}+\mathrm{H^{+}}, \tag{3}\]  
\[\mathrm{CO_{2}+R_{1}R_{2}NH}\rightleftharpoons R_{1}R_{2}NH^{+}COO^{-} \tag{4}\]  
\[\mathrm{R_{1}R_{2}NH^{+}COO^{-}+R_{1}R_{2}NH}\rightleftharpoons R_{1}R_{2}NCOO^{-}+R_{1}R_{2}NH_{2}^{+}, \tag{5}\]  
\[\mathrm{R_{1}R_{2}NH^{+}COO^{-}+H_{2}O}\rightleftharpoons R_{1}R_{2}NCOO^{-}+H_{3}O^{+}, \tag{6}\]  
\[\mathrm{R_{1}R_{2}NH^{+}COO^{-}+OH^{-}\overset{k_{\mathrm{OH^{-}}}}{\to}R_{1} R_{2}NCOO^{-}+H_{2}O. \tag{7}\]  
In Equations (2) and (3), the reaction constants are \(k_{\mathrm{OH^{-}}}\) and \(k_{\mathrm{H_{2}O}}\), respectively. In Equation (4), the forward reaction and reverse reaction constants are \(k_{2}\) and \(k_{-1}\), respectively. In Equations (5)-(7), the amine, OH\({}^{-}\) and H\({}_{2}\)O can be expressed as a base B, i.e., the three equations can be expressed as a single equation:  
\[\mathrm{R_{1}R_{2}NH^{+}COO^{-}+B\overset{k_{\mathrm{b}}}{\to}R_{1}R_{2}NCOO^{ -}+BH^{+}}. \tag{8}\]  
The forward reaction rate equation at quasi-steady state becomes:  
Figure 1:0  
In most case, \(k_{-1}/\sum k_{b}[B]<1\) resulting simple second-order kinetics is obtained:  
Figure 1:1  
Considering the reactions (2) and (3), the overall rate was found to be:  
Figure 1:2 \begin{table}
\begin{tabular}{c c c c c c} \hline
**Items** & **MEA** & **DIPA** & **TEA** & **AMP** & **PZ** \\ \hline M.W. (g/mol) & 61.084 & 133.19 & 149.188 & 89.138 & 86.136 \\ Density (g/cm\({}^{3}\)) & 1.0117 & 0.992 & 1.126 & 0.934 & 1.100 \\ BP (\({}^{\circ}\)C) & 170 & 249 & 335.4 & 165.5 & 146 \\ Solubility in water at 20 \({}^{\circ}\)C & Miscible & Miscible & Miscible & Miscible \\ Vapor pressure (pa) (20 \({}^{\circ}\)C) & 64 & 2 & 1 & 40 & 10.66 \\ PK\({}_{a}\) & 9.50 & 8.80 & 7.76 & 9.70 & 9.78 \\ Reaction rate constant, \(k_{2}\) (m\({}^{3}\)/s\(\cdot\)kmol) (25 \({}^{\circ}\)C) & 3630 & 2585 & 2202 & 810.4 & 48,533 \\ Activation energy \(E_{a}\) (kJ/mol) & 41.2 & 39.9 & 36.9 & 41.7 & 33.7 \\ \hline \end{tabular}
\end{table} 
Table 1: Physical and chemical properties of amines [10; 39; 40; 41; 42]. The total rate of all CO\({}_{2}\) reactions in an aqueous solution is thus represented by the sum of the reaction rates. Where the \(k_{obs}\) is:  
\[k_{obs}=\left(\frac{k_{2}[\text{R}_{1}\text{R}_{2}\text{NH}]}{1+\frac{k_{-1}}{ \sum k_{b}[B]}}\right)+k_{\text{H}_{2}\text{O}}[\text{H}_{2}\text{O}]+k_{\text{ OH}^{-}}[\text{OH}^{-}]. \tag{12}\]  
If \(k_{-1}/\sum k_{b}[B]<<1\), the \(k_{obs}\) becomes  
\[k_{obs}=k_{2}[\text{R}_{1}\text{R}_{2}\text{NH}]+k_{\text{H}_{2}\text{O}}[ \text{H}_{2}\text{O}]+k_{\text{OH}^{-}}[\text{OH}^{-}]. \tag{13}\]  
The tertiary alkanolamines (denoted here as R\({}_{3}\)N such as TEA) and PZ can also be expressed as shown in Equation (11) for similar kinetics as [R\({}_{1}\)R\({}_{2}\)NH] with replacement of [R\({}_{1}\)R\({}_{2}\)NH] by [R\({}_{3}\)N] or [PZ] [38; 39].