## 3 Results and Discussion
### Density and Excess Molar Volume of the Binary Mixtures
\[V^{E}=V-\left(x_{1}V_{1}^{0}+x_{2}V_{2}^{0}\right) \tag{1}\]0  
\[V^{E}=V-\left(x_{1}V_{1}^{0}+x_{2}V_{2}^{0}\right) \tag{1}\]1  
Table 4 presents the calculated partial molar volume \(\overline{V_{1}^{\infty}}\) of amines at infinite dilution in H\({}_{2}\)O with molar volume \(V_{1}^{0}\) of pure amines. The proposed temperature dependency for the Redlich-Kister coefficients (\(A_{i}\)) was able to calculate \(\overline{V_{1}^{\infty}}\) with a deviation around 1% AARD compared to literature data. The partial molar volume \(\overline{V_{1}^{\infty}}\) of amines were smaller than the corresponding molar volume \(V_{1}^{0}\) of pure amines. This can be explained for MDEA, DMEA and DEEA by the existence of (partially) ice-like structure in pure H\({}_{2}\)O [30], which is more open than a nearly close packed arrangement, enables to fit (partially) amine molecules into the open or empty spaces in liquid H\({}_{2}\)O [29]. [PERSON] [30] explained structure making solute and structure breaking solute based on the sign of \(\left(\partial^{2}\overline{V_{1}^{\infty}}/\partial T^{2}\right)_{p}\), in which the positive sign is associated with structure making solute, while the negative sign is associated with structure breaking solute. The study shows that for all considered tertiary amines, variation of \(\overline{V_{1}^{\infty}}\) with temperature is linear (\(R^{2}>0.999\)) by making the first derivative of \(\overline{V_{1}^{\infty}}\) with respect to temperature a positive constant. This does not provide any information about second derivation for a positive or a negative sign. A similar observation was reported by [PERSON], [PERSON], [PERSON], and [PERSON] [29] for MDEA. Accordingly, this does not indicate that MDEA, DMEA, and DEEA in dilute aqueous mixtures can be considered as either net structure makers or net structure breakers. Figure 2a,b illustrate the composition dependence of the partial molar volume of MDEA in (MDEA + H\({}_{2}\)O), DMEA in (DMEA + H\({}_{2}\)O), and DEEA in (DEEA + H\({}_{2}\)O) at 298.15 K and 353.15 K, respectively. Figure 2a shows a minimum value for \(\overline{V_{1}}\) around \(x_{1}=0.04\) for MDEA and DMEA at 298.15 K and it disappears with the increase of temperature, as shown in Figure 2b. The accuracy of the data fit was determined by average absolute relative deviation (AARD) and absolute maximum deviation (AMD) as given in Equations (12) and (13). A density correlation based on a Redlich-Kister type polynomial for \(V^{E}\) and density deviation defined as \(ln(\rho_{\gamma})\) in Equation (15) were examined to fit the measured densities of MDEA + H\({}_{2}\)O, DMEA + H\({}_{2}\)O and DEEA + H\({}_{2}\)O mixtures at different concentrations and temperatures. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{6}{c}{**Mixtures**} \\ \cline{2-7}  & \multicolumn{2}{c}{**MDEA (1) + H\({}_{2}\)O (2)**} & \multicolumn{2}{c}{**DMEA (1) + H\({}_{2}\)O (2)**} & \multicolumn{2}{c}{**DEEA (1) + H\({}_{2}\)O (2)**} \\ \cline{2-7}  & \(a_{0}\) & \(a_{1}\) & \(a_{0}\) & \(a_{1}\) & \(a_{0}\) & \(a_{1}\) \\ \hline \(A_{0}\) & \(-7.847\) & \(0.0111\) & \(-7.363\) & \(0.00313\) & \(-10.120\) & \(0.00884\) \\ \(A_{1}\) & \(5.378\) & \(-0.00932\) & \(6.103\) & \(-0.01065\) & \(5.082\) & \(-0.00770\) \\ \(A_{2}\) & \(-2.584\) & \(0.00663\) & \(-1.532\) & \(0.00017\) & \(-2.175\) & \(0.00491\) \\ \(A_{3}\) & \(8.187\) & \(-0.02062\) & \(18.490\) & \(-0.05285\) & \(13.530\) & \(-0.04196\) \\ \(A_{4}\) & \(1.599\) & \(-0.00537\) & \(-0.774\) & \(0.00274\) & \(-2.203\) & \(0.00395\) \\ \(A_{5}\) & \(-15.300\) & \(0.03798\) & \(-29.660\) & \(0.08247\) & \(-16.060\) & \(0.05570\) \\ \hline AARD (\%) & \multicolumn{2}{c}{\(0.007\)} & \multicolumn{2}{c}{\(0.015\)} & \multicolumn{2}{c}{\(0.011\)} \\ AMD (kg\(\cdot\)m\({}^{3}\)) & \multicolumn{2}{c}{\(0.97\)} & \multicolumn{2}{c}{\(1.04\)} & \multicolumn{2}{c}{\(0.80\)} \\ \hline \hline \end{tabular}
\end{table}